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This paper presents the formulation of a finite element method for nonlinear Kirchhoff rods (i.e. without transverse shear strain) in the general three-dimensional setting defined by a Cosserat director treatment of the cross sections attached to the rod's axis. The new element is based on a G 1 interpolation of the rod's geometry in terms of Hermite shape functions of the rod's axis (including its tangent defining the tangential director), while the transversal directors defining the different bending and torsional responses of the rod consider a Lagrangian interpolation of the section directors. This direct interpolation of the directors, as opposed of underlying rotation vectors, assures the objectivity of the proposed formulation. In fact, the invariance properties of the resulting finite element are analyzed in detail, assuring the correct resolution of the local fundamental equilibrium relations between forces and moments, hence avoiding the so-called "self-straining" associated to separate treatments of the rod's geometry and its kinematics. Several representative numerical simulations are presented illustrating these properties as well as the appropriateness of the proposed formulation for the analysis of thin rods undergoing large finite deformations in the three-dimensional range. • The paper develops a new finite element for Kirchhoff rods. • Such rods involve no transverse shear, leading to a high-order formulation. • The fully nonlinear geometrically exact range in the 3D setting is considered. • A detailed analysis of the invariance of the proposed finite element is presented. • Numerical tests compare with analytical solutions and other literature proposals. [ABSTRACT FROM AUTHOR]

The present paper introduces a global/local approach for the analysis of three-dimensional (3D) stress states of composite laminated structures. It consists of a two-step procedure. In particular, the first step makes use of finite element modeling based on classical 2D plate elements, whereas a refined layer-wise model based on Carrera Unified Formulation (CUF) is adopted to extract the 3D stress and strain fields in some critical regions that may have arbitrary dimensions. This approach allows dealing with large local areas, increasing the accuracy of the static solution, along with the possibility of embedding this technique in more complex procedures, such as the least-weight design of large heterogeneous complex assemblies, stiffness optimization, or localized progressive failure analysis. The numerical results shown in this paper want to assess the physical and numerical validity of the global/local approach. Particular attention is focused on the choice of the dimensions of the local area (patch) subjected to detailed refined analysis. Also, the convergence properties of the present hybrid FE model are discussed. The first examples deal with laminated composites. Then, the advantages of this methodology are further highlighted by considering free-edge problems and a complex wing structure. • Global to local 3D stress state analysis of composite structures. • Classical finite element software tool is coupled with layerwise CUF formulation. • The method can deal with failure onset mechanisms, including free-edge effects. • A full wing structure is analyzed. [ABSTRACT FROM AUTHOR]

The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The fracture flow is driven by the cubic law, and the contact conditions prevent fractures from self-penetration. A stable finite element discretization is proposed for the displacement-pressure-flux formulation. The resulting nonlinear algebraic system of equations and inequalities is decoupled using a robust iterative splitting into the linearized flow subproblem, and the quadratic programming problem for the mechanical part. The non-penetration conditions are solved by means of dualization and an optimal quadratic programming algorithm. The capability of the numerical scheme is demonstrated on a benchmark problem for tunnel excavation with hundreds of fractures in 3D. The paper's novelty consists in a combination of three crucial ingredients: (i) application of discrete fracture-matrix approach to poroelasticity, (ii) robust iterative splitting of resulting nonlinear algebraic system working for real-world 3D problems, and (iii) efficient solution of its mechanical quadratic programming part with a large number of fractures in mutual contact by means of own solvers implemented into an in-house software library. • A numerical method for accurate resolution of flow and mechanics in fractured rock is presented. • Discrete fracture-matrix approach links processes in rock mass and fracture network. • Robust iterative splitting enables solving nonlinear hydro-mechanical problems. • Efficient algorithm for quadratic programming solves non-penetration conditions on fractures. • Parallel implementation is capable of handling complex geometries with hundreds of fractures in 3D. [ABSTRACT FROM AUTHOR]

• A novel surrogate-based crack identification method is presented. • Structure frequency shift characteristics is analyzed. • The crack identification is converted to an optimization problem. • Numerical examples and experimental validation prove satisfactory precision. A novel crack identification method is presented in this paper for cantilever beam-type structures within the scope of vibration-based damage identification. Natural frequencies are more easily to be measured yet are weakly sensitive to damage in comparison to other dynamic parameters such as mode shape and damping ratio. Therefore, this paper develops a surrogate-based crack identification method in order to overcome the low sensitivity of frequency to damage. The surrogate model was constructed using radial point interpolation method (RPIM) and subsequently trained with the frequency shift database established from parametric finite element analysis (FEA) modeling of cracked/ non-cracked cantilever beams. On this basis, the crack identification problem had been converted to a standard optimization model with crack length and location as design variables. Subsequently, genetic algorithm (GA) was employed for solving the optimization model to achieve crack parameters. In the end, numerical examples and experimental test have been conducted to validate the developed method, revealing maximum relative errors within 0.5% and 2.5%, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the statistical finite element method is developed further to synthesize distributed rail response data with nonlinear finite element model predictions within and outside the measured loading range. In the data-generating model of the statistical finite element method, the distributed sensing data is decomposed into a finite element model component, a model-reality mismatch component, and a noise component. Each component is considered uncertain and is represented as a Gaussian random vector with a corresponding prior density. The finite element prior density is updated using the Bayesian statistical framework in light of the distributed fiber optic sensing data. The calculated posterior density enables one to infer the true structural response. The required finite element prior density is determined by solving a conventional stochastic forward problem using a polynomial chaos expansion of random fields and a non-intrusive pseudo-spectral projection approach. In this paper, a lab test involving a section of a rail (i.e., a beam-column structural member) instrumented with distributed fiber optic sensors and subjected to axial load causing progressive lateral buckling is considered to demonstrate the use of the statistical finite element method to improve rail response prediction. The results show improved prediction of true rail strain in linear and nonlinear regimes compared with a pure finite element model-based prediction. • Statistical finite element method enables integration of nonlinear model and sensor data. • Model selection/misspecification & data uncertainty incorporated using Bayesian formalism. • A polynomial chaos expansion is utilized to derive the necessary finite element prior. • The proposed approach is validated with progressive buckling tests and strain data. [ABSTRACT FROM AUTHOR]

This paper aims for developing topology optimization methodology to design the shape of electrodes in Dielectrophoresis (DEP)-based devices. The DEP force is due to a non-uniform electric field induced by applied voltages to the electrodes. Shape of the electrodes has the principal effect on the direction and magnitude of the DEP force. In medical therapy microfluidic devices, DEP force is used for cell sorting and cell separation. While the direction and magnitude of the DEP force are desired to be determined and maximized respectively, the magnitude of the electric field should be minimized to avoid damaging cells. Approaching these goals is counter intuitive where the existing electrode designs are basic. Therefore, a detailed finite element model (FEM) is developed for DEP force and electric field to formulate an optimization problem to maximize the DEP force in a particular direction while there is a constraint on electric field's magnitude. Using the developed FEM, explicit formulations for sensitivity analysis are derived to implement a gradient-based topology optimization. The performance of developed methodology is assessed numerically to determine the direction of the DEP force and constraining the electric field and experimentally in a practical case study of particle trapping in a microfluidic channel. • Topology optimization can produce novel electrode shapes for DEP devices. • Sensitivity analysis is provided for topology optimization of electrodes in DEP devices. • Optimal electrodes can determine direction of DEP force and minimize electric field. • 2D optimal electrodes are efficient in real 3D microfluidic applications. • Optimal electrodes are efficient for particle manipulation in a micro channel. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel thermal deformation formulation for elastic bodies' thermomechanical simulation with total Lagrangian smoothed particle hydrodynamics (TLSPH), which employing fixed reference configuration. We utilize implicit corotated TLSPH as a base methodology to address tensile instability and enhance the robustness of simulation. The reference configuration of heat transfer model is updated, but the reference configuration of thermal deformation model is fixed like TLSPH. As particle's temperature is changed, the inter-particle distance in reference configuration is updated by using linear thermal expansion theory. Validation involved two basic cantilever beam loading cases and a thermomechanical analysis with heat-induced thermal deformation on a cantilever beam. The TLSPH simulation results were compared against Finite Element Method simulations and analytical solutions, demonstrating equivalent accuracy across all tests. This study indicates the potential for conducting a wide array of simulations involving thermal deformation using the TLSPH method, which efficiently supports parallel computing on an individual particle basis. • An implicit corotated total Lagrangian smoothed particle hydrodynamics (SPH) is employed for simulating elastic bodies. • A novel methodology for thermal deformation, based on the TLSPH framework, is introduced. • To verify basic structural analyses, dynamic oscillation simulations are performed. • For thermomechanical validation, the simulations analyzing heat transfer and thermal deformation are carried out. [ABSTRACT FROM AUTHOR]

• This Shape Optimization allows to achieve Uniform Strength for entire Structure. • The Uniform Strength Beam shape is derived analytically for whatever type of load. • Proposed procedure work with a generic section with one axis of symmetry. • Optimization as a search for zeros of kinematic-congruence and balance conditions. • Optimization workflow given fast results also for very large-size Frame Structures. This paper provides a procedure to obtain the uniform strength of frame and lattice structures. Uniform strength condition is achieved by performing the shape optimization of all beam elements of the structure. The beam shape which guarantees uniform strength is analytically deduced from the one-dimensional Timoshenko model. The optimization problem presents itself as the search for the zeros of the objective-functions vector, which is a non-linear system of equations representing the kinematic-congruence and forces balance at every node of the structure. The analytical formulation of the optimization problem allows to construct the objective-functions vector without the use of external structural computation, i.e. not recurring to any Finite Element Analysis to accomplish iterations. This latter feature entails a great advantage in terms of computing time required to perform optimization. The proposed analytical formulation allows to directly insert the uniform strength condition into the objective-functions vector, transforming the optimization into an unconstrained problem. Some examples are shown in which the performance of the optimization procedure is discussed in terms of robustness and rate of computational complexity while increasing the degrees of freedom of the structure. The reliability and the quality of the optimization are verified through Finite Element Analysis. [ABSTRACT FROM AUTHOR]

• Propose a neural networks-based line element (NNLE) method for large deflection frame analysis. • Significantly outperform the line finite element method in efficiency. • Perform great modeling flexibility and compatibility with the exiting numerical approaches. • Simplify the implementation of machine learning (ML) in large-scale structural analysis. • Provide a novel strategy for seamlessly integrating finite element methods and ML techniques. The line finite element method (LFEM) is the predominant simulation method in structural design due to its robustness in large-scale structural analysis. However, it sometimes suffers from the tedious computational process due to its fine-mesh requirement to ensure accuracy. The machine learning (ML) technique provides an efficient mesh-free alternative but necessitating tremendous training datasets for modeling large-scale structural systems. In this paper, a novel numerical framework, named the neural networks-based line element (NNLE) method, synergizing the unique advantages of the finite element method and ML technique, is proposed and presented within the context of large deflection frame analysis. The neural networks (NN) model is only trained for modeling single components, thereby significantly diminishing the model scale and the required training dataset. Then, the NN model is used to formulate a new NNLE and implemented within the existing LFEM framework to simulate the entire structural system. Extensive examples are performed to demonstrate the accuracy, efficiency, compatibility, and flexibility of the proposed NNLE method compared with the conventional LFEM and ML techniques. It is convinced that the proposed NNLE method will offer new insights into the combination of the traditional finite element method and the emerging ML approach. [ABSTRACT FROM AUTHOR]

This paper introduces a formulation of the robust topology optimization problem that is tailored for designing fiber-reinforced composite structures with spatially varying principal mechanical properties. Specifically, a methodology is developed that incorporates the spatial variability in the engineering constants of the composite lamina into the concurrent topology (i.e., material distribution) and morphology (i.e., fiber orientation distribution) optimization problem for the minimization of the robust compliance function. The spatial variability in the mechanical properties of the lamina is modeled as a homogeneous random field within the design domain by means of the Karhunen-Lo e ´ ve series expansion, and is thereafter intrusively propagated into the stochastic finite element analysis of the composite structure. To carry out the stochastic finite element analysis per iteration of the optimization cycle, the first-order perturbation method is utilized for approximating the current state variables of the physical system. The resulting robust topology and fiber orientation optimization problem is formulated step-by-step for the minimization of the robust compliance function. With the view of solving the optimization problem at hand by means of gradient-based solution algorithms, the first-order derivatives of the involved design functions w. r. t. the associated design variables are analytically derived. The present work concludes with a series of numerical examples, focusing on the benchmark academic case studies of the 2D cantilever and the half part of the Messerschmitt-Bölkow-Blohm beam, aiming to demonstrate the developed methodology as well as to explore the effect that different parameterization instances of the random field bear on the predicted topology and morphology of the beams. • A methodology for designing robust composites under material uncertainty is presented. • The impact of the material uncertainty level on the design's topology is examined. • Higher uncertainty levels are shown to result in refined topological designs. [ABSTRACT FROM AUTHOR]

• Quadrilateral overlapping finite elements are developed to solve incompressible fluid flows; • Novel stable pairs of elements that satisfy the inf-sup condition are proposed; • The stability of the elements is tested using the inf-sup test; • The elements are polynomial-based, insensitive to distortions and for use in AMORE; • The element interpolations can also be used in incompressible solid mechanics. The purpose of this paper is to investigate the performance of a certain family of low-order quadrilateral finite elements in the solution of the stationary Navier-Stokes equations governing incompressible fluid flows. These finite elements are derived from the 'overlapping finite elements', first developed for the solution of problems in solid mechanics [5,9,48] and incorporate features of both meshfree and traditional finite element methods. One of their most remarkable properties is the insensitivity to mesh distortions. Also, since the Shepard functions are replaced by a suitable interpolation, the resulting basis functions are entirely polynomial, which allows the numerical integration of the weak forms to be performed with few integration points [6,49]. We also discuss the theoretical reasons for the stability of the solutions, that is, the absence of spurious pressure modes, and show that the proposed discretization scheme passes the relevant inf-sup test. [ABSTRACT FROM AUTHOR]

• The collective performance of Masonry Aggregates affects the individual units. • A novel BIM to FEM framework for Masonry Aggregates is outlined. • The Level of Information Need for solid FEA of Masonry Aggregates is defined. • An automated process from IFC to tetrahedron finite elements is developed. • The developed methods follow Open BIM logic. Masonry building aggregates are complex historical structures comprising interconnected buildings. The safety of each building depends not only on its structural integrity but also on the interactions with neighbouring structures and their collective performance. The structural assessment of such complex constructions can benefit from BIM methodology. The latter eases modelling complicated solid geometries and assigning mechanical properties information essential for developing a reliable finite element model. Thus far, BIM to finite element analysis procedures applied to historic constructions have remained laborious, semi-automatic, and based on proprietary software. This paper introduces an open-source automated solid finite element analysis method using OpenBIM data (IFC). The tool implemented automatically creates tetrahedron mesh and assigns mechanical properties, self-weights, and fixities at the structure's base. The methodology is applied to an actual masonry building aggregate to validate its capability of working with complex geometries and scalability. [ABSTRACT FROM AUTHOR]

• A methodology for analysis of large-scale masonry structures is presented which incorporates an inelastic macroscopic framework coupled with a series of artificial neural networks. • The neural networks serve the purpose of identification of material functions embedded in anisotropic formulation as well as the specification of localization plane. • The data required for training of neural networks is generated using 'virtual experiments' that involve a mesoscale finite element analysis of masonry wallets. • Finite element analysis of a large masonry wall with multiple openings is carried out. The results are compared with those based on a detailed mesoscale model. This paper presents a methodology for analysis of large-scale masonry structures. The approach involves development of a series of artificial neural networks which enable the identification of main variables employed in the macroscopic formulation that incorporates an inelastic constitutive law with embedded discontinuity. The data required for training of neural networks is generated using 'virtual experiments', whereby the 'equivalent' anisotropic response of masonry is obtained through a mesoscale finite element analysis of masonry wallets. The paper outlines the procedure for identification of approximation coefficients describing the orientation-dependency of strength, and other relevant parameters. A numerical example is provided involving analysis of a large masonry wall with multiple openings. The results of macroscale approach are compared with those based on a detailed mesoscale model for the same geometry and boundary conditions. [ABSTRACT FROM AUTHOR]

Exploring the wave propagation in nano-waveguides enables the development of on-chip nano-resonators, leading innovative capabilities that enhance acoustics and micro-mechanics. This paper conducts a numerical investigation into the dynamic properties of periodic nano-waveguides. The Second Strain Gradient (SSG) elasticity, which captures the size effects, is used in the determination of the constitutive relations. The weak form including the element matrices is deduced by the Hamilton's principle. Furthermore, a finite element method, based on the periodic structure theory, is introduced to explore the free wave propagation by solving the eigenvalue problems. The stiffness hardening phenomenon manifested in the dispersion curves, band structures, and energy flow vector fields is discussed. The sensitivity of higher order parameters existing in the SSG theory is analyzed. The numerical investigation for wave propagation in the periodic nano-waveguides through the SSG theory is an innovative work, highlighting the significance of the proposed methodology in explaining the special dynamic characteristics of complex nano-waveguides. • Modeling of 3D nano-waveguides by second strain gradient theory. • Eigenvalue problems within 2D wave finite element method framework. • 2D wave motion properties in two different nano-waveguides. • Sensitivity of higher order parameters existing in second strain gradient elasticity. [ABSTRACT FROM AUTHOR]

A new approach is proposed to account for the impact of sprain variables for computational simulation of fracture in quasi-brittle materials. For an isotropic solid, these variables are equal to the Laplacians of the components of the displacement field, and they were introduced in a recent study by Zhang and Bazant to resolve spurious mesh effects for cases involving softening material response. This is possible by establishing localization-resisting forces which are conjugate to the displacements with respect to a sprain energy functional, defined as a function of the sprain variables. To enable the evaluation of the sprain variables in a conventional, C 0 continuum finite element approximation, this paper introduces a set of scalar fields, each being weakly equal to the Laplacian of one of the components of the displacement vector field. This leads to a straightforward implementation with standard continuum (solid) elements, eliminating the need for approximations satisfying higher continuity requirements or for ad-hoc, finite-difference algorithms which were adopted in the original pertinent work for the calculation of the sprain variables. • Use of localization-resisting forces in continuum simulations of strain softening, to eliminate spurious mesh-size effects. • These forces are governed by a set of scalar fields, weakly equivalent to the Laplacians of the displacement components. • Weak equivalence allows to obtain the Laplacians of the displacement field with conventional, C0 finite element approximations. • The method is found to eliminate spurious effects of mesh size and of mesh orientation with respect to crack propagation path. [ABSTRACT FROM AUTHOR]

• A new methodology for multi-parameter identification of concrete dams is proposed. • For the first time, polynomial chaos expansion and slime mould algorithm are integrated. • A very high computational efficiency is achieved using the proposed methodology. This paper presents a novel methodology that combines polynomial chaos expansion and slime mould algorithm for multi-parameter identification of concrete dams. This methodology not only incorporates the merits of low computational cost in the polynomial chaos expansion and fast convergence of slime mould algorithm, but also considers the priori uncertainty in the input parameters by introducing statistical probability theory. By considering two examples with different complexity, this paper verifies the effectiveness of the proposed method with a univariate simply supported beam model, followed by a complex multivariate dam model to demonstrate its practicability in real engineering problems. In addition, parameter sensitivity analysis of the dam model is conducted at an extremely low cost by polynomial chaos expansion based on Sobol' indices. Furthermore, the conventional parameter identification methods based on optimization methods directly combined with the finite element model are employed for comparison, highlighting two distinct advantages of the proposed method: (i) the proposed method improves the computational efficiency by nearly 52 times while ensuring a high accuracy, and (ii) the classical non-population optimization algorithm, Bayesian optimization, is used for comparison, revealing the outstanding performance of slime mould algorithm in terms of convergence speed and robustness. The application of the proposed algorithm is not only limited to dams, but also it can be extended to any structure. [ABSTRACT FROM AUTHOR]

• This paper presents an improved algorithm for the Moore-Penrose continuation method. • Its ability to compute solution curves with critical points is greatly improved. • Difficulties observed using the standard approach are not encountered. • Easy implementation. Using typical solution strategies to compute the solution curve of challenging problems often leads to the break down of the algorithm. To improve the solution process, numerical continuation methods have proved to be a very efficient tool. However, these methods can still lead to undesired results. In particular, near severe limit points and cusps, the solution process frequently encounters one of the following situations: divergence of the algorithm, a change in direction which makes the algorithm backtrack on a part of the solution curve that has already been obtained and omitting important regions of the solution curve by converging to a point that is much farther than the one anticipated. Detecting these situations is not an easy task when solving practical problems since the shape of the solution curve is not known in advance. This paper will therefore present a modified Moore-Penrose continuation method that will include two key aspects to solve challenging problems: detection of problematic regions during the solution process and additional steps to deal with them. The proposed approach can either be used as a basic continuation method or simply activated when difficulties occur. Numerical examples will be presented to show the efficiency of the new approach. [ABSTRACT FROM AUTHOR]

• Higher-order layer-wise plate models for composite variable angle tow plate analysis. • Passive damping using viscoelastic inter-layers with frequency-dependent properties. • Mixed interpolation of tensorial components for more efficient and accurate solutions. In this paper, the damped free-vibration and frequency response analysis of variable-angle-tow composite plates embedding viscoelastic layers with frequency-dependent properties are performed. The governing equations are derived from the Principle of Virtual Displacements and higher-order Layer-Wise models are used for the unknown variables description in the thickness direction, furthermore a nine-node finite plate element is employed to solve them. The plate formulation presented in this paper is more efficient with respect to three-dimensional approaches, typically used for this kind of structures, and it is more accurate than existing reduced order methods thanks to the use of the mixed interpolation of tensorial components technique, employed to solve the problem of the shear and membrane locking phenomena. Different multilayered structures have been considered, laminated with unidirectional cross-ply layers or with curvilinear fibers path ones. The use of viscoelastic soft sheets permits to have a passive damping of the structural vibration. The frequency dependent properties of the viscoelastic materials are described through the use of a Kelvin-Voigt model. Numerical solutions are presented for the analysis of variable-angle-tow composites with different boundary-conditions and various lamination schemes. [ABSTRACT FROM AUTHOR]

• Strength-based structural/material layout optimization for solid reinforced concrete. • The design cost is minimized based on the individual price of concrete and reinforcement. • The optimization is strength-based, i.e., strength scaling parameters on the concrete and reinforcement ratios are used. • The material layout is defined based on the concrete strength scaling parameters and reinforcement ratios. Whether monetary, environmental, or otherwise, the cost of the structure is always an important aspect when designing reinforced concrete. A structure with a low cost is desirable, but other considerations must be made. First and foremost, the structures should be safe. The two conditions define the structural optimization problem that this paper seeks to solve as finding the structure with the lowest cost, which is also safe. Validation of reinforced concrete in the ultimate limit state is often performed using plasticity and strength-based methods. This paper combines Finite Element Limit Analysis (FELA) with a yield criterion that includes material layout variables to create a strength-based structural optimization framework for solid reinforced concrete structures. The yield criterion combines the Modified Mohr–Coulomb criterion, where variables scale the compressive strength, with the inclusion of smeared reinforcement, where variables scale the reinforcement ratios. The framework is presented and shown in examples using free optimization and examples where material layout variables in parts of the structure are coupled and optimized as a group. [ABSTRACT FROM AUTHOR]

Tangled (non-convex) elements, i.e. elements with negative Jacobian determinant, can lead to erroneous results in the standard finite element method (FEM). Constructing tangle-free, well-structured meshes for complex geometries is often impossible. Hence there is a need to explore analysis methods that can directly handle such tangled meshes. In this paper, we propose the isoparametric tangled finite element method (i-TFEM) for free and forced vibration problems over tangled meshes. By employing piece-wise invertible mapping, a variational formulation is derived, leading to a simple modification of the standard FEM stiffness and mass matrices with the incorporation of additional compatibility constraints. Moreover, i-TFEM reduces to standard FEM for non-tangled (regular) meshes. The proposed method is implemented for three types of elements: 4-node quadrilateral, 9-node quadrilateral, and 8-node hexahedral elements. The numerical results demonstrate that i-TFEM is able to consistently handle general tangled (non-convex) elements, enabling convenient meshing for complex geometries. • Isoparametric tangled finite element method (i-TFEM) is proposed for free and forced vibration problems over tangled meshes. • To handle concave elements using i-TFEM, simple modifications to the standard FEM stiffness and mass matrices are needed. • I-TFEM is implemented for three element types: 4-node quadrilateral, 9-node quadrilateral, and 8-node hexahedral elements. • The numerical results demonstrate that i-TFEM consistently handles general non-convex elements. [ABSTRACT FROM AUTHOR]

• FEM analyzes of two representative historic railroad arch masonry bridges are shown. • Careful selection of the masonry properties is crucial and always required. • Modern traffic loads may contribute to the damage of masonry railroad bridges. • Cohesive zone modeling provides efficient description of masonry cracking. • Broad analysis of numerous masonry bridges require effective approaches as shown. The problems encountered during the analyzes of structural response of historic masonry railroad arch bridges are described in this paper. The attention is mainly focused on the stiffness of the masonry arches, their strengths and appropriate estimation of railroad load intensity. Issues related to computational modelling of two, existing, almost 130 years old masonry arch railroad bridges are presented in this context. The main properties and results of detailed inspection of the structures are shown. Computational models that were created in the finite element method environment in order to efficiently describe the responses of the bridges under typical loading conditions and estimate their load carrying abilities are presented. The outcomes of several nonlinear static analyses that were conducted for this purpose are discussed. What is more the results of finite element analyses are reviewed against the inspected bridge condition and final conclusions are formulated on that basis. All the analyses allowed to find the possible causes of the deterioration of the bridges condition. [ABSTRACT FROM AUTHOR]

This paper presents a numerical model of coupled hydro-mechanical behaviour of partially saturated soils. The model is based on Bishop's effective stress concept and the Cam-Clay model, with the compression stiffness influenced by the effect of partial saturation. The mechanical model is accompanied by the simplified water transport model where the water pressure is the only variable and van Genuchten moisture retention curve was adopted. The governing equations are discretized in the framework of the finite element method, and the resulting model is implemented in the in-house open source software package SIFEL. To improve convergence of the Newton-Raphson method used at the global level of the equilibrium finding, the algorithmic stiffness matrix was derived for the used stress return algorithm. A numerical examples of foundation problem illustrates the effective application of the model and proved that the model can capture wetting collapse. • Coupled hydro-mechanical model for partially saturated soils. • Improvement of the model performance by the algorithmic stiffness matrix for the cutting plane stress algorithm. • The effect of the wetting collapse can be captured by the model, as demonstrated in the example. • Comparison of model performance on the partially and fully saturated cases of the footing strip problems. [ABSTRACT FROM AUTHOR]

This paper introduces a novel hybrid formulation of a peridynamics-based machine learning model for thermal diffusion analysis in one-dimensional and two-dimensional problems with evolving discontinuities. The hybrid model employs a multivariate linear regression approach to establish the relationship between the temperature values of material points, their neighboring points, and the applied external heat flux. The thermal modal analysis method uses the finite element method to generate training and testing data. An efficient numerical procedure is also developed to couple the peridynamics model and the peridynamics-based machine learning model. The model is analyzed under multiple configurations of micro-thermal conductivity functions for one-dimensional thermal bar problems, under both steady-state and transient loading conditions, to identify the configuration that exhibits superior convergence behavior towards the local solution. Furthermore, benchmark problems demonstrate the high accuracy of the formulated hybrid model, including the analysis of thermal plates with discontinuities, such as a plate with a hole, a plate with a pre-existing insulated crack, and plate with a bi-material interface with stationary and evolving discontinuances. The hybrid model effectively captures intricate discontinuities and boundaries while being computationally efficient, indicating its potential for thermal diffusion analysis in one- and two-dimensional problems with stationary and evolving discontinuities. • The peridynamics-based machine learning model is proposed for diffusion problems. • An efficient scheme is proposed to couple peridynamics and machine learning models. • Machine learning data is generated using modal analysis for different thermal conditions. • The efficiency and robustness of the model is demonstrated through numerical examples. • The model is straightforward to extend to diffusion problems associated with pitting corrosion. [ABSTRACT FROM AUTHOR]

• The use of the Embedded Finite Element Method (E-FEM) to simulate local material heterogeneities is analyzed in detail. • A new fully consistent weak discontinuity enhancement function is proposed. • Basic simulations are used to compare the classical approach, commonly used in literature, and the new fully consistent approach proposed in the paper. • A discussion evaluates both model performance and ease of implementation. This paper analyses in detail the use of the Embedded Finite Element Method (E-FEM) to simulate local material heterogeneities. The work starts by a short review on the evolution of weak discontinuity models within the E-FEM framework to discuss how they account for the presence of multiple materials within a single element structure. A theoretical basis is introduced through some mathematical weak discontinuity definitions and the Hu-Washizu variational principle, for then establishing a set of requirements for retaining variational and kinematic consistency for any weak discontinuity enhancement proposal. From a general definition of a displacement enhancement field, two particular enhancement functions are derived by considering different consistency requirements: one which has been typically used in previous works and other which truly possesses variational consistency. A discussion is held on enhancement stability properties and the impact to global finite element solution processes. In the end, numerical simulations are made to assess the performance of each of these enhancements on the task of modelling a classical bi-material layered 3D tension problem and a more realistic heterogeneous sample having spherical inclusions of different radii. The final discussion evaluates both model performance and ease of implementation. [ABSTRACT FROM AUTHOR]

• The paper proposed a physics-informed DNN framework for forecasting the hysteretic curves of S-shaped dampers. • The proposed physics-informed DNNs were calibrated numerically and experimentally. • The physics-informed DNNs can be used for the seismic design and mechanical characteristics assessment of S-shaped dampers Numerical simulation that combines finite element methods and experimental data has been recognized as effective in modeling hysteretic behaviors and capturing the principle mechanical trend of passive energy dissipation devices. However, the seismic design and mechanical characteristics assessment for passive energy dissipation devices require a laborious effort and massive computational resources to tune mechanical-oriented parameters. Particularly, the potential risk of departure from the actual system is rising for the desirable seismic design of dampers due to the numerical model simplification and assumption. To eliminate the potential weakness of numerical models, this paper explores a surrogate model by implementing physics-informed deep neural networks (DNNs) to approximate hysteretic behaviors of S-shaped steel dampers. The proposed physics-informed DNNs mainly consists of recurrent neural networks (RNNs) and long short-term networks (LSTMs), which can encode the Bouc-Wen model into the direct graph and incorporate the effect of design-oriented geometry parameters. To validate the generality of the network, the optimization model was calibrated numerically and experimentally, respectively, which exhibits good performance in predicting nonlinear behaviors of different dampers with reasonable accuracy. The proposed physics-informed DNNs can be an alternative to relieve the laboriousness of the seismic design and mechanical characteristics assessment of passive energy dissipation devices. [ABSTRACT FROM AUTHOR]

• A multi-scale beam model is derived using FE2 framework and absolute nodal coordinate formulation. • It has both the efficiency of absolute nodal coordinate formulation and multi-scale framework. • Performance of the proposed method is demonstrated through numerical examples. In this paper, a multi-scale modeling approach for the dynamic response of flexible multibody system made of composite material is suggested using the absolute nodal coordinate formulation (ANCF) – multilevel finite element (FE2) method. On many occasions, the analysis of composite structures requires a multi-scale modeling approach. FE2 method is one of the famous multi-scale modeling methods. And it is a versatile computational homogenization approach that is commonly applicable to many different materials. Because the present FE2 is capable of computing the mechanical response at two different scales simultaneously, ANCF element will be used at the macroscopic scale. And the microscopic RVE at each macroscopic integration point will be obtained by the finite element method. Since ANCF element uses only the absolute nodes and gradients, the mass matrix will be constant. Due to such characteristics, when combined with FE2, the linearization process will become easier compared against the existing formulation. And Coriolis or centrifugal force will not need to be considered in the dynamic formulation. Therefore, computational cost will be reduced, and the relevant algebraic manipulation will become simplified. Several numerical examples are presented to demonstrate the improved accuracy and diminished computational cost of the present suggestion. [ABSTRACT FROM AUTHOR]

• Propose a smart component model replacement (SCMR) approach to simulate large-scale nonlinear structure. • The SCMR approach can finely simulate the local damage and failure mechanism in structures. • Present "replacement" strategies for smoothly replacing between different models. • The efficiency and accuracy of SCMR approach are verified by three application examples. This paper proposes a novel smart component model replacement (SCMR) approach that is not only efficient for large-scale nonlinear structural analysis, but also accurate in the refined simulation of components of interest. The method creates a FE model with a relatively coarse mesh to simulate the entire structure. During analysis, when a component is identified to predefined criteria defined by the users, its model will be replaced by another more refined "substructure" model that can simulate the damage and failure more accurately. A few "replacement" strategies are presented for smoothly transiting between different models: (1) A gradually transiting strategy is presented to avoid the possible jumps of responses due to the model differences to guarantee numerical stability; (2) The historical boundary conditions are applied to the substructure model to address the historical dependence of responses; (3) The boundary connection between main and substructure is considered by using a flexible client/server technology, to simplify the replacement. The SCMR approach is verified by three application examples. The results demonstrate that the proposed modeling approach can efficiently perform large-scale nonlinear structural analysis, while capturing the failure mechanism in RC structures well. [ABSTRACT FROM AUTHOR]

This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to Micro Electro Mechanical Systems. The constitutive model adopted accounts for the hysteretic and electrostrictive response of the piezoelectric material by resorting to the Landau-Devonshire theory of ferroelectrics. Results are validated with full-order simulations operated with a harmonic balance finite element method to highlight the reliability of the proposed reduction procedure. Numerical results show a remarkable gain in terms of computing time as a result of the dimensionality reduction process over low dimensional invariant sets. Results are also compared with experimental data to highlight the remarkable benefits of the proposed model order reduction technique. • Model order reduction for structures with geometric and piezoelectric nonlinearity. • Direct computation of the invariant manifold from finite element problem. • Efficient technique accounting for electrostrictive response of the piezoelectric. • High accuracy of the results compared to full-order simulation. • Application to micro-electro mechanical systems with complex geometry. [ABSTRACT FROM AUTHOR]

• A modified stain energy release rate method is proposed to enable the method for solid element. • An algorithm is proposed to map the crack information obtained by vision method in the FE model. • The effectiveness and generality of the proposed framework are validated using three cracking FE configurations. Vision inspection information of damages in civil engineering structures is hard to be transformed into an analysis-available resistance model to conduct in-service condition assessment. This paper proposes an updating crack-embedded finite element modeling framework using periodical vision inspection information, which offers a convenient crack embedding approach for safety assessment of cracked reinforced concrete (RC) frame structures. For this purpose, a modified stain energy release rate (SERR) method is proposed to enable the method for solid element with high accuracy. Consequently, an algorithm is proposed to map the crack information obtained by vision method in the FE model. The combination of modified SERR method and proposed mapping algorithm could achieve flexibility matrix updating of cracked element. In addition, the effectiveness and generality of the proposed framework are validated using three cracking configurations. This research can provide a feasible framework for the rapid condition assessment of in-service civil engineering structures, showing a great prospect of intelligent disaster prevention. [ABSTRACT FROM AUTHOR]

This publication presents a novel numerical avenue for the assessment of masonry structures. To circumvent the labor-intensive finite element method modeling and pre-processing step, the isogeometric analysis is enhanced within this contribution to cope with the necessities for masonry structures. This incorporates the study of apparent kinematic shell formulations, including their respective properties. Additionally, the connection towards non-linear material laws is outlined, and an empirically evaluated approach for the element size regularization is proposed. This generic approach would be inherently valid for other size dependent constitutive material models, as e.g. concrete models. The current paper is explored in the context of a number of experimental problems. These validation examples are used to provide structural assessments that extend beyond the scope of the experiment. Finally, a potential example that provides an outlook towards anticipated applications is presented. • Advancing the isogeometric analysis to cope with shell-based masonry structures. • Proposing a damage model in the context of the isogeometric analysis. • Newly proposed element length regularization technique for NURBS. • Enhancement of parametric and CAD-integrated workflow for masonry analysis. • Comprehensive mechanical assessments of masonry structures. [ABSTRACT FROM AUTHOR]

• A novel stochastic homotopy method is proposed to solve static problems involving arbitrarily distributed random variables. • The optimal homotopy series expansion is obtained by minimizing the stochastic residual error. • The proposed method shows better convergency and efficiency than the aPC method in the case of non-Gaussian random field. • This method is successfully applied to the stochastic static analysis of the large-scale engineering structure. The modelling of realistic engineering structures with uncertainties often involves various probabilistic distribution types, which bring forward higher requirements for the generality of stochastic analysis methods. This paper proposes a novel stochastic homotopy method to evaluate the static response of the structure with random variables of arbitrary distributions. In this method, a homotopy series expansion is used to approximate the stochastic static response, and the optimal form of the expansion can be determined by minimizing the residual error about the stochastic static equilibrium equation regardless of distribution types of random variables. The numerical results of a logarithmic function and a thin plate show that the new method exhibits excellent accuracy and stability compared to the homotopy stochastic finite element method depending on the sample selection. Compared with the arbitrary polynomial chaos method (aPC), the proposed method is more efficient under equivalent accuracy. On the other hand, as the expansion order increases, this new method shows better convergence than the aPC method and the perturbation stochastic finite element method in the case of non-Gaussian distributed random variables of large fluctuation. In addition, a cable-stayed bridge example illustrates the application of the proposed method on the large-scale structure. [ABSTRACT FROM AUTHOR]

• The wave input method has a deficiency in expressing complex incident site waves. • A random non-uniform wave input method is proposed for seismic response analyses. • The new method is expressible for complex incident waves and motion differences. To improve the deficiency of the wave input method (WIM) in expressing complex incident site waves, in this paper, a random non-uniform wave input method (RNUWIM) is derived from the use of the random incident waves and the visco-elastic boundary condition. The random incident waves are generated and adjusted by the comparison of the horizontal ground motion's response spectrum and the target spectrum, so that they are representative of the actual wavefield in project sites. Furthermore, the RNUWIM is implemented and verified by the finite element method. The result shows that the RNUWIM inherits the advantages of the WIM in simulating the wave propagation effect and the radiation damping effect. In the new method, the spatial variation of ground motions such as time delays, peak variation, and time-history shape differences can be simulated synthetically. The errors of RNUWIM in ground acceleration, velocity, and displacement at the reference point are respectively 3.23%, 0.66%, and 0.07% in one case, which proves the efficiency of the RNUWIM in seismic response analyses. [ABSTRACT FROM AUTHOR]

• Beam finite element-based buckling analysis of perforated thin-walled members. • Displacement mode-based beam model allowing for the cross-section discontinuity. • Enhanced approximation of element displacement field by using level-set functions. • Decomposition of any coupled buckled shape to a set of pure buckling modes. • Illustrative examples showing the accuracy and efficiency of the proposed approach. This paper presents a numerically efficient tool for linear buckling predictions of perforated thin-walled bars within the framework of generalized beam theory (GBT). GBT-based beam finite element methods (GBT-FEM) have been well developed for eigenvalue buckling analyses of non-perforated thin-walled bars. The novelty of this paper consists in an extension of the standard GBT to the scope of thin-walled members with arbitrarily shaped and placed holes. This is achieved by combining the standard GBT and the extended finite element method (X-FEM). More specifically, insert a set of locally supported enrichment functions, accounting for the discontinuities on displacement fields arising from the cross-section cut-outs/holes, into the GBT-based finite element approximations of the member configuration spaces, using the partition of unity method (PUM), where a set of level-set functions are used to describe the geometric profiles of hole edges, i.e., with the hole edges being the zero level sets, and also used to construct the enrichment functions. The proposed approach makes it possible to calculate the deformation mode participations for any perforated thin-walled members as the classic GBT for non-perforated ones. Finally, the proposed approach is calibrated against the shell/solid finite element analysis with four illustrative examples. It can be found that the presented approach is of higher computation efficiency than the shell model. [ABSTRACT FROM AUTHOR]

• Helical strands analysis is addressed rigorously with homogenization theory. • Strand response is non-linear due to contact interactions between its components. • Different models with solid and beam finite elements are used. • Numerical results are compared to those coming from analytical models. This paper proposes a computational approach for studying the overall behaviour and local stress state of strand-type structures. This method is based on the homogenization theory of periodic beamlike structures, with the local problem posed on the strand axial period being solved using the finite element method. This approach fully utilises the strand's helical symmetry, thus minimising the size of the computational domain. Consequently, accounting for geometric complexity and contact interactions, which are of paramount importance for bending loads, is more straightforward. The numerical model mesh size can also be reduced thanks to the use of beam elements, and one objective of this paper is to assess the accuracy of such a model in comparison with solid element models and analytical results. These comparisons are performed on both single-layer and multi-layer strands. Results demonstrate the capability of the proposed computational approach to accurately capture the nonlinear bending behaviour stemming from the stick-slip transition as well as local stress distributions. As for the beam model, it apparently offers a very good compromise between accuracy and numerical efficiency. [ABSTRACT FROM AUTHOR]

• A finite element formulation for time analysis of free layer damping plates is proposed. • The damping layer is modelled by a five-parameter fractional derivative model. • The proposed formulation is based on the homogenisation of plates. • Grünwald-Letnikov and Newmark methods are used for the numerical integration. • The validation is completed by means of a model with hexahedral finite elements. This paper presents a finite element formulation specifically developed for the transient dynamic analysis of free layer damping plates, in which the viscoelastic behaviour of damping layers is modelled by means of fractional derivatives. This formulation is based on the homogenisation of thin multi-layered plates, adapted to consider fractional derivatives. Then, a fractional matrix equation system is reached, and the time response is solved by means of the implicit Newmark method in conjunction with the Grünwald-Letnikov discretisation of the fractional derivatives. The validation of the method is carried out by comparing the results of three different numerical applications with the ones provided by a finite element model built with hexahedral elements. As conclusion, it can be pointed out that the proposed finite element formulation based on the homogenisation of multi-layer plates reproduces accurately the time response of plates with surface damping treatments. In addition, this method allows conventional plate mass and stiffness matrices to be used to model each individual layer, without requiring specific formulations. [ABSTRACT FROM AUTHOR]

• The spatially uncertain parameters are described by the interval field model with upper and lower bounds. • An interval iterative method is proposed for static response analysis of structures with spatial uncertainties which can effectively avoid the overestimation existing in traditional interval analysis. • The upper and lower bounds of the responses obtained by the proposed method could envelop the actual response bounds. Parameters with spatial uncertainties are very common in practical engineering, which could have a significant effect on structural performances. Different from the framework of probability theory, the interval field model describes the spatial uncertainty with upper and lower bounds rather than the probability distribution function or other statistical characteristics. By introducing the interval field model into finite element analysis and solving the resulting interval finite element equilibrium equation, the upper and lower bounds of structural responses can then be obtained. This paper proposes an interval iterative method for static displacement response analysis of structures with spatial uncertainties, effectively improving the overestimation existing in traditional interval analysis due to dependency problems and obtaining a compact interval envelope of the exact response bounds. Firstly, the spatially uncertain parameters described by the interval field are represented by the interval Karhunen–Loève (K-L) expansion, based on which the interval finite element equilibrium equation is formulated. Secondly, the interval finite element problem is decomposed into several subproblems, and an interval iterative method is developed for an envelope solution of the structural response bounds. Finally, the accuracy and efficiency of the proposed method are verified by several numerical examples. [ABSTRACT FROM AUTHOR]

• Developing seismic demand prediction models via SR methods in a probabilistic manner. • Proposing the MGGP and MBBP based models for seismic demand prediction. • Considering aleatoric and epistemic uncertainties for SR model development. • Using evolutionary correlation coefficient for the feature selection process. • Using closed-form mathematical expressions for generating bridge fragility curves. The resilience assessment of existing structures and designing new resilient ones need to have a precise estimation of seismic responses of the structures traditionally carried out by time-consuming calculations of finite element method. This paper presents interpretable, reliable, and fast prediction models developed by two novel branches of the symbolic regression approach (multigene genetic programming and multi biogeography-based programming) in a probability manner for curved bridges. These newly developed techniques seek to find interpretable equations with arbitrary forms that conform to a specific dataset. The reliable prediction models were developed considering the different uncertainties involved, including mechanical, geometrical, structural, and seismic uncertainties. Due to a large number of input variables for the bridge, the evolutionary correlation coefficient was employed to identify the most influential parameters for seismic demands of bridge components. Parameters with the highest correlation were set as inputs for symbolic regression algorithms, generating closed-form mathematical expressions to predict seismic demands. The resulting explicit models present a fast and accurate model that do not require further simulation or the seismic demand model assumptions to develop bridge fragility curves. In comparison to cloud approach and multiple strips analysis, the new method generates fragility curves with less dispersion. [ABSTRACT FROM AUTHOR]

• A three-stage approach to approximate non-stationary and discontinuous functions. • Clustering of joint input–output to identify discontinuities or different behaviors of the system. • Dirichlet process mixture models to automatically infer the number of clusters. • Support vector machines to partition the input space according to identified clusters. • Gaussian process regression to make predictions in identified sub-domains. Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have provided a way to solve otherwise intractable problems. A crucial aspect in surrogate modelling is the assumption of smoothness and regularity of the model to approximate. This assumption is however not always met in reality. For instance in civil or mechanical engineering, some models may present discontinuities or non-smoothness e.g. , in case of instability patterns such as buckling or snap-through. Building a single surrogate model capable of accounting for these fundamentally different behaviours or discontinuities is not an easy task. In this paper, we propose a three-stage approach for the approximation of non-smooth functions which combines clustering, classification and regression. The idea is to split the space following the localized behaviors or regimes of the system and build local surrogates that are eventually assembled. A sequence of well-known machine learning techniques are used: Dirichlet process mixtures models (DPMM), support vector machines and Gaussian process modelling. The approach is tested and validated on two analytical functions and a finite element model of a tensile membrane structure. [ABSTRACT FROM AUTHOR]

• Optimization framework for the modified shear strength reduction method with the pore pressure. • Evaluation of three different Davis? modifications of the shear strength reduction method. • Mesh adaptive solution for stability analysis coupled with the unconfined seepage problem. • Development of in-house Matlab codes and their validation against Plaxis and Comsol Multiphysics. • Solution of embankment stability problems following from geotechnical practice. In this paper, an optimization variant of the shear strength reduction method is introduced and used for the solution of embankment stability problems with unconfined seepage. The optimization framework is based on approximations of non-associated Mohr–Coulomb plastic models with associated ones, especially by using various Davis' approaches. Next, the finite element method is considered and mesh adaptive solution concepts are developed for both the unconfined seepage and stability problems. In-house codes in Matlab are used for their implementation. Finally, two numerical examples inspired by geotechnical practice are investigated in order to demonstrate the accuracy of the optimization framework and to evaluate three different Davis' approaches. The results are compared with commercial codes in Plaxis and Comsol Multiphysics. [ABSTRACT FROM AUTHOR]

• Data-driven analysis of geometric and material nonlinear behavior for frame structures is proposed. • A data-driven approach can be used to substitute the classic finite element nonlinear analysis. • The dataset is collected from the nonlinear analysis and a yield surface equation. • Six ensemble learning methods are used to train and validate the dataset of nonlinear frame analysis. • Yield surface values at all plastic hinge locations can be predicted using proposed method. Although many different nonlinear analysis techniques for steel frame structures, they causes the increase in total computational cost. A data-driven approach can then be used to substitute the classic finite element nonlinear analysis including second order methods and inelastic modelling. In this paper, a novel data-driven method using ensemble learning models for geometric and material nonlinear analyses of frame structures is proposed. For this approach, the data acquisition process and machine learning-based models are needed to train a large amount of dataset, which is collected from the nonlinear analysis and a yield surface equation. Ensemble learning algorithms are then used to build the data-driven models. After training, the sequence of plastic hinge formation in steel frame structures can be predicted without any nonlinear analysis process. In that situation, the data-driven model is more effective, especially in practical cases with the lack of experimental information due to limited sensors. The validity of the proposed method has been demonstrated by several numerical examples. [ABSTRACT FROM AUTHOR]

• A mass source term is derived from the modified continuity equation. • Geometric conservation law is satisfied in edge-based smoothed finite element method. • An efficient and stable semi-implicit coupling scheme is presented accordingly. • Viscoelastic fluid–structure interaction is modeled by variable-node smoothing cells. In this paper, a new partitioned semi-implicit coupling algorithm is developed for unsteady viscoelastic fluid–structure interaction in association with an edge-based smoothed finite element method (ESFEM). Stabilization techniques tailored for the viscoelastic fluid subproblem are naturally integrated into the hybrid explicit/implicit coupling framework to achieve the enhanced stability. In particular, a mass source term derived from the modified continuity equation in the finite-element context enables the ESFEM to fulfill the geometric conservation law on variable-node smoothing cells during the subiterations. Moreover, both multi-field equations and interface conditions are easily discretized with the ESFEM which enjoys high flexibility of smoothed Galerkin weak-form integral. Desirable numerical results are given for two benchmark problems. [ABSTRACT FROM AUTHOR]

• The combined fiber-interface model is established based on the theory of micromechanics. • The multiple cracking behavior of SHCC is achieved via finite element simulation. • The method of critical matrix cracking strength is proposed to estimate the potential of bending strain hardening. Strain-hardening cementitious composites (SHCC) are a class of fiber-reinforced cementitious composites characterized by strain hardening behavior accompanied by multiple cracking, which is designed by tailoring matrix, fiber, and fiber/matrix interface based on the micromechanics theory. At present, there are several numerical simulation methods to study the multiple cracking behavior, such as discrete crack model, unity finite element method, 3D smeared crack model, multiscale constitutive models, and lattice model. However, it is difficult to provide a good balance between accuracy and computational efficiency due to the vast number of fiber and the complex relationship between fibers, matrix, and interface. This paper developed a combined fiber-interface constitutive model based on the single fiber pull-out theory, and established a combined unit. A three-dimensional two-phase finite element model was established, which had been proved to be effective on simulating the cracking behavior of SHCC. Furthermore, the effects of fiber volume fraction and matrix cracking strength on the four-point bending properties of SHCC were investigated. Further study showed that there was a critical matrix cracking strength for a specified fiber and matrix. This value can optimize the design of SHCC to achieve high strength and high toughness performance. [ABSTRACT FROM AUTHOR]

• Beams with general boundary conditions subjected to moving oscillators with damping. • Approximate closed-form solutions for both beam and moving oscillator displacements. • Solution derived through an expansion approach for small oscillator-beam mass ratio. • Simple analytical expressions explicitly depend on the coefficient of the polynomials. • Straightforward application of the solutions for any boundary condition. In this paper, the dynamic response of an Euler-Bernoulli beam with general boundary conditions (BCs) and subject to a moving oscillator is examined. Notably, novel approximate closed-form expressions are determined for the vertical responses of both the beam and the moving oscillator, specifically considering the effect of damping in these systems, commonly omitted in standard approaches in the literature. In this regard, a modal superposition procedure is adopted and combined with an appropriate expansion-based approach of the dynamic response of the system, which naturally arises considering the oscillator-beam mass ratio to be reasonably small. Further, general boundary conditions are treated exploiting the use of a suitable set of orthogonal polynomial functions as beam mode shapes. In this manner, novel direct expressions for the response of the system are derived, in which the mode shapes coefficients explicitly appear. This leads to a straightforward application of the proposed solution, irrespective of the chosen BCs. Several numerical examples are presented to assess the reliability and accuracy of the proposed approach, considering different cases of beam BCs, and moving oscillator's parameters. Results are validated by comparison with the data of finite element analyses, and numerical solutions of the complete system of governing equations. [ABSTRACT FROM AUTHOR]

• Developed a geometrically nonlinear fiber-based frame element considering bond-slip. • Implemented the new element in an object-oriented finite element framework. • Validated the element for behavior simulation of four experimental RC columns. • Assessed the commonly-used perfect bonding assumption using the new element. In structural modeling of reinforced concrete (RC) structures, a common assumption lies in perfect bonding between steel reinforcing bars and the surrounding concrete. This paper aims to assess this assumption and investigate the need and importance of considering imperfect bonding (i.e., steel bar slippage or bond-slip) for predicting the nonlinear behavior of RC columns. To this end, an efficient finite element model capable of capturing bond-slip is required to evaluate the effect of imperfect bonding. Thus, this study first developed a geometrically nonlinear fiber-based frame element considering steel bar slippage and implemented this element in OpenSees with hybrid corotational transformation. Subsequently, using the newly developed element, the effect of imperfect bonding on the behavior of RC columns was investigated. In this regard, the role of bond-slip was studied under different scenarios, including hooked or unhooked ends of longitudinal steel bars in the anchorage area, low or high load levels, and short- or long-duration earthquake ground motions. The results reaffirm the need for prudent consideration of imperfect bonding for advanced finite element modeling of RC structures in several scenarios. [ABSTRACT FROM AUTHOR]

[Display omitted] • Lattice cross sections can be generated by combination of geometric features. • Autoencoder extracts essential information from lattice cross-sectional designs. • Recurrent neural network can predict response of lattice at different strain rates. • Trained model retains prediction accuracy on similar but unseen lattice designs. This paper investigates the structure–property relations of thin-walled lattices, characterized by their cross-sections and heights, under dynamic longitudinal compression. These relations elucidate the interactions of different geometric features of a design on mechanical response, including energy absorption. We proposed a combinatorial, key-based design system to generate different lattice designs and used the finite element method to simulate their response with the Johnson–Cook material model. Using an autoencoder, we encoded the cross-sectional images of the lattices into latent design feature vectors, which were supplied to the neural network model to generate predictions. The trained models can accurately predict lattice energy absorption curves in the key-based design system and can be extended to new designs outside of the system via transfer learning. [ABSTRACT FROM AUTHOR]

[Display omitted] • Identification of primary and secondary creep parameters. • Heuristic algorithm to avoid local minima. • Gradient–based algorithm to ensure finding the global minimum. • Fine-tuning of elastic constants for cylinders in harsh environments. In this paper, a Finite Element Model Updating (FEMU) procedure is developed to find the best creep parameters for filament-wound cylinders under radial compression in harsh environmental conditions. Three winding angles are considered, each under three different hygrothermal conditions. The two–stage creep model captures i) primary creep through a time–hardening approach whilst ii) secondary creep is captured by Norton's law. Given the high number of parameters in this two–stage creep model and the complexity of determining them experimentally, the FEMU routine utilises an optimisation scheme that sequentially couples a Genetic Algorithm (GA) with a gradient-based (GB) Levenberq-Marquardt Algorithm (LMA) to find all required creep input parameters to feed the model that best simulates experimental results. This framework finds the global optimum through an initial screening of the optimum area within the design space with GA, clearing the path to allow the GB algorithm to find the global optimum, substantially reducing the chance or even avoiding falling in local minima. The global search is driven by experimental data of cylinders loaded in radial compression under aggressive environments. The numerical results show excellent agreement with experimental results with reasonably low computational efforts. [ABSTRACT FROM AUTHOR]

• We improve the performance of the 2D-MITC4 solid finite element in distorted meshes. • The assumed strain field of the original 2D-MITC4 element is simplified. • The geometry dependent Gauss integration scheme is introduced. In this paper, we improve the performance of the 2D-MITC4 element for analysis of plane stress and plane strain problems. While the element shows excellent convergence behavior in regular meshes, it exhibits accuracy loss in distorted meshes, as many other elements do. We focus on improving performance in distorted meshes for general use in engineering practice. We simplify the assumed strain field of the original 2D-MITC4 element and introduce the geometry dependent Gauss integration scheme, in which integration points vary according to element geometry distortion. Consequently, a new 2D-MITC4 element is developed. The new 2D-MITC4 element passes the basic tests: patch, zero energy mode, and isotropy tests. Through various numerical examples, improved convergence behaviors of the new element are demonstrated, especially in distorted meshes. [ABSTRACT FROM AUTHOR]

• The spatial discretisation of continuum models with micro-inertia by finite elements is analysed. • The versions with micro-inertia of several classical models with analytical solutions are studied. • The suitability of the novel use of different mass matrices is evaluated via dynamic analyses. • Formulations allowing finite element sizes larger than the relevant length-scale are developed. • Accurate and computationally efficient numerical models are achieved. In this paper, the finite element discretization of non-classical continuum models with micro-inertia is analysed. The focus is on micro-inertia extensions of the one-dimensional rod model, the beam bending theories of Euler–Bernoulli and Rayleigh, and the two-dimensional membrane model. The performance of a variety of mass matrices is assessed by comparing the natural frequencies and their modes with those of the associated discrete systems, and it is demonstrated that the use of higher-order mass matrices reduces errors and improves convergence rates. Furthermore, finite element sizes larger than the corresponding physical length scale are shown to be sufficient to capture the natural frequencies, thus facilitating numerical models that are not only reliable but also computationally efficient. [ABSTRACT FROM AUTHOR]

• We present an edge center-based gradient-smoothing element for thermoelasticity. • Gradient smoothing is based on edge center to obtain smoother gradient field. • Superior performance is demonstrated in 2D and 3D analyses. In this paper, an edge center-based gradient-smoothing element method is proposed for coupled thermoelasticity problems. The main achievement in our work is to construct the linear gradient field inside the element and ensure the consistency of gradient at the junction center of the element, including edge center of triangular element and face center of tetrahedral element. Hence, smoother stress and temperature gradient fields using low-order element are obtained in coupled thermoelasticity analysis without additional post-processing. With the proposed methods, superior accuracy and convergence characteristics are demonstrated compared with other methods through a series of 2D and 3D numerical tests. [ABSTRACT FROM AUTHOR]

• We propose two methods to control the discretization error introduced by the finite element method during the construction of kriging-based metamodels that will be used for the estimation of probability of failure by Monte Carlo samplig. • AGSK-MCS (Adaptive Guaranteed State Kriging - Monte Carlo Sampling) relies discretization error bounds on the performance function that can be obtained from a posteriorierror estimators. This algorithm only uses learning points for which error bounds enable to guarantee the state (safe of failure) to build the kriging-based metamodel. This meta-model is built from computations done on 2 different mesh sizes and is therefore a multi fidelity meta model. • AMSK-MCS (Adaptive Mesh Size Kriging - Monte Carlo Sampling) is a method that takes advantage of the mesh convergence rate of the finite element problem to compute a mesh size parameterized Kriging metamodel (AMSK). It enables to compute the probability of failure at any mesh size thus allowing a reliability-based mesh convergence study. By tending the mesh size to 0, it offers the possibility to compute an estimation of the probability of failure no polluted by the discretization error. This paper presents two approaches to tackle the issue of discretization error in the reliability assessment of structures. The first method (AGSK-MCS for Adaptive Guaranteed State Kriging Monte Carlo Sampling) uses discretization error bounds to guarantee the state safe or failed of the points used to build the Kriging metamodel of the limit state function. Two kriging metamodels interpolating lower and upper bounds can be constructed. These metamodels allow to compute discretization error bounds on the probability of failure through Monte Carlo sampling, which can then be used to validate the choice of the mesh. However, discretization error bounds are not available for any solver and any mechanical problem. In that case, a Mesh Size parameterized Kriging (MSK) metamodel can be used to check mesh convergence of the probability of failure. First, finite element simulations are spread on different mesh sizes. Second, the metamodel is used to compute the probability of failure for a given set of mesh sizes using Monte Carlo estimation. The mesh convergence of the probability of failure can be checked and may guide the user toward remeshing. These two strategies are illustrated on two 2-D mechanical problems. [ABSTRACT FROM AUTHOR]