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A new shell element has been proposed for geometrically non-linear, finite element analyses of axially moving paper web. Web instability problems of paper travelling in a printing system, such as wrinkling and fluttering, pose special challenges in the numerical analyses. For examples, these are finite bending stiffness (as opposed to membrane), orthotropy, and non-uniform distributions of mechanical and hygro-properties (in different length scales). The new formulation has accounted for paper transport velocity and paper bending stiffness based on a mixed Lagrangian–Eulerian description of the motion. A natural coordinate system has been employed in the analytical and finite element formulations. Benchmarking with different finite elements in various tests showed that the proposed element is indeed more stable and reliable for the chosen application than existing elements. The usability of the shell element has been successfully demonstrated by two example problems: wrinkling of stretched isotropic and orthotropic membranes, and the vibration of a web showing a speed-tensioning effect above a critical web transport velocity. [Copyright &y& Elsevier]

• A homogenized finite element (FE) and a rigid block (RB) model are presented. • The numerical problems are formulated using mathematical programming. • A numerical case study of a masonry church was considered. • Predicted failure mechanisms and collapse load multipliers are compared. The aim of this paper is to show to what extent a simple constitutive model can adequately describe the collapse mechanisms of historic masonry structures under horizontal seismic loads. Referring to block masonry, the paper presents the formulation and the numerical implementation of a constitutive relationship for modeling masonry structures regarded at a macroscopic scale as homogenized anisotropic continuum. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in a FE code by means of a minimization algorithm directly derived from the Haar-Karman principle. A sensitivity analysis to mechanical and geometrical parameters was carried out to show the influence on the predicted response of small-scale wall components from the literature. The model is then used for the analysis of a numerical case study which is representative of a masonry church subjected to horizontal seismic action. The result of the model will be compared with those obtained by a rigid block model (RBM) of the same small-scale masonry prototypes and of the church building. In the paper, the results of the two models are discussed and analyzed in the way to highlight the weakness and the potentiality of the two different approaches. [ABSTRACT FROM AUTHOR]

• Distribution effect on the mechanical properties of dual-phase lattice is ascertained. • Balanced mechanical properties are achieved through Sudoku based lattice design. • A statistical parameter is defined to depict the distribution characteristics. • Scattered distribution of reinforcement cells is beneficial to the dual-phase lattice. In this paper, the effect of the distribution pattern of the reinforcement phase on the mechanical properties was studied for the simple-cubic matrix dual-phase lattices given the same second phase proportion. Two reinforcement phases, the body centered cubic and the face centered cubic cells, were investigated. Specifically, a novel distribution pattern of reinforcement phase inspired from Sudoku algorithm was proposed to design the dual-phase lattices with balanced elastic modulus, strength and energy absorption properties. Comparisons were made for mechanical performances of five types of distributions, i.e., the layer distribution, column distribution, Sudoku distribution, random distribution and symmetry distribution through extensive finite element simulations. The results indicate that the scattered distribution of the reinforcement phase is beneficial to the investigated mechanical properties. To guide the design of dual-phase lattices, a parameter called degree of concentration is introduced to describe the distribution of reinforcement phase. In general, the mechanical properties are inversely related to degree of concentration. The proposed Sudoku dual-phase lattice possesses zero degree of concentration along any of the three principle directions, thus exhibits advantageous isotropic mechanical properties. This paper provides a new avenue for the design of multi-phase lattice materials. [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]

The paper reports the results of a numerical investigation on the relevance of web-triggered local–distortional interaction on the ultimate strength of a large number of cold-formed steel fixed-ended (plain) lipped channel, zed, hat and rack-section columns. These results concern columns with various geometries (cross-section dimensions and unrestrained length) and yield stresses, ensuring a wide variety of combined ratios between the (i) distortional and local critical buckling stresses ( R DL ) and (ii) yield and non-critical buckling stresses ( R y ). To avoid interaction with global buckling, all columns have global critical buckling stresses much higher than their local, distortional and yield counterparts. The aim of this study is to identify combinations of these ratios for which L–D interaction is relevant, in the sense that it affects visibly the column elastic and elastic–plastic post-buckling behaviours, ultimate strength and failure mechanism – special attention is devoted to the ultimate strength erosion. The numerical ultimate strength data obtained are then compared with the predictions of (i) the currently codified DSM (Direct Strength Method) strength curves for the design of columns failing in local and distortional modes and (ii) available DSM-based design approaches specifically developed to handle local–distortional interactive failures. Then, experimental results available in the literature concerning lipped channel and rack-section columns failing in local–distortional interactive modes are used to assess the quality of the estimates provided by the DSM-based design approaches. Finally, the paper closes with some considerations on the design of cold-formed steel columns undergoing L–D interaction. [ABSTRACT FROM AUTHOR]

• A deep long short-term memory (LSTM) network is developed for nonlinear structural response modeling. • Two input-output schemes (LSTM-s and LSTM-f) are presented. • The deep learning model is capable of modeling both elastic and inelastic response of buildings. • An unsupervised learning algorithm is used to cluster the seismic inputs for training enhancement. • The approach was successfully verified by both numerical and experimental examples. This paper presents a comprehensive study on developing advanced deep learning approaches for nonlinear structural response modeling and prediction. Two schemes of the long short-term memory (LSTM) network are proposed for data-driven structural seismic response modeling. The proposed deep learning model, trained on available datasets, is capable of accurately predicting both elastic and inelastic response of building structures in a data-driven fashion as opposed to the classical physics-based nonlinear time history analysis using numerical methods. In addition, an unsupervised learning algorithm based on a proposed dynamic K-means clustering approach is established to cluster the seismic inputs in order to (1) generate the least but the most informative datasets for training the LSTM and (2) improve the prediction accuracy and robustness of the model trained with limited data. The performance of the proposed approach is successfully demonstrated through three proof-of-concept studies that include a nonlinear hysteretic system, a real-world building with field sensing data, and a steel moment resisting frame. The results show that the proposed LSTM network is a promising, reliable and computationally efficient approach for nonlinear structural response prediction, and offers significant potential in seismic fragility analysis of buildings for reliability assessment. [ABSTRACT FROM AUTHOR]

• Investigate the effects of hydrostatic pressure and anisotropic in-situ stress fields on blast-induced damage to rock. • The image processing technique is employed to quantitatively assess blast-induced damage to rock under different in-situ stress fields. • The mathematical relationship between the damage variable and in-situ stress fields is established. In-situ stress significantly affects rock blast damage but there is a paucity of quantitative assessments of damage evolution in rocks affected by confining pressure. The present paper analyses the effect of envelope pressure on blast-induced rock damage through theoretical analysis and numerical simulations. Damage clouds obtained from numerical simulations are processed using image processing techniques. The concept of the damage variable (η) is proposed to facilitate the presentation of the image processing results. The damage variable is found to be negatively correlated with the hydrostatic pressure (P x) at the same moment, in equiaxial in-situ stress fields. In contrast, in anisotropic in-situ stress fields, η is not negatively correlated with P x due to the presence of hoop tensile stresses in the rock. The mathematical relationship between η and P x in equiaxial and anisotropic stress fields are established. An anisotropic damage variable (η k) is introduced to describe the effect of the anisotropy ratio (K) on rock damage, which is found to increase with increasing values of K. The sharp increase in K equal to 4 and 5 is explained in terms of the state of the rock stress distribution under static loading. This study provides insights into the effect of in situ stress on rock blast damage and presents new approaches for analyzing and presenting the data. [ABSTRACT FROM AUTHOR]

Abstract: The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric boundary element Method (IGABEM) that only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementations. Examples of Matlab® code are given whenever possible to aid understanding of the techniques used. [Copyright &y& Elsevier]

Abstract: This paper presents shaking-table test results of a two-story steel portal frame with bolted connections. The aim of these tests is to understand the inelastic behaviour of frame structures subjected to dynamic loads. Moreover, the purpose of these tests is to study changes in modal parameters due to the development of Low-Cycle Fatigue damage in frame connections. A nonlinear numerical simulation is performed using a Fatigue Damage-Based Hysteretic model. A comparison of results obtained from numerical analysis and those of shaking-table tests is presented. The paper concludes that the proposed numerical method can predict the response of the damaged frame. [Copyright &y& Elsevier]

Highlights • New geometrically exact beam formulation for elastic/elastoplastic analyses of thin-walled members. • New beam element involving the interaction between global and local deformations. • Improved GBT-based approach for kinematic parameterization of the deformed configurations. • Beam equations of equilibrium in terms of shell-type stress resultants and stress couples. • Less computational cost for an equivalently accurate analysis compared to shell finite elements. Abstract A new nonlinear cross-section deformable beam formulation based on generalized beam theory (GBT) is presented for elastic/elastoplastic analyses of thin-walled members undergoing arbitrary deformations, such as large deflections, finite rotations, distortional/local buckling, and out-of-plane warping. For rigorous numerical analyses of thin-walled structures, considering both the global and local deformation effects, shell finite elements are widely used. This paper aims at providing a more computationally efficient and structurally clarifying alternative to simulate prismatic and curved thin-walled members. Compared to the traditional beam elements and other beam formulations based on higher-order beam theories, we improved the kinematic description of member cross-section displacement field, where the kinematic parameterization is performed on two scales, i.e., global member scale and local wall scale; especially, the local wall deformations are described by means of the predetermined GBT modes which are structurally meaningful and allow for the cross-section deformations. Beam equations of equilibrium are built on the local wall scale in terms of shell-type stress resultants and stress couples; therefore, the present beam formulation owns the feature of a shell model. A Galerkin method based beam finite element is developed to solve the equilibrium equations. Finally, six illustrative examples are examined for the validity of the proposed beam formulation. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the development and illustrates the application of a beam finite element based on Generalised Beam Theory (GBT) and intended to analyse the elastic post-buckling behaviour of thin-walled steel members exhibiting arbitrary open cross-section and with non-standard support conditions (e.g., in-span bracing systems). After briefly reviewing the main concepts and procedures required to obtain the GBT system of non-linear equilibrium equations, the paper describes the steps involved in the numerical implementation (incremental–iterative strategy) of a non-linear beam finite element that incorporates the influence of the non-standard support conditions. Finally, the application and capabilities of the proposed GBT-based beam finite element are illustrated by means of the presentation and discussion of numerical results concerning the post-buckling behaviour of lipped I-section columns and lipped channel columns and beams with and without localised displacement restraints. For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the commercial code Ansys. [Copyright &y& Elsevier]

Abstract: Starting from the micro-structural definition of the stress tensor, Rothenburg and Bathurst (1989) derived a stress–force–fabric relationship for granular materials by approximating the directional distributions of the fabric, more specifically, the contact normal density distribution in this paper and the contact forces with Fourier functions and integrating over directions. This paper aims to assess the validity of the two key assumptions made during their derivation using particle-based numerical simulation in the cases of proportional loading and non-proportional loading. These two assumptions are (i) the 2nd-rank Fourier functions adopted are good enough to approximate the directional distributions of contact normal densities and contact forces and (ii) the principal directions of contact forces and contact normal density are coaxial. Numerical simulations have been carried out to conduct virtual experiments on the behaviour of isotropic specimens to monotonic loading, of isotropic specimens to stress rotation, and of anisotropic specimens to monotonic loading. The first one stands for the case of proportional loading while the latter two are non-proportional loading paths involving rotation of the frame of principal stresses and the frame of fabric, respectively. The directional distributions of contact normal density and contact forces are traced during these three typical loading processes. The simulation results indicate that the 2nd-rank Fourier functions give reasonable approximations, while the coaxial assumption is generally not valid in non-proportional loading. In the case that the principal directions of contact normal density and contact force differ, a more general expression of the stress–force–fabric relationship is required. This research can help to improve our understanding of the stress state and hence shear strength of granular materials based on the particle scale investigation. [Copyright &y& Elsevier]

Abstract: The Finite Element Method is the most commonly used prediction technique to model the harmonic behavior of poroelastic materials. A major disadvantage of this method is its practical frequency limitation in that the computational efforts become prohibitively large at higher frequencies. A recently developed Wave Based Method is an efficient alternative deterministic prediction technique which aims at relaxing this frequency limitation by using exact solutions of the governing equations to approximate the field variables. This paper discusses the application of the Wave Based Method for the particular case that stress singularities are present in corners of the poroelastic domain. Based on an asymptotic analysis, the paper derives a criterion to predict the presence of stress singularities and proposes a suitable set of enrichment functions to extend the conventional set of expansion functions. The beneficial effect of incorporating these functions on the convergence of the Wave Based Method is illustrated by means of a numerical validation study. [Copyright &y& Elsevier]

In this paper, a novel 3D detailed micro-model to analyse the mechanical response of masonry panels under in-plane and out-of-plane loading conditions is proposed. The modelling approach is characterized by textured units, consisting of one brick and few mortar layers, represented by 3D solid finite elements obeying to plastic-damage constitutive laws. Textured units are assembled, accounting for any actual 3D through-thickness arrangement of masonry, by means of zero-thickness rigid-cohesive-frictional interfaces, based on the contact penalty method and governed by a Mohr-Coulomb failure surface with tension cut-off. This novel approach can be fully characterized by the properties obtained on small-scale experimental tests on brick and mortar and on small masonry assemblages. The interface behaviour appears consistent with small-scale tests outcomes on masonry specimens. Experimental-numerical comparisons are provided for the in-plane and out-of-plane behaviour of masonry panels. The accuracy, the potentialities and the efficiency of the modelling approach are shown and discussed. [ABSTRACT FROM AUTHOR]

Abstract: In stochastic finite element problems the solution of a system of coupled linear random algebraic equations is needed. This problem in turn requires the calculation of the inverse of a random matrix. Over the past four decades several approximate analytical methods and simulation methods have been proposed for the solution of this problem in the context of probabilistic structural mechanics. In this paper we present a new solution method for stochastic linear equations. The proposed method is based on Neumann expansion and the recently developed joint diagonalisation solution strategy. Unlike the classical Neumann expansion, here only the inversion of a diagonal matrix is needed. Numerical examples are given to illustrate the use of the expressions derived in the paper. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an exact finite strip method is developed for the free vibration analysis of axially moving viscoelastic plates. Using the differential equation that governs the vibration of plates traveling at a constant axial speed, and utilizing the rheological models to model the viscoelastic behavior of materials, the exact stiffness matrix of a finite strip of plate is extracted in the frequency domain. Terms of this matrix are implicit functions of the eigenvalues of free vibration, in-plane forces, viscoelasticity parameters, axial speed and the geometry of the plate. By assembling the stiffness matrices of these finite strips, the global stiffness matrix of a plate moving on intermediate rollers is obtained, from which the eigenvalues defining the free vibration of the plate are extracted within the domain of complex numbers using a suitable algorithm. These values (that represent the exact frequencies of the plate vibration and damping) can be used as a benchmark to evaluate the accuracy of other numerical techniques. Finally, by presenting a set of numerical examples, the effects of axial speed and viscoelastic parameters on the free vibration of moving plates are examined in this paper. [Copyright &y& Elsevier]

Abstract: This paper presents a straightforward and generally applicable method for detection and elimination of errors in semi-analytical design sensitivities for any kind of FE-formulation. The basic property of the semi-analytical approach is that derivatives of the stiffness matrix and the load vector are approximated by finite differences. Obviously, truncation errors occur by this method which depend on the chosen step size and the kinematic assumptions of the mechanical model. The accuracy problems in the semi-analytical sensitivity analysis result from these approximation errors [Barthelemy B, Haftka RT. Accuracy analysis of the semi-analytical method for shape sensitivity calculation. Mech Struct Mach 1988;18:407–32]. In this contribution two beam elements (Euler–Bernoulli kinematics, Timoshenko kinematics) are utilized to emphasize the consequences of the approximation errors by an analytical computation of the error terms. These two elements show serious differences in the errors of the sensitivities. The ideas gained by these simple 1-d elements are extended further to 3-d elements with Reissner–Mindlin and Kirchhoff kinematics. The errors of the finite difference approximation of the derivatives may become serious, so it is necessary to correct them to obtain exact sensitivities. There exists a great variety of methods in the literature which try to eliminate the errors in the design sensitivities. Important contributions are published by Haftka and Adelmann, Mlejnek, Cheng and Olhoff, V. Keulen and De Boer among many others. In this paper, a method for the computation of correction factors based on product spaces of rigid body rotation vectors is presented. A straightforward derivation yields to a rigid body condition for the stiffness matrix derivative. The approximation of this derivative violates this rigid body condition due to the changed basis of the perturbed element. By the proposed method one obtains a set of correction factors related to the rigid body rotation vectors of the specific finite element. Due to the modification of the approximated stiffness matrix derivative by this set of factors one finally gets ‘exact’ sensitivities. The improved approximation of the stiffness matrix derivative satisfies the above mentioned rigid body condition. The basic advantage of the proposed method is the efficiency and the independence on the Finite Element formulation. In contrast to many other correction methods published so far, this approach is applicable to all kind of Finite Elements without major modifications. This gives rise to general shape optimization algorithms for a huge amount of finite elements without the necessity to derive each single element analytically. [Copyright &y& Elsevier]

Abstract: This paper introduces an algorithm for coupling the boundary element method and the scaled boundary finite element method. Although the particular application concerns the determination of stress intensity factors at crack tips, the approach is general in nature. The motivation for the work is the combination of the semi-analytical solution accuracy of the SBFEM with the geometric flexibility of the BEM for general engineering usage. The paper presents the development of the algorithm along similar lines to FEM/BEM coupling approaches. Example problems verify the accuracy of the approach, even for coarse discretisations, and demonstrate excellent convergence properties of the algorithm. [Copyright &y& Elsevier]

Abstract: This paper describes a response surface based optimisation technique for the calculation of envelope frequency response functions (FRFs) of imprecisely defined structures using the interval and fuzzy finite element method. The authors developed a hybrid – global optimisation and interval arithmetic – procedure for interval and fuzzy envelope FRF calculation. This hybrid approach reduces the computational cost of the analysis compared to a full global optimisation approach and reduces the conservatism on the envelope FRF compared to a full interval arithmetic approach. Still, the optimisation step is the computationally most expensive part of the algorithm. To handle industrially sized applications, a very efficient optimisation procedure is imperative. The response surface based procedure described in this paper decreases the computational cost of a fuzzy envelope FRF calculation with a factor 50 or more compared to the commonly used two-level full factorial design of experiments, while giving a comparable accuracy. [Copyright &y& Elsevier]

Abstract: Uncertainty and variability modelling tools greatly enhance the value of virtual prototypes at the different design stages of a CAE process. The fuzzy analysis technique is suited to deal with models containing subjective non-deterministic parameters. This technique is finding its way to different disciplines of mechanical engineering. The objective of this paper is to increase the value of this technique in early stages of mechanical design procedures. For this purpose, new numerical procedures are proposed. First, the degree of influence is introduced. This new concept measures the relative effect of highly uncertain design properties on the performance of a design. Next, this paper proposes a new reduced optimisation scheme in order to improve the computational efficiency of the interval analysis, which is at the core of the implementation of the fuzzy technique. The practical applicability of the newly developed procedures is demonstrated on two numerical applications from the automotive industry. The analysed models represent the design at the conceptual stage, and contain parameters with a high and subjective level of uncertainty. The parametrised models are used to demonstrate the value and efficiency of the developed numerical procedures: significant parameters are identified using the degree of influence analysis, the optimal configuration is identified through an interval analysis based on the reduced optimisation scheme, and finally the fuzzy technique is applied as design space exploration tool. [Copyright &y& Elsevier]

Abstract: This paper presents a coupled particle and finite element method for fluid–shell structure interaction analysis. The Moving Particle Semi-Implicit (MPS) method is used to analyze fluid flow and the MITC4 shell element is used in the FEM analysis of the structure. This paper considers partitioned coupling between the fluid and structural solvers. In order to satisfy compatibility in the employed partitioned coupling scheme, the Neumann–Dirichlet condition is applied to both the fluid and the structure. A symplectic time integration scheme is used to preserve energy when analyzing the shell structure. If the frequencies of the shell analysis are much higher than those of the MPS fluid solver, its time integration scheme is sub-cycled. When the presented coupling scheme was applied to simulate the sloshing phenomenon in an elastic thin shell structure, fluid fragmentation and large structural deformations were observed. [Copyright &y& Elsevier]

Still today, structural design is often based on simplified hand-calculation formulas for special cases, which is tedious to apply and do not cover more general situations. To improve the situation, the paper presents a FE-program for analysis of strength and deformation of arbitrary beam cross sections of steel and concrete loaded by all six force and moment components. The program is based on (1) an enhanced beam theory with three-dimensional state of stress, (2) multi-surface elasto-plasticity for modeling of the materials and (3) efficient numerical algorithms (mesh adaptive FEM, arc-length method, etc.). The paper presents the theory behind the program and some initial numerical testing to show how the program works. The initial numerical testing on steel and reinforced concrete beam sections loaded in bending, shear and torsion show promising results. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is the development of a refinement procedure able to operate in the context of the constrained natural element method (C-NEM). The C-NEM was proposed by the authors in a former work [Yvonnet J, Ryckelynck D, Lorong P, Chinesta F. A new extension of the natural element method for non-convex and discontinuous domains: the constrained natural element method (C-NEM). Int J Numer Methods Eng 2004;60:1451–1474] and its main meshless features, that allow to describe large domain changes as well as to handle fixed or moving discontinuities, were analyzed in [Yvonnet J, Chinesta F, Lorong P, Rynckelynck D. The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces. Int J Thermal Sci 2005;44:559–569; Yvonnet J, Lorong P, Ryckelynck D, Chinesta F. Simulating dynamic thermo-elastoplasticity in large transformations with adaptive refinement in the natural element method: application to shear banding. Int J Forming Process 2005;8:347–363]. Sometimes, in order to improve the interpolation accuracy for describing boundary layers or an anisotropic behavior, new nodes must be added, removed or repositioned. The interpolation in the vast majority of meshless techniques is free of mesh quality requirement. Thus, introduction, elimination or repositioning of nodes is a trivial task, because no geometrical restrictions exist. In this way, nodes can be added without geometrical checks in the regions where the solution must be improved (identified by using an appropriate error indicator). For this purpose, in this paper an a posteriori error indicator will be proposed and tested in some linear elastostatic problems benchmarks involving different levels of difficulty (stress concentration, solution singularities,…) all of them with a known exact solution. The computational implementation of this error indicator is very simple, and when it is used in tandem with an efficient refinement procedure, which makes use of the meshless features of the C-NEM, provides an accurate adaptation procedure, specially appropriate in the C-NEM framework. [Copyright &y& Elsevier]

Abstract: It has recently been demonstrated that, for pressure die casting, high rates of heat extraction are possible with the use copper–alloyed dies suitably protected with a thermally sprayed steel layer. The structural integrity of dies of this type is paramount as the thermally sprayed layer has the potential to de-bond necessitating repair or retirement of the dies. In this paper, an efficient three-dimensional elastostatic stress model for the pressure die casting process is described. The collocation based boundary element method is used for the prediction of transient stress fields over a thermally stabilised casting cycle. A peculiar feature of the pressure die casting process is that transient thermal penetration into the die is limited to regions close to the surface of the die cavity and nozzle. The presence of a transient thermal field necessitates the evaluation of domain integrals in the boundary element stress formulation. Two methods for evaluating these integrals are presented in the paper: (i) a simplex method on a mesh local to the cavity surface; (ii) a modified reciprocity method utilising Gaussian radial-basis functions, interpolating on a perturbed thermal field. The simplex method is shown to be superior, providing high accuracy, stability and computational efficiency. The dies present a multi-domain environment for stress predictions making it necessary to utilise a suitably constructed coarse preconditioner to enhance numerical stability and provide for efficient computation. A multiplicative Schwarz method is presented that enables parameter matrix accelerated GMRES to be applied on each domain. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted strain fields are compared with strain gauge measurements obtained on a purpose built rig designed to be representative of the casting process. [Copyright &y& Elsevier]

Abstract: This paper describes impact analyses of armor composites using concurrent coupling of scales through asymptotic expansion homogenization (AEH) in elasto-plastic and transient settings. The AEH method is applied with an explicit time integration algorithm for the transients and an updated Lagrangian scheme for the large displacements. The primary aim of this paper is to present numerical validations against the experiments of S. Zhuang, G. Ravichandran and D.E. Grady [An experimental investigation of shock wave propagation in periodically layered composites. J Mech Phys Solids 2003;51:245–65] and S. Zhang [Shock wave propagation in periodically layered composites, PhD thesis, California Institute of Technology, Pasadena, CA, 2002] to demonstrate the validity of the computational method for layered armor composites. A parallel computer program was developed to handle the parallel computations across multiple scales and then integrated with a widely available explicit dynamics finite element program. A brief scalability study demonstrates the computational viability of the method. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a two-dimensional infinite element method (IEM) for modeling elastostatic problems with imbedded geometric singularities (e.g. re-entrant corners and cracks) in an unbounded domain. In this method, the primary problem domain is subdivided into several sub-domains which are modeled using a large number of layer-wise elements. The method is formulated based on the conventional finite element method (FEM) and uses the similarity partition concept and certain matrix condensation operations. All degrees of freedom related to the sub-domain are condensed and transformed to form an infinite element (IE) with the master nodes on the boundary only. Each IE is regarded as a regular finite element, and the IE stiffness matrix is assembled into the system stiffness matrix. The corresponding time in the modeling stage, the number of degrees of freedom, and the required PC memory storage are significantly reduced for these computations. Numerical examples are presented in this paper to show the performance of the proposed method, compared with the corresponding analytical or FEM numerical solutions. [Copyright &y& Elsevier]

Abstract: In the present paper uncertainty-based design optimization of structures is carried out. A description of uncertainties via bounds on the uncertainty variables is adopted. An anti-optimization technique, which searches for the combinations of uncertainties yielding the worst responses, is used to tackle these Bounded-But-Unknown uncertainties of non-convex or discontinuous nature. This anti-optimization technique is computationally very expensive and can become impractical for real world applications, in particularly when expensive numerical response evaluations are involved. In order to reduce the number of expensive numerical response evaluations, a modified anti-optimization technique is proposed in the present paper. This enhanced anti-optimization technique incorporates design sensitivities and database technique and is further modified to use parallel computing in order to increase the computational efficiency. The enhanced anti-optimization technique is studied on the basis of test examples from literature and a Microelectromechanical Systems (MEMS) structure. A comparison between results for the examples, clearly shows an improvement in computational efficiency for the anti-optimization technique, due to the use of sensitivities, database and parallel computing. The enhanced anti-optimization technique can be applied efficiently to general problems involving uncertainties of non-convex or discontinuous nature. [Copyright &y& Elsevier]

Abstract: In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goal-oriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used. [Copyright &y& Elsevier]

Abstract: In the paper, research results on a special joint of a new type of steel cooling tower are presented. The structural members are tubular elements with high radius-to-thickness ratios. The 3D jointing and the bolted connections result in extremely complex joints that should be studied by experiments and advanced analysis. This paper focuses on the numerical modelling of two joint prototypes. The models are verified by test results. Virtual experiments are completed to study the elastic load-transfer as well as the ultimate behaviour. On these bases, the failure modes are determined and characterized, and the design procedure is improved. [Copyright &y& Elsevier]

Abstract: This paper deals with the finite element modelling and analysis of end-plate joints in steel frames, under monotonic and cyclic loading conditions. In the first part of the paper the main characteristics of possible computational models are summarised and discussed, including remarks on finitisation possibilities, the applicable material models, non-linear solution algorithms, necessary verification procedure. The second part of the paper presents a set of numerical examples, demonstrating the process of systematic model verification on a shell finite element model for the cyclic analysis of bolted end-plate joints. [Copyright &y& Elsevier]

Abstract: The study of the effect of bonding between concrete and composite plates, when epoxy adhesive is used, is the objective of this paper. The results of an analytical and experimental study on the behavior of concrete blocks joined with carbon–fiber-reinforced polymer (CFRP) plates are discussed in this paper. For it, several specimens were tested through adherence tests. Numerical analyses included nonlinear finite element modeling incorporating a damage material model for concrete. In general, good correlations were obtained between the experimental and the numerical results. [Copyright &y& Elsevier]

It is somewhat impossible to define a general methodology for optimizing all structural problems. In this paper, we merely want to present an approach that integrates the available analysis software with complex optimization problems. The proposed methodology follows two main steps. First, the problem definition must be established, expressing explicit relationships between design variables and objective functions plus constraints. In order to do this with whichever problem may arise, we use interpolation schemes on a collection of different designs. The second step, is the minimization of the problem using any relevant technique, which could be applied. Both steps can be repeated in an iterative process, to find a minimum. Initially, the paper describes the main drawbacks of constrained optimization, later, a general methodology is proposed, so as to overcome these problems and finally a couple of assessment examples are presented. [Copyright &y& Elsevier]

The possibility of having, in parts 1-1 and 1-2 of Eurocode 3, the same approach for the design of beam-columns and for lateral–torsional buckling, was investigated by the authors in previous papers using a numerical approach, where it was concluded that those assumptions could be made.In the present paper, a new approach for lateral–torsional buckling has been used with the formulae for the design of beam-columns at elevated temperature based on prEN 1993-1-1 combined with the formulae from prEN 1993-1-2. In both cases the results obtained are much better than the current design expressions, when compared with those obtained in the numerical calculations. [Copyright &y& Elsevier]

A modern conceptual design of a bridge structure should be open to wide criteria to endow the structure with static, dynamic and ductile characteristics sufficient to tackle the seismic events. The fulfillment of these requirements, as well as the exploration and the verification of innovative structural schemes, can be achieved only by using refined analysis formulations and effective numerical tools.The structural scheme considered in this paper is based on two-blade slender bridge piers. This kind of pier is a structural element subdivided into two parts, each with different geometric and mechanical properties. The first part has a box section and it is very stiff while the second part is made of two flexible blades connected at the top. This scheme has two purposes: the transmission of vertical loads to the foundation structures and the possibility to allow horizontal displacements (due to thermal effects, concrete shrinkage, etc.) without the use of cinematic mechanisms.In order to evaluate the structural performance of such a bridge pier, with regards to its stiffness, strength and ductility, a nonlinear analysis is clearly required.A proper evaluation of such performance is essential in order to achieve an optimized structure, with respect to the vertical and the horizontal loads.In the present study, the structural performances of the pier are evaluated using a solid finite element formulation. In this kind of analysis one cannot forget that the real world is affected by uncertainty, and one has to keep it into account. In general, there are several ways to reach this goal, for example one can use a probabilistic approach or a fuzzy approach. In this paper the uncertainty, involved in the reliability assessment, is modeled using a fuzzy criterion. [Copyright &y& Elsevier]

This paper presents results of numerical simulations for impact effects in panel-like structures using solid and shell element modeling techniques. Three examples from experiments in literature have been numerically analyzed. The nonlinear transient dynamic analysis code, LS-DYNA is used in the simulations to model projectiles and panel-like targets. It is found that models established for panel-like targets using solid shell elements cannot only save significant computational effort, but also produce good results as long as the panel-like targets satisfy certain conditions. A criterion that governs the validity of modeling panel-like targets with shell elements is proposed in the paper. [Copyright &y& Elsevier]

• Multi-objective optimization approach to maximize the structural performance. • A surrogate model was used for reducing manufacturing costs. • SunFlower optimization was used to find the optimal configuration of the structure. • The compression, torsion and modal performance were evaluated. • The obtained results can be very useful in the design of this kind of structures. In this paper, the authors carried out the optimization of an isogrid structure considering six different responses: Tsai-Wu failure index under compression and torsion efforts; instability coefficient under compression and torsion efforts; mass and natural frequency. The response surface methodology was used to find the functions that describe the model from the data found by numerical analysis; and a new optimization algorithm called SunFlower Optimization (SFO) was used to find the best possible configurations. This paper shows something unprecedented in the literature to date when evaluating the compression, torsion, and modal performance of an isogrid tube. The simultaneous evaluation of several responses brings something more real to the scientific world, the results obtained here suggest that the optimal configuration for one response can be very bad for others and the use of a multi-objective optimization solved this problem. [ABSTRACT FROM AUTHOR]

The objective in this paper is to present some new insights into an implicit direct time integration scheme, the Bathe method, for the solution of the finite element equations of structural dynamics. The insights pertain to the use of the parameters in the method, and in particular the value of the time step splitting ratio. We show that with appropriate values of this ratio large amplitude decays can be obtained as may be desirable in some solutions. We give the theoretical analysis of the method for the parameters used, including for very large time steps, and illustrate numerically the new insights gained. [ABSTRACT FROM AUTHOR]

Conventionally, the seismic response of primary structures such as buildings and secondary systems such as piping is evaluated through uncoupled analyses. Many studies have illustrated that the two systems interact in many different ways (mass interaction, non-classical damping, phasing, etc.). An analysis of the coupled system is not only rational but also eliminates the excessive conservatism that exists in an uncoupled analysis. Consequently, fragility assessments based on uncoupled analysis are also incorrect and a coupled analysis must be conducted in such evaluations. However, nonlinear analyses of such complex systems particularly in the context of fragility assessment, which requires a large number of nonlinear analyses, becomes computationally prohibitive. Tadinada and Gupta (2017) presented an equivalent elastic limit state concept with an intent to reduce the computational effort needed in these assessments and yet evaluate the seismic fragility with sufficient accuracy. This paper outlines some of the limitations that have been experienced in the use of originally proposed equivalent limit-state formulation and presents valuable enhancements. The novel contribution of this study is focused on accounting for the effect of uncertainty in nonlinear characteristics and the effect of non-classical damping. Unlike the originally proposed formulation, the proposed formulation also considers the asymmetric variation of the equivalent limit state with respect to tuning ratio. Furthermore, a Bayesian approach is incorporated into the proposed methodology for increasing the accuracy of seismic fragilities in the case of tuned or nearly tuned primary-secondary systems. Numerical examples are used to illustrate that the modified form improves the accuracy for both the tuned and the detuned systems. In summary, the proposed approach provides an efficient framework of seismic fragility assessment and risk evaluation for coupled systems. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology for the identification and quantification of spatial uncertainty, modelled as an interval field. In order to make a realistic assessment of the spatial uncertainty on the model parameters, the dimensionality of the interval field as well as its constituting base functions and interval scalars have to be identified. For this purpose, this work introduces an identification method based on objective measurement data. The specific challenge in this context lies in the fact that a continuous spatial input parameter has to be identified on a high-resolution discretised model of the structure under consideration, based on possibly high-dimensional measurement data set, obtained in the result domain of the analysed model. In the presented method, the field dimensionality is quantified based on the concept of effective dimension of the measurement data. The base functions of the interval field are identified by minimising the difference between the gradients of the halfspaces respectively bounding the measurement data and the realisations of the interval field. The method is illustrated using two case studies: an dynamic model of a cantilever beam and a quasi-static model of a cast pressure vessel. It is shown that the presented methods are capable of accurately identifying the interval field uncertainty that is present on the model parameters, and that this identification is robust against the size of the measurement data set. [ABSTRACT FROM AUTHOR]

In this paper, a method to compute explicit solutions for laminated plate with arbitrary hole position is presented using a variable separation method. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x , y , the transverse coordinate z and the coordinates X T , Y T of the hole position. As the parameterized problem involves the geometry, a mapping transformation is introduced to refer to a fixed reference configuration. This choice yields to an iterative process that consists of solving a 2D and three 1D problems successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element Method is used. The functions of X T and Y T are discretized with linear interpolations. Mechanical tests with different numbers of layers are performed to show the accuracy of the method and its capacity to capture local effects and 3D state of the stress near the curved free-edge. [ABSTRACT FROM AUTHOR]

Sudden changes in the structural and geotechnical properties of railway tracks along its course are normally associated with subgrade stiffness transitions, differential settlements and, ultimately, hanging sleepers that reduce the performance of the railway system. This paper aims at analysing and quantifying the impact of such situations, particularly cut-fill transitions combined with the presence of culverts, on the train-track system response. A cut-fill transition on a buried culvert is used as case study for which track geometry and stiffness evaluation data were available. A numerical model, considering the coupled train-track interaction, was developed using a 3D FEM dynamic analysis tool that was further improved here with a mixed implicit-explicit time integration scheme. The results suggest that the faster degradation rates typically found at similar locations are mostly related to the development of early permanent deformations in the subgrade layers, rather than to sudden stiffness transitions, which then aggravate the problem by causing important dynamic amplifications in the train-track interaction. Therefore, numerical approaches similar to the one presented herein can be valuable tools for designers and railway infrastructure managers in order to anticipate and mitigate such negative effects at these locations. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method to control the spurious deformation mode conventionally found in a non-ordinary state-based peridynamic formulation. The proposed approach introduces a higher-order approximation for a deformation gradient tensor in order to suppress oscillations from the zero-energy mode. The results are compared to those determined by other available methods. The findings of this study well demonstrate that the proposed method provides highly effective solutions for controlling zero-energy modes in peridynamic models. Contrasting other available zero-energy control methods, the proposed method remains robust for relatively large horizon sizes. The method is incorporated by implicit weight functions in peridynamics. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis based on the finite element method to simulate blast-induced hard rock fracture propagation. Three different approaches are compared: the extended finite element method, with a cohesive zone model to represent the growth of fractures; the conventional finite element method using a remeshing technique and based on the linear fracture mechanics; the element deletion method to simulate a rock fragmentation process. The rock mass is a sound granite that remains linear elastic right up the breakage. Two numerical examples are presented in order to discuss the advantages and limitations of each approach. [ABSTRACT FROM AUTHOR]

This paper presents a coupled Bonded Particle and Lattice Boltzmann Method (BPLBM) for modelling fluid–solid interactions in engineering, e.g. geomechanics. In this novel technique, the Bonded Particle model is employed to describe the inter-particle interactions, and the bonds between contacted particles are assumed to be broken when the tensional force and/or tangential force reach a certain critical value; while the Lattice Boltzmann method is used to model the fluid phase, and the Immersed Moving Boundary (IMB) scheme is utilised to resolve the fluid–solid interactions. Based on this novel technique, the investigation of hydraulic fracturing is carried out. The onset and propagation of hydraulic fracture are successfully captured and reproduced. Numerical results show that the coupled BPLBM is promising and efficient in handling complicated fluid–solid interactions at the grain level in hydraulic fracturing. [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]

• A truly self-starting new representation of the ρ ∞ -Bathe method is redesigned. • A new composite time integration framework is designed for first-order systems. • A novel composite [ i -Integration] design applied to first/second-order systems. • In-depth comparisons between the composite method and the well-known GS4 framework. Due to the lack of and limited work done for first/second-order systems useful for multidisciplinary problems, this paper proposes a new and novel composite isochronous integration ([ i -Integration]) analysis framework to solve first/second-order transient systems via a single computational framework. The main contributions are summarized as follows: (1) The ρ ∞ -Bathe method is newly reformed to an identical truly self-starting representation with the absence of acceleration and is more efficient for practical applications; (2) The novel [ i -Integration] process is applied to automatically generate a family of time integration algorithms for first/second-order transient systems, whilst preserving features of second-order time accuracy, unconditional stability, controllable numerical dissipation in high-frequency, and truly self-starting; (3) The newly proposed algorithms design framework provides a unified toolkit to solve first/second-order transient systems in a single analysis and hence is more effective for coupled problems and numerical analysis of fluid/heat transfer/structure-type transient simulations. Numerical examples encompassing a manufactured example, the C-F heat conduction model, and the thermal stress wave problem are demonstrated to validate the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper presents an efficient computational method for predicting the onset of buckling of axially loaded, corrugated or stiffened cylindrical shells. This method is a modification of the Bloch wave method which builds on the stiffness matrix method. A numerical method and an efficient algorithm have been developed to implement the proposed method in the commercial finite element package Abaqus. Numerical examples have shown that, compared to the nonlinear buckling analyses based on detailed full finite element models, the proposed method can obtain highly accurate buckling loads and buckling modes and can achieve very significant reductions in computational time. [ABSTRACT FROM AUTHOR]

Formulations of a four-node quadrilateral element fitted to numerical manifold method (NMM) with continuous nodal stress called Quad4-CNS (NMM) element for two-dimensional (2D) crack analysis are presented. This Quad4-CNS (NMM) element can be considered as a development of the recently published four-node quadrilateral element with continuous nodal stress (Quad4-CNS). In contrast to the four-node iso-parametric quadrilateral element (Quad4), the Quad4-CNS element has higher order of global approximations, much better accuracy and continuous nodal stress. Moreover, it is free from the “linear dependence” which otherwise cripples many of the partition of unity (PU) based methods with high order global approximations. Due to the adoption of two cover systems, namely, the mathematical cover and physical cover, the NMM is capable of solving continuous and discontinuous problems in a unified way. The purpose of this paper is to synergize the advantages of both the Quad4-CNS element and the NMM to precisely model linear elastic fracture problems. A number of numerical examples indicate the accuracy and robustness of the present Quad4-CNS (NMM) element. [ABSTRACT FROM AUTHOR]

In this paper, a 4-node quadrilateral quasi-conforming element for couple stress theory is proposed. The formulation starts from truncated Taylor expansion of stresses, then the stress-function matrix is treated as weighted function to weaken the strain-displacement equations. Finally the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy of the element. Numerical results show that the proposed new model can pass the C 0 - 1 patch test and possesses excellent precision even when the element shape degenerates into triangle or concave quadrangle, which can capture the scale effects of microstructure. [ABSTRACT FROM AUTHOR]

This paper deals with a new explicit framework for numerical dynamic analysis that could be applied to any explicit-implicit time integration, i.e. predictor-corrector time integrations. For this purpose, Dynamic Relaxation method is combined with the explicit-implicit time integrations so that the proposed algorithm is performed by full vector operations. This subject helps to obtain an explicit algorithm, which does not involve solving simultaneous system of equations in each time increment, even linear one. Moreover, the number of corrections, which is the main concern in the explicit-implicit algorithms, is selected automatically in the suggested procedure. Afterwards, some numerical examples are solved to illustrate the validity and the robustness of the proposed algorithm. Results show that applying the proposed framework to the higher order explicit-implicit integrations exhibits excellent accuracy in comparison with the well-known implicit Newmark- β and Wilson- θ schemes. Simplicity, more stable integration, automated procedure and vector operations are some of the salient features of the proposed algorithm. [ABSTRACT FROM AUTHOR]