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In this paper, an extended finite element model is developed for accurate and effective modelling of the tensile strain-hardening and multiple-cracking behaviour of engineered cementitious composites (ECC) under uniaxial tension. The crack is modelled using the cohesive zone model with a simplified cohesive constitutive model accounting for the matrix and fibre bridging effect, and multiple cohesive zones are adaptively embedded within the model upon the occurrence of sequential cracking based on the extended finite element method (XFEM). The extended finite element model is implemented in the ABAQUS via the user element subroutine (UEL) for the numerical analysis of the tensile behaviour of ECC. Material randomness including random matrix flaws and random fibre distribution, which can significantly affect the tensile behaviour of ECC, has been accounted for in the proposed model. Three ECC mixes are modelled and good agreement between the computed and experimental results demonstrates the effectiveness of the proposed method for modelling the tensile behaviour of ECC. It is also shown that the two aspects of material randomness should be considered simultaneously in the model. [ABSTRACT FROM AUTHOR]

The objective of this paper is to assess the reliability and effectiveness of the method of finite spheres, a truly meshless overlapping finite element method, for the solution of practical three-dimensional linear elasticity problems. Advantages include simplified discretization and the elimination of element distortion. The method is implemented in the ADINA finite element program through a user-supplied element subroutine. The solutions of three increasingly complex three-dimensional problems are studied (1) to establish the reliability of the method for practical linear elasticity problems and (2) to assess the effectiveness of the method as compared to the standard finite element method. The solutions indicate that the method of finite spheres is between one and two orders of magnitude more expensive in computational time than the standard finite element method. This is still a promising result since there are significant time savings for the method of finite spheres during the pre-processing phase, particularly in the discretization of complicated three-dimensional geometries and because the overlapping sphere elements can be directly coupled to traditional finite elements. [ABSTRACT FROM AUTHOR]

In this paper, we present the formulations of two four-node quadrilateral membrane finite elements with rotational degrees of freedom to analyze geometric linear and nonlinear plane problems. They are based on a plane adaptation of the space fiber rotation concept that considers virtual rotations of a nodal fiber within the element enhancing the displacement vector approximation of low-order elements. An updated Lagrangian approach is chosen to describe large displacement with small strain kinematics. Several geometric linear and nonlinear benchmarks are presented to assess the performance of the proposed membrane elements and the obtained results demonstrate their efficiency. [ABSTRACT FROM AUTHOR]

Concrete is an heterogeneous structural material whose constitutive behaviour is strictly depending on the mechanical properties of the aggregates and the cement paste. A large number of methods have been devoted to the prediction of the mechanical properties of this material by means of meso-scale analysis. The paper concerns a new meso-scale model of concrete, that considers the composite as a multi-phase material. The numerical description of the meso-scale structure is attained using a random method that allocates at each Gauss point of the finite element discretisation of the Representative Volume Element (RVE) a specific phase of the mixture: aggregate, cement paste, void. Each phase is characterised by a specific non linear constitutive model, whose parameters have been determined by means of experimental tests on the components. More experimental tests have been performed on concrete samples, and they have been numerically reproduced by means of the proposed procedure. Numerical simulations of cyclic uniaxial compression tests have shown the ability of the meso-model to correctly predict the peak strength, the tangent and secant elastic stiffness of the mixture for strains above the peak strain, even adopting a relatively coarse finite element discretisation of the RVE. [ABSTRACT FROM AUTHOR]

In this paper we present a wave-based technique for modelling waveguides equipped with piezoelectric actuators in which there is no need for common simplifications regarding their dynamic behaviour, the interaction with the waveguide or the bonding conditions. The proposed approach is based on the semi-analytical finite element (SAFE) method. We developed a new piezoelectric element and employed the analytical wave approach to model the distributed electrical excitation and scattering of the waves at discontinuities. The model was successfully verified numerically and validated against an experiment on a beam-like waveguide with emulated anechoic terminations. [ABSTRACT FROM AUTHOR]

The paper presents an algorithm for buckling analysis of thin-walled laminated composite beam-type structures. One-dimensional finite element is employed under the assumptions of large displacements, large rotation effects but small strains. The equilibrium equations of a prismatic and straight spatial beam element are formulated using the virtual work principle. Stability analysis is performed in load deflection manner using corotational formulation. The cross-section mid-line contour is assumed to remain not deformed in its own plane, whereas the shear strains of middle surface are neglected. Laminates are modelled on the basis of classical lamination theory. Results have been validated on test examples. [ABSTRACT FROM AUTHOR]

In this paper, the Hamiltonian approach developed for beam with solid cross-section is generalized to deal with beams consisting of thin-walled panels. The governing equations of plates and cylindrical shells for the panels are cast into Hamiltonian canonical equations and closed-form central and extremity solutions are found. Typically, the end-effect zones for thin-walled beams are much larger than those for beams with solid cross-sections. Consequently, extremity solutions affect the solution significantly. Correct boundary conditions based on the weak form formulation are derived. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are found to be in good agreement with those of plate and shell FEM analysis. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce and demonstrate a robust methodology for solving multi-constrained 3D topology optimization problems. The proposed methodology is a combination of the topological level-set formulation, augmented Lagrangian algorithm, and assembly-free deflated finite element analysis (FEA). The salient features of the proposed method include: (1) it exploits the topological sensitivity fields that can be derived for a variety of constraints, (2) it rests on well-established augmented Lagrangian formulation to solve constrained problems, and (3) it overcomes the computational challenges by employing assembly-free deflated FEA. The proposed method is illustrated through several 3D numerical experiments. [ABSTRACT FROM AUTHOR]

Ice forces on bottom-founded structures can be measured by load panels or identified from response measurements. This paper presents a comparison between the measured and identified dynamic ice forces acting on the Nordströmsgrund lighthouse. The dynamic ice forces are identified from the measured responses using a recently developed joint input-state estimation algorithm in conjunction with a reduced-order finite element model. A convincing agreement between the measured and identified forces was found. The response predictive ability of the algorithm is further used to estimate the response of the structure at unmeasured locations including at the ice-action point. [ABSTRACT FROM AUTHOR]

The objective in this paper is to improve the performance of the 4-node MITC quadrilateral shell finite element, referred to as the MITC4 element (Dvorkin and Bathe, 1984). We propose a new MITC4 shell element, the MITC4+ element, in which the mid-surface membrane strain components are assumed using the concept of the MITC method. The tying membrane strains are obtained from four triangular domains which subdivide the mid-surface of the 4-node quadrilateral shell element. This approach alleviates locking that can happen when the MITC4 shell elements are geometrically distorted in curved geometries. Several basic tests including the isotropy, zero energy mode, and patch tests are performed. Through the solution of various shell problems, the convergence behavior of the MITC4+ shell element is studied to show the improvements reached. [ABSTRACT FROM AUTHOR]

A new truly-mixed finite element for the analysis of viscoelastic beams is presented that is based on the additive decomposition of the bending moment in a viscoelastic and a purely elastic contribution. Bending moments are the primary variables that belong to H 2 ( 0 , ℓ ) whereas the kinematic variables (that are the velocities and not the displacements as usual) are globally discontinuous and elementwise linear. As for the peculiarities of the proposed finite element, results from relaxation and creep numerical tests are presented in much detail and a quadratic convergence assessed for all the variables involved. In the second part of the paper, a fast approach to structural (sizing) optimization, set as a topology optimization problem, of such viscoelastic beams is presented in the presence of time-dependent objective functions. Within a gradient-based minimization scheme that is solved via the method of moving asymptotes (Svanberg, 1987), a dual sensitivity analysis approach is derived and representative numerical results presented and discussed in much detail. [ABSTRACT FROM AUTHOR]

The extended scaled boundary finite element method (X-SBFEM) based on the level set method (LSM) is proposed in this paper to combine the advantages of the scaled boundary finite element method (SBFEM) and the extended finite element method (XFEM). The level set method (LSM) algorithm is applied to further develop the X-SBFEM, especially for the crack propagation problem. The Heaviside enrichment function is used to represent a jump across a discontinuity surface in a split element, and the non-smooth behavior around the crack tip is described using the semi-analytical SBFEM. The stiffness of the region containing the crack tip is computed directly, and the generalized stress intensity factors of many types of singularities are obtained directly from their definitions using consistent formulas. In the numerical simulations, a square plate with an edge crack under tension, a three-point bending beam, a four-point shear beam and a dam (the Koyna dam) with a single propagating crack are modeled. The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load–displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results. [ABSTRACT FROM AUTHOR]

This paper describes a procedure for taking into account distributed loads in the calculation of the harmonic response of a cross-ply laminated circular cylindrical shell using the dynamic stiffness method. This work is a direct continuation of a previous work concerning isotropic materials. Equivalent loads are established on element boundaries to determine the response of the system. Therefore, the vibration analysis is solved with numerical examples in order to determine the performances of this approach. The method allows reducing both the size of the model and computing time, and ensures higher precision compared to the finite element method. [ABSTRACT FROM AUTHOR]

This paper presents the topology optimization based on a semi-analytical mixed scaled boundary finite element method (SBFEM) for problems involving incompressible materials using a moving iso-surface threshold method (MIST). The mixed SBFEM does not have volumetric issues in the presence of incompressibility and it can pass the inf–sup stability conditions without requiring any mesh-dependent and stabilization parameters. Thus the topology optimization of incompressible materials is also possible based on the mixed SBFEM. The solutions of stress and strain in the mixed SBFEM are derived semi-analytically. A response function in MIST is chosen as the mutual strain energy density which is formulated by the stress and the strain obtained in the mixed SBFEM. Numerical examples including the optimal design problems of compressible and incompressible materials as well as the rubber mounts containing incompressible solid and fluid are presented. The present results are also verified with the available reference results. [ABSTRACT FROM AUTHOR]

The theory proposed in the paper provides a new approach for the modelling of multiple material discontinuities. The scope of this work is restricted to numerical methods and in particular an approach that utilises the benefits of traditional continuous finite element approximations but enhanced with an increased capacity for handling material discontinuities. The approach is founded on transport forms of the governing conservation laws describing discontinuous physics by means of bespoke moving control volumes and the non-physical field concept. The theory is demonstrated through its application to steady-state and transient flyer impact-plate problems for which analytical results are available. [ABSTRACT FROM AUTHOR]

In this paper, we simplify the error estimation technique developed for the Craig–Bampton (CB) method (Kim et al., 2014). The original formulation is simplified by neglecting insignificant terms, a new error estimator is obtained, and thus computational cost is significantly reduced with negligible accuracy loss. In addition, the contribution of a specific substructure to a relative eigenvalue error can be estimated using the new formulation, in which the estimated relative eigenvalue error is represented by a simple summation of the substructural errors estimated. Therefore, the new formulation can be employed for error control by using the detailed errors estimated for a certain substructure. Through various numerical examples, we verify the accuracy and computational efficiency of the new formulation, and demonstrate an error control strategy. [ABSTRACT FROM AUTHOR]

This paper presents a novel class of smoothing techniques based beta finite element method ( β FEM) for modeling of crystalline materials. The method is first examined by a simple standard patch test and applied in elastic problems. It is then implemented to model the anisotropic plastic deformation of rate-independent single crystals and bi-crystal. Several representative examples are studied to demonstrate the capability of proposed method with the integration algorithm for capturing the strain localization and dealing with plastic incompressibility. It is also performed to simulate the mechanical behavior of polycrystalline aggregates through modeling the synthetic microstructure constructed by Voronoi tessellation technique. [ABSTRACT FROM AUTHOR]

In this paper a unified finite element methodology based on gradient-elasticity is proposed for both two- and three-dimensional problems, along with some considerations about the best integration rules to be used and a comprehensive convergence study. From the convergence study it has emerged that for both two and three-dimensional problems, the implemented elements show a convergence rate virtually equal to the corresponding theoretical values. Recommendations on optimal element size are also provided. Furthermore, the ability of the proposed methodology to remove singularities in statics has been demonstrated through a couple of examples, in both two and three dimensions. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinear reduced-order modelling methodology for finite-element models of structures with slender subcomponents and inertia represented by lumped masses along main load paths. The constructed models have dynamics described by 1-D intrinsic equations of motion, which are further written in modal co-ordinates. This yields finite-dimensional approximations of the system dynamics with only quadratic nonlinearities. Evaluation of the problem coefficients is performed from static condensation of the original model on the lumped masses. The method exploits the multi-point constraints typically used to obtain sectional loads in aircraft aeroelastic analysis. The technique is illustrated on simple 3D structural models built using solid elements. [ABSTRACT FROM AUTHOR]

In the current paper a novel procedure to select the optimal solution both for seismic retrofitting of existing RC buildings and for super-elevation of existing masonry constructions has been implemented by using three different Multi-Criteria Decision Making (MCDM) (TOPSIS, ELECTRE and VIKOR) methods. The procedure application has been faced with reference to two case studies. The first intervention has been studied on a real full-scale 3D RC structure retrofitted with different seismic protection devices mainly based on metal materials, whose performances were experimentally evaluated in a previous research project. All the applied MCDM methods have provided the same result, that is the dominating role exerted by aluminium shear panels for seismic retrofitting of the analysed structure. On the other hand, different innovative and traditional constructive systems have been examined to increase the number of floors of existing masonry buildings. The effectiveness of these interventions in improving the base building behaviour has been proved on a typical building of the South Italy. The study results, achieved by using the three MCDM methods inspected, have provided as an optimal solution the cold-formed steel systems thanks to their prerequisites of lightness, economy and sustainability. [ABSTRACT FROM AUTHOR]

A finite element model is developed in this paper to simulate the degradation of cement-based materials when subjected to aggressive agents, including deionized water and sodium sulfate solutions. The proposed model includes three main modules, i.e. the ionic diffusion module, the chemical reaction module, and the damage quantification module. A modified Poisson–Nernst–Planck model is developed to model the diffusion of multiple ions in the ionic diffusion module. The cracking suction effect is accounted for the suction action caused by newly-formed unsaturated cracks with potential to accelerate the entire diffusion process. In the chemical reaction module, chemical interactions between ions and cement hydration products are solved based on a local equilibrium assumption. Different approaches in dealing with the simulation of the decalcification process of ill-crystallized Calcium Silicate hydrate (C–S–H) are discussed. The entire reactive diffusion mechanism is achieved by using the operator splitting approach to couple the ionic diffusion and the chemical modules. In the damage quantification module, the diffusivities of material are evaluated at the end of each time step based on the change of porosity and propagation of cracking. Two mechanisms of precipitation of hydration products, i.e. through-solution and topochemical reactions, are discussed in the light of their distinct contributions to the cracking propagation. The proposed model is applied to model the experiments reported in the literature and the computed results are also compared with those obtained from other available models. It is found that the results obtained from the proposed model agree very well with those from experiments and generate more accurate predictions than other models. [ABSTRACT FROM AUTHOR]

This paper reports the parallel implementation of a hybrid-mixed stress finite element model for the analysis of three-dimensional structures. The stress and the displacement fields in the domain and the displacement fields on the static boundary are independently approximated. All field equations are imposed in a weighted residual form and Legendre polynomials are used to define the approximation bases. The parallel implementation of the model uses a message passing scheme based on the MPI standard. For the parallel solution of the governing system, two distinct approaches are tested. The first corresponds to the use of a third-party parallel direct solver code, named MUMPS. The second uses an in-house developed hybrid solver inspired by the FETI method and designed to deal with the typical pattern of the hybrid-mixed stress model governing system. Some numerical examples are discussed to illustrate the effectiveness and performance of the adopted parallel approach. [ABSTRACT FROM AUTHOR]

This paper focuses on the application of structural topology optimisation technique to design steel perforated I-sections as a first attempt to replace the traditional cellular beams and better understand the mechanisms involved when subjected to bending and shear actions. An optimum web opening configuration is suggested based on the results of parametric studies. A FE analysis is further employed to determine the performance of the optimised beam in comparison to the conventional widely used cellular type beam. It is found that the optimised beam overperforms in terms of load carrying capacities, deformations, and stress intensities. Barriers to the implementation of the topology optimisation technique to the routine design of beam web are highlighted. [ABSTRACT FROM AUTHOR]

Sandwich panels are usually modeled by considering only asymmetric motion which assumes the core deforms by transversal shearing without any compressive deformation over the thickness. This assumption is acceptable for panels with relatively stiff and thin cores. However, symmetric motion becomes important when the core is thick or soft. Under such conditions, the compressive deformation over the core thickness becomes significant. This paper addresses the prediction of the Sound Transmission Loss (STL) and composite Damping Loss Factor (DLF) of sandwich panels with either thin or thick cores as well as stiff or soft (viscoelastic) cores. Both the skin and the core are assumed to be orthotropic. A spectral finite element based approach is developed wherein the stress and strain components in each layer are described using the properties in that layer for a forced trace wave number and heading direction. The proposed approach provides a reliable and numerically efficient tool to account for the compressive deformation effect of thick orthotropic sandwich layers. Moreover, the proposed model is also able to consider panels with multiple of layers with varying properties. [ABSTRACT FROM AUTHOR]

In this paper, variable-node elements (VNEs) based on the cell-based smoothed finite element method (CS-FEM) are proposed with emphasis on their applications for elasto-plastic finite deformation. The formulation of CS-FEM is extended to cover elastic–plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elasto-plastic deformations is remedied by relaxing volumetric strain through its mean value. In addition, the existing VNEs limited to linear elastic analysis is extended to analysis of elasto-plastic deformations with the aid of CS-FEM. The comparison with the conventional finite elements and Abaqus demonstrates the effectiveness and accuracy of the present approach. [ABSTRACT FROM AUTHOR]

• A computational microplane model bridging mesoscale inelastic fracture to macroscale fracture is presented. • The model is for predicting the inelastic material behavior in 3D stress. • The model is formulated to be more intuitive than the spectral microplane model. • An explicit algorithm for the model is developed and coded into a VUMAT subroutine. • The computational cost of the model is much less than that of competing mesoscale ones. In this paper, a microplane model based on cylindrical geometry where the cylinder axis coincides with the longitudinal direction is developed for a general 3D inelastic fracturing analysis by finite element method of transversely isotropic fiber reinforced polymer composites. The model bridges the mesoscale material behavior to macroscale one using the stress equilibrium approach developed for cylindrical geometry. To this end, Microplane level stress–strain relations for tension, compression and shear for both longitudinal and transverse directions are formulated. An explicit algorithm is formulated and coded into a VUMAT user subroutine for use with ABAQUS. The model is suitable for the analysis and design of large structures made of fiber reinforced polymer composites unlike the competing mesoscale models because of its much lower computational cost. A detailed metodology for the calibration of the model is identified. The model is calibrated against the common test data available in the literature using this metodology and the predictive capacity of the model is demonstrated by comparing the model predictions with test data in longitudinal tension, lateral tension, longitudinal compression, lateral compression, longitudinal shear and rare size effect in bending tests including post-peak fracture available in the literature. [ABSTRACT FROM AUTHOR]

• A new non-intrusive SFEM is proposed for efficient uncertainty propagation of plates. • Probability density functions of stochastic responses and structural reliabilities are achieved. • For Gaussian random thickness, linearly elastic plate yields non-Gaussian response. • Increasing correlation length and variability of random field reduces plate's reliability. Currently, several intrusive stochastic finite element methods (SFEMs) such as perturbation method and spectral SFEM are widely applied for stochastic response analysis of continuous structures. However, the intrusive SFEMs need to modify conventional finite element formulations to establish the stochastic stiffness matrix, and cannot calculate the probability density function of structural response and the reliability straightforwardly. This paper proposes a new non-intrusive SFEM for efficiently computing stochastic responses and reliabilities of plates in a unified way. Firstly, the direct probability integral method (DPIM) is developed to obtain the probability density function of stochastic response by solving probability density integral equation (PDIE). Secondly, the non-intrusive SFEM based on DPIM decouples the deterministic finite element analysis and PDIE to calculate the stochastic responses and reliabilities of uncertain plate structures, and the discretization and quantification of random fields of elastic modulus and thickness are implemented through Karhunen-Loève expansion. Finally, several examples of uncertain Kirchhoff and Mindlin plates demonstrate the efficiency and versatility of the proposed non-intrusive method by comparing with the results from Monte Carlo simulation and literature. The effects of correlation length, mean and variability of random field on the probability distribution of responses and the reliabilities of plates are revealed. For Gaussian random thickness, the linearly elastic plate yields non-Gaussian distributed responses. Increasing the correlation length and variability of random field reduces the reliabilities of plates. [ABSTRACT FROM AUTHOR]

• The upper and lower response bounds are obtained through a series of sequential simulations. • The proposed sequential simulation method is applicable to interval uncertainty analysis of structural or system response with multiple DOFs. • The contributive samples for the response bounds over the whole concerned domain can be identified simultaneously. • The sequential simulation strategy is demonstrated to be more efficient than the direct MC simulation for response bounds evaluation. Prediction of response bounds of structures with interval uncertainties is a major concern in interval finite element analysis. In many cases, the structural response is a variable regarding to physical parameters such as location, node, time, or other degrees of freedom. Different kinds of interval methods have been proposed and developed for response bounds analysis, which mainly include the interval arithmetic-based methods, optimization methods, perturbation methods, etc. This paper proposes a sequential simulation strategy for response bounds analysis of structures with interval uncertainties, through which we aim to find the upper and lower bounds by implementing the simulation procedure sequentially. The proposed sequential simulation strategy suggests an initial sampling and simulation, from which those contributive samples that result in the current upper or lower response bound are retained. In the subsequent simulation sequence, local samples within neighborhoods of the present contributive samples as well as a set of global samples are generated for the input interval uncertainties. With such a simulation procedure, the response bounds are expected to expand outwards sequentially until convergence. By illustration and comparison, the proposed sequential simulation strategy is proved to be more efficient than the direct simulation method for structural response bounds analysis. [ABSTRACT FROM AUTHOR]

• We present the strain-smoothed MITC3+ shell finite element for nonlinear analysis. • The total Lagrangian formulation is adopted allowing for large displacement kinematics. • Its performance is demonstrated in geometrical and material nonlinear analyses. This paper presents the strain-smoothed MITC3+ shell finite element for nonlinear analysis. The strain-smoothed MITC3+ shell element, recently developed for linear analysis, significantly improves the membrane behavior of the MITC3+ shell element while retaining its excellent bending behavior. The achievement is attained by adopting the strain-smoothed element (SSE) method to the membrane strain field. To extend its formulation to nonlinear analysis, the total Lagrangian formulation is employed allowing for large displacements and rotations. Through various numerical examples, we verify that the strain-smoothed MITC3+ shell element also shows the superior performance in geometrical and material nonlinear analyses. [ABSTRACT FROM AUTHOR]

In this paper, a mixed formulation based on the scaled boundary finite element method (SBFEM) is proposed for nearly incompressible linear elasticity. The problems with strong discontinuities in nearly incompressible linear multi-materials are analyzed. The proposed technique avoids volumetric locking and non-physical pressure oscillations at near incompressible limit without requiring any mesh-dependent or stabilization parameters. The pressure field is introduced but it is not independently unknown in the proposed technique. The pressure and displacement are interpolated identically on the boundary. Standard polynomial shape functions and high order line-elements are used. The governing equation of mixed SBFEM in displacement is derived based on the virtual work principle. The displacement, stress and pressure fields along the radial direction are represented analytically, which permits the stress intensity factors to be directly evaluated by definition. [ABSTRACT FROM AUTHOR]

This paper proposes a fine-grained implementation of matrix-free Conjugate Gradient (CG) solver for Finite Element Analysis (FEA) using Graphics Processing Unit (GPU) architectures. The use of GPU computing in FEA is today an active research field. This is primary due to current GPU sparse solvers are partially parallelizable and can hardly make use of Data-Level Parallelism (DLP) for which GPU architectures are designed. The proposed GPU instance takes advantage of Massively Parallel Processing (MPP) architectures performing well-balanced parallel calculations at the Degree-of-Freedom (DoF) level of finite elements. The numerical experiments evaluate and analyze the performance of diverse GPU instances of the matrix-free CG solver. [ABSTRACT FROM AUTHOR]

This paper presents the development of a new concept, the Embedded Unit Cell (EUC) approach, to calculate local responses in elastic media. The EUC approach is based on a multi-scale formulation of non-periodic domains to evaluate the local/micro response where stress concentrations are expected. The formulation is based on alternative boundary conditions which is not restricted to periodic assumptions of the unit cell response that is required in the classical theory. This approach provides a reduced computational cost model of the macroscopic/global problem while preserving the accuracy at the microscale problem. We conclude with a numerical verification study. [ABSTRACT FROM AUTHOR]

For the harmonic analysis of plate bending problems, the Finite Element Method (FEM) is a commonly applied numerical technique. Its element concept with polynomial approximation functions, however, limits its applicable frequency range because of a strongly increasing computational cost. The Wave Based Method (WBM) has can relax this by using wave functions, which satisfy the governing differential equations. This paper derives two distinct particular solution sets for distributed loads in the WBM. Two numerical validations show the improved efficiency as compared to the FEM. The novel approach is also applied to a plate under a TBL excitation. [ABSTRACT FROM AUTHOR]

In this work, two iterative BEM–FEM coupling procedures are discussed, taking into account nonlinear models and adaptive spatial discretizations. In both procedures, optimal relaxation parameters are computed (speeding up the convergence of the iterative coupling) and non-matching discretizations at common interfaces are allowed (enabling more versatile adaptive approaches). A single unified iterative loop is considered in order to deal with all the focused iterative solutions simultaneously (i.e., nonlinear analysis, adaptive analysis and coupling analysis), rendering a very efficient methodology. At the end of the paper, numerical results are presented, illustrating the good performance of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper applies the asymptotic homogenization method to predict effective properties of periodic heterogeneous beam structures. A improved FEM formulation and algorithm of the unit cell problems is developed. The effective properties are rewritten in terms of the nodal quantities of the FEM model of the unit cell. With this approach, periodic beam structure of complicated microstructure can be modeled by various elements and modeling techniques and solved by using the commercial software as a black box. Numerical examples illustrate the versatility and efficiency of the method. Finally, the size effect of basic cell in thickness direction is studied. [ABSTRACT FROM AUTHOR]

Many systems in engineering, theoretical physics and other domains of natural sciences can be investigated using a linear mathematical model having the character of a differential system defined within a given network. This network may consist of one-dimensional elements characterised by local coordinate systems. These elements (recti- or curvilinear) are interconnected at nodes, through which energy, mass and stiffness properties of the elements are transmitted as a function of time. The system as a whole is generally determined by some boundary conditions or assumed to be interconnected with other subsystems. Elements of the system are considered to have continuously distributed parameters (mass, stiffness, conductivity, etc.). External energy may be supplied through boundary conditions or by excitation of elements at nodes. The problem of the system’s response, or a relevant eigenvalue problem, can be understood as a problem of a differential system on an oriented graph. This graph is a corresponding geometrical representation of the system investigated, where elements of the graph represent individual beams of the system. Therefore the physical part of the problem is fully included in the original differential system, but without any indication of its domain shape. As illustrations of this theoretical study, the conventional Slope Deflection Method (SDM), developed in the past for statics and later for dynamics of continuous frames are outlined in this paper, along with some illustrations from other branches. It should be noted that the character of the resulting algorithm is similar to the FEM if special macro-elements provided by direct solution of the relevant differential system are used. High numerical stability of the approach used here is a significant strength in comparison with other procedures. This follows from the principal attributes of the proposed method. Easy implementation of the theory into existing software packages is possible. [ABSTRACT FROM AUTHOR]

In this paper, an a posteriori error estimator of the recovery type is developed for the gradient elasticity theory of Aifantis. This version of gradient elasticity can be implemented in a staggered way, whereby solution of the classical equations of elasticity is followed by solving a reaction–diffusion equation that introduces the gradient enrichment and removes the singularities. With gradient elasticity, singularities in the stress field can be avoided, which simplifies error estimation. Thus, we develop an error estimator associated with the second step of the staggered algorithm. Stress-gradients are recovered based on the methodology of Zienkiewicz and Zhu, after which a suitable energy norm is discussed. The approach is illustrated with a number of examples that demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

This paper proposes a stochastic response analysis method for the scaled boundary finite element method (SBFEM), through which the statistical characteristics of the structural responses subject to random uncertainty can be efficiently calculated. In the proposed method, an approximate approach is given to solve the first four statistical moments of the random responses of SBFEM. The probability density functions of the structural responses are calculated using the maximum entropy principle constrained by the calculated moments. The semi-analytical gradients of the responses with respect to the random variables are solved by developing an improved sensitivity analysis method of SBFEM. The proposed method is then applied to the structural reliability analysis and the probabilistic fracture mechanics analysis. Four numerical examples are investigated to demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the static and dynamic modal behavior of the MITC3+ triangular shell element (Lee and Bathe, 2004; Lee et al., 2014). We focus on bending-dominated situations because such shell problems are particularly difficult to solve when using low-order elements. For comparison, the pure displacement-based (DISP3), MITC3 and MITC4 shell elements are also studied. First, static mode solutions are performed for a single right-angled shell element and an assemblage of two right-angled shell elements. The detailed strain fields are established in the bending modes. This study provides insight into how shear locking occurs on the mode level. We then analytically show how the MITC3+ shell element properly represents the pure bending conditions in a two-sided clamped plate problem. Considering free plate and free hyperboloid shell problems, we finally present the excellent performance of the MITC3+ shell element in dynamic mode solutions. [ABSTRACT FROM AUTHOR]

This paper investigates two FEM–BEM coupling formulations for acoustic fluid–structure interaction (FSI) problems, using the Finite Element Method (FEM) to model the structure and the Boundary Element Method (BEM) to represent a linear acoustic fluid. The coupling methods described interconnect fluid and structure using classical or localized Lagrange multipliers, allowing the connection of non-matching interfaces. First coupling technique is the well known mortar method, that uses classical multipliers and is compared with a new formulation of the method of localized Lagrange multipliers (LLM) for FSI applications with non-matching interfaces. The proposed non-overlapping domain decomposition technique uses a classical non-symmetrical acoustic BEM formulation for the fluid, although a symmetric Galerkin BEM formulation could be used as well. A comparison between the localized methodology and the mortar method in highly non conforming interface meshes is presented. Furthermore, the methodology proposes an iterative preconditioned and projected bi-conjugate gradient solver which presents very good scalability properties in the solution of this kind of problems. [ABSTRACT FROM AUTHOR]

Embedded elements (EE) present a potential for an effective solution of interpenetration of yarn volumes, excluding the need for creation of continuous meshes in the matrix and in the reinforcement. The paper investigates application of contact algorithm to eliminate the interpenetration and introduces a stiffness correction in volumes made redundant because of coincidence of the embedded and the host meshes. Different fibre configurations (two intersecting yarns and a 3D woven reinforced composite) are considered and a good agreement is observed between the continuously meshed and EE models in prediction of the homogenised properties and strain–stress profiles in loaded unit cells. [ABSTRACT FROM AUTHOR]

Continuation methods have proved to be very powerful tools when solving large finite element problems. However, implementation of these methods often require modifications to the standard finite element method. As a finite element code is already very complex, we would like to implement the continuation method as efficiently as possible. In this paper, we present a new implementation technique based on a Schur complement approach for the Moore–Penrose continuation method. This method facilitates the detection of bifurcation points and also enables branch following. Numerical examples will be presented and analyzed using the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a new computational framework is introduced for the analysis of three dimensional linear piezoelectric beams using hp -finite elements. Unlike existing publications, the framework is very general and suitable for static, modal and dynamic scenarios; it is not restricted to either actuation or energy harvesting applications and, moreover, it can cope with any anisotropy or electric polarisation orientation. Derived from first principles, namely the fundamental equations of continuum piezoelectricity, a new set of beam balance equations is presented based on a Taylor series expansion for the displacement and electric potential across the cross section of the beam. The coupled nature of the piezoelectric phenomenon at a beam level arises via a series of mechanical (and electrical counterparts) stress and strain cross sectional area resultants. To benchmark the numerical algorithm, and in order to aid prospective researchers, a new closed-form solution is presented for the case of cantilever type systems subjected to end tip mechanical/electrical loads. To the best of the authors’ knowledge, the analytical solution for this prototypical example has not been previously presented. Finally, some numerical aspects of the hp -discretisation are investigated including the exponential convergence of the hp -refinements and the consideration of linear or quadratic electric potential expansions across the cross section of the beam. [ABSTRACT FROM AUTHOR]

The paper presents numerical simulations of punching shear in a reinforced concrete slab-column configuration formerly tested in the laboratory. A brief description of the test program at the University of Waterloo is reported. For the simulation, a symmetric quarter of the test configuration is employed. Full three-dimensional finite element discretized geometry is considered together with elastic–plastic reinforcement embedded as truss elements in concrete. Two regularized numerical models of concrete, formulated within elastic–plastic-damage theories, are applied. The first one, called gradient damage, is refined by an additional averaging equation where gradient enhancement involves an internal length scale. In the second one, called rate-dependent damaged plasticity model, a viscoplastic strain rate is introduced. The results for the first model implemented in FEAP and the second model from ABAQUS are discussed in detail. Different issues of numerical simulation to properly predict punching shear behaviour in the slab-column configuration are presented. [ABSTRACT FROM AUTHOR]

This paper presents an interior-point implementation method of the relaxed strain energy function to model the stress distribution in membranes in the presence of wrinkles. The relaxed strain energy function is reformulated using the interior-point method. This formulation is proven to be quasi-convex with respect to the deformation gradient. A set of governing equations for the membrane is developed in the standard finite element format. The solution to this set of equations is obtained using the interior-point method, and several numerical examples are presented for validation. The proposed method is shown to converge and to be robust and efficient. [ABSTRACT FROM AUTHOR]

This paper presents a numerical (shell finite element) investigation aimed at assessing the performance of the current Direct Strength Method (DSM) provisions against distortional failure to estimate the ultimate strength of fixed-ended cold-formed steel lipped channel and rack-section columns (i) subjected to various uniform temperature distributions caused by fire conditions and (ii) exhibiting different room-temperature yield stresses, covering a wide distortional slenderness range. In particular, the work addresses how does the temperature-dependence of the steel material behaviour, which is felt through both the (reduced) Young’s modulus and nominal yield stress values, influences the quality (accuracy and safety) of the column ultimate strength predictions provided by the DSM distortional strength curve. Six different temperature-dependent steel constitutive laws are considered, namely (i) two models prescribed in part 1.2 of Eurocode 3 (EC3), for cold-formed and hot-rolled steel, and (ii) four experimentally-based analytical expressions recently reported in the literature. The DSM column ultimate strength estimates are compared with the numerical failure loads obtained through geometrically and physically non-linear Ansys shell finite element analyses incorporating critical-mode initial imperfections with small amplitudes. [ABSTRACT FROM AUTHOR]

This paper presents the development of a 3D nonlinear finite element (FE) model to capture and predict the response of shear deficient simply supported reinforced concrete (RC) beams strengthened externally with aluminum alloy plates. Five FE models were developed based on experimental tests conducted by the authors in a previous investigation. The experimental program included four RC beams strengthened in shear with externally bonded structural aluminum alloy plates of grade 5083–0 and tested under four-point loading to failure. The use of this material instead of the conventional fiber reinforced polymer (FRP) materials seemed to be very promising in enhancing both the strength and ductility of the strengthened specimens. The beams were designed to fail in shear and then strengthened with aluminum alloy plates with different strip spacing and orientation. The developed FE models have exact geometry, nonlinear material properties and boundary conditions to that of the experimental specimens. The FE models employed material constitutive laws for the concrete in tension and compression, yielding of the aluminum plates and flexural steel reinforcement. The developed FE models also incorporated the interfacial bond behavior at the aluminum concrete interface. The predicted FE results for the load–midspan deflection are compared to the measured experimental data. Close agreement was found between the predicted and measured results at all stages of loading for the tested specimens. For the maximum load and maximum mid-span deflection, it is observed that the Mean Absolute Percent Error (MAPE) of the prediction for the five specimens is 1.19% and 4.31% and the Normalized Mean Square Error (NMSE) is 0.0005 and 0.004, respectively. It could be concluded that the developed FE model could be used in future investigations to predict the performance of shear deficient RC beams externally strengthened with aluminum alloy plates with different configurations and orientations. [ABSTRACT FROM AUTHOR]

The goal of this paper is to characterise the variability of two important design parameters of thermoplastic honeycomb sandwich beams from the analysis of experimentally determined resonance frequencies and mode shapes of a limited number of test beams, under free boundary conditions. The design parameters are the Young’s modulus of the skin in length direction of the beam and the out-of-plane shear modulus of the honeycomb core. These two independent parameters are expressed as random fields using a Karhunen–Loève series expansion of the covariance matrix, available after updating the finite element models using the experimental vibration data. The random variables of this series expansion are expressed in terms of a Hermite polynomial chaos. The aleatory uncertainty is modelled by the Gaussian random variables while the epistemic uncertainty is described by the randomness of the polynomial chaos coefficients. An estimation of the uncertainty resulting from the experimental and numerical modal analysis is discussed, along with its influence on the two considered stiffness parameters. [ABSTRACT FROM AUTHOR]