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Abstract This work deals with the structural behaviour, ultimate strength and design of fixed-ended cold-formed steel (CFS) lipped channel columns experiencing various levels of local-distortional-global buckling mode interaction (more or less close critical local, distortional and global loads). First, a comparison between experimental results, obtained from three tests carried out at The University of Hong Kong (UHK), and the corresponding A baqus shell numerical simulations are presented and discussed – the UHK test campaign is reported in Part I of this two-part paper. The comparison (i) involves equilibrium paths, deformed configurations, failure loads and collapse mechanisms, and (ii) provides enough evidence to ensure that the numerical model developed may be deemed validated. Then, this numerical model is employed to perform a parametric study, aimed at obtaining numerical failure load data concerning lipped channel columns experiencing different levels of local-distortional-global interaction – 368 fixed-ended columns, exhibiting different geometries (cross-section dimensions and lengths) and various yield stresses, thus covering a wide slenderness range. Finally, the present (Part II) paper also assesses the quality of the failure load estimates provided by various design approaches, based on the Direct Strength Method (DSM), for CFS columns affected by the triple coupling phenomenon under consideration. This assessment is based on the comparison with both (i) experimental failure loads, namely those reported in Part I and others collected from the literature, and (ii) numerical failure loads, obtained from A baqus shell finite element analyses (SFEA) and either reported in this work or gathered from previous publications by the authors. [ABSTRACT FROM AUTHOR]

In this paper, a numerical formulation for the analysis of viscoelastic functionally graded materials under finite strains is presented. The general constitutive modeling is described within the context of Lagrangian and isotropic visco-hyperelasticity. The specific models selected are the compressible neo-Hookean hyperelastic law, the Zener rheological model and the isochoric evolution law described in terms of the rate of the viscous right Cauchy-Green stretch tensor. The material coefficients may vary smooth and continuously along one direction according to the power law. The viscous update is performed via the exponential rule. The main novelty of this paper is the use of gradually variable viscoelastic coefficients in the finite strain regime. Four numerical examples involving functionally graded materials and finite viscoelastic strains are originally analyzed to assess the formulation proposed: a bar under uniaxial extension, a block under simple shear, the Cook’s membrane and an elastomeric bridge bearing. Isoparametric solid tetrahedral finite elements of linear, quadratic and cubic orders are employed. The influence of the material viscoelastic parameters on the mechanical behavior is analyzed in detail. Results confirm that mesh refinement provides more accuracy and the present model can reproduce large levels of viscoelastic strains in functionally graded materials. [ABSTRACT FROM AUTHOR]

• Axial-only deformable 4-node element for heterogeneous limit analysis modeling. • Suitable modeling of ring flexibility in masonry arch bridges is very necessary. • New element can produce an accurate load prediction compared with the on-site test. • Better ring flexibility will significantly reduce the power dissipation in backfill. • Different constitutive linearizations will highly affect the element deformability. This paper proposes a novel limit analysis block element to model the ring behavior in masonry arch bridges, with consideration of axial deformation induced by both bending and axial compressing motions. The governing formulation is established based on the kinematic theorem. After constructing the velocity field of the block element, the new compatibility condition is put forward, followed by a discussion of possible linearization for the element constitutive model. A new heterogeneous limit analysis formulation that accounts for the deformability of the elements is given at the end. For benchmarking purposes, the collapse of an 80-block arch is first investigated to understand the influence of using different constitutive linearizations. Then, the proposed element is applied to analyze the collapse of a practical bridge involving arch-fill interactions. The results indicate a great necessity of considering the deformability of the ring when analyzing the collapse of masonry arch bridges. Compared with previous experimental results of Prestwood Bridge, employing the rigid modeling for the ring will lead to a significantly overestimated load prediction (about 46.3%) while the proposed deformable brick element with quadrilateral-linearized constitutive can produce a very accurate prediction (bias within 1%). Adoption of the hexagon linearization will give rise to a comparatively inflexible block behavior and the corresponding ring performs analogous to the rigid case. Finally, the model proposed gets over the main shortcoming exhibited by a beam discretization of the ring, namely the potential over-flexibility of the bridge arch, induced by the simplification of the actual geometry. [ABSTRACT FROM AUTHOR]

• A new method is proposed for solving equilibrium equations of geometrically nonlinear structures. • A likelihood function is introduced based on the nonlinear equilibrium equations. • This likelihood function reaches its maximum value at the solutions of equilibrium equations. • Nested sampling algorithm is exploited to maximize the likelihood function and thus to find the solution(s). • The proposed method finds distinct deformation states of a structure undergoing large deformations. Geometrically nonlinear structures are extensively used as load-carrying systems or energy harvesting devices. The main characteristics of their behaviour include complex and/or multi-equilibrium paths. In this paper, a new method is proposed for analysing these structures wherein distinct deformation states of a structure under applied loads (forces or displacements) are directly obtained. Using the concepts of finite element approximations, the proposed method first establishes the nonlinear equilibrium equations for a structure undergoing large deformations. Then, contrary to the well-established incremental-iterative path-following methods that appeal to linearization concepts and use an arc-length constraint to solve the nonlinear equilibrium equations, the proposed method tries to directly find the solutions to these equations. To this end, a likelihood function is introduced based on the nonlinear equilibrium equations. This function is defined such that it reaches its maximum value at the solution(s) of the equilibrium equations. To maximize this likelihood function, the nested sampling algorithm is exploited. This algorithm explores the solution phase space thoroughly and finds the deformation state(s) that satisfy the nonlinear equilibrium equations. An application of the proposed method to analysing geometrically nonlinear truss structures is given and three truss structures are solved to demonstrate the capabilities of this method. [ABSTRACT FROM AUTHOR]

This paper investigates the structural response of RC framed buildings subjected to accidental/abnormal loads (explosion, impact and other hazards). Several existing national or international design codes (GSA 2003, DoD 2009, 2013) provide limited guidelines for the assessment of progressive collapse resistance in the design process and the alternate load path method is widely used in current structural design codes. Since the progressive collapse is a dynamic and nonlinear event the structural components undergo nonlinear deformations before failure. In this study the nonlinear procedures (NSA and NDA) are applied. These types of analyses imply significant computational power and time costs. In addition, the reinforced concrete framed structures are able to develop multiple post flexural resisting mechanisms. These are currently not considered in the structural analyses performed according to GSA2003 and DoD2009 provisions. Thus, the first objective of this paper is to identify by numerical computation the presence and contributions of such supplementary resisting mechanisms. A further objective is to determine what will be the influence on the accuracy of results when, starting from the original structure, the number of its bays is successively reduced; also, what is the efficiency in saving run-time costs when such simplified models are considered in the analysis. The study reveals that in order to resist abnormal loads, RC structures are able to develop supplementary resisting mechanisms beyond the flexural behavior and respectively, important time savings are obtained without significantly affecting the results accuracy. [ABSTRACT FROM AUTHOR]

Hyperelastic materials are extensively employed in a wide range of applications. Although there are well-established models for describing the mechanical behavior of the hyperelastic materials, relatively few papers have attempted to rank different models. This paper aims to identify parameters of some constitutive models for pure and simple shear of an incompressible isotropic hyperelastic material under large deformations, and also aims to propose a strategy to rank different models. The constitutive models considered in the present analysis are the following: Mooney–Rivlin, Yeoh, Ogden (1 and 2 terms), Lopez-Pamies (1 and 2 terms), and Gent. In the first part of the paper, the Bayesian framework is applied for the identification of the parameters of the models, where experimental data are used to update the prior probabilistic model of the unknown parameters. The Maximum a Posteriori Estimate is obtained, and the error between the model prediction and the experimental data is computed to rank the models. In the second part of the paper, the Bayesian framework is again employed, but now as an strategy for model selection. Instead of ranking the models using the error between the model prediction and the experimental result, more ingredients, such as the Ockham factor, are taken into account for the model selection. The results indicate that all models and experimental results for pure shear are in good agreement, but Mooney–Rivlin, Gent and Yeoh models were not able to well describe the available experimental data from simple shear. The best model for pure shear is Mooney–Rivlin and the best model for simple shear is Ogden (2 terms), considering the available experimental data and the criteria proposed in the present paper. [ABSTRACT FROM AUTHOR]

In this paper, a solid finite element formulation applied to the analysis of functionally graded materials (FGMs) under finite elastoplastic deformation with mixed hardening is presented. The main novelty of this paper is the use of gradually variable material coefficients in finite elastoplastic strain regime. The numerical simulations are performed with the same constitutive models but with different variations of the material coefficients. Full integration and high order tetrahedral elements are used. Results show that high order elements and mesh refinement avoids general locking problems. Finally, the differences (regarding final results) between the homogeneous and the FG cases are depicted. [ABSTRACT FROM AUTHOR]

A typical manufacturing failure in powder bed additive manufacturing (AM) is caused by the collision between the already printed structure and the powder recoater due to large thermal deformation. This paper presents a density-based topology optimization (TO) approach to concurrently design parts and their supports that are not susceptible to such a manufacturing failure. The thermal deformation during the layer-by-layer AM process is predicted based on an inherent strain method, and the top surfaces' upward deformations are constrained below the powder layer thickness to avoid recoater collision. To increase the design freedom of TO, the parts and their supports are composed of lattice unit cells with different volume fractions, whose effective stiffness matrixes are predicted by the numerical homogenization and surrogate models. Besides, an overhang constraint and a two-field-based length scale control formulation are also utilized, ensuring overall manufacturability. With the proposed approach, lightweight structures with optimized mechanical properties and controllable manufacturing qualities can be obtained. Numerical examples are given to demonstrate the effectiveness of the proposed approach. • Concurrent topology optimization approach to design the parts and their supports. • Additive manufacturing process simulation model based on inherent strain method. • New thermal deformation constraint to avoid recoater collision. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of ∣φ(x, y, t)∣⩽ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier–Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. [Copyright &y& Elsevier]

Abstract: We present in this paper MITC shell elements for large strain solutions of shell structures. While we focus on the 4-node element, the same formulation is also applicable to the 3-node element. Since the elements are formulated using three-dimensional continuum theory with the full three-dimensional constitutive behavior, they are referred to as 3D-shell elements. Specific contributions in this paper are that the elements are formulated using two control vectors at each node to describe the large deformations, MITC tying and volume preserving conditions acting directly on the material fiber vectors to avoid shear locking, and a pressure interpolation to circumvent volumetric locking. Also, we present solutions to some large strain shell problems that represent valuable benchmark tests for any large strain shell analysis capability. [Copyright &y& Elsevier]

Abstract: In this paper, a new geometrically exact beam formulation is presented, aiming at calculating buckling (bifurcation) loads of Euler–Bernoulli/Vlasov thin-walled beams with deformable cross-section. The resulting finite element is particularly efficient for problems involving coupling between lateral-torsional buckling and cross-section distortion/local-plate buckling. The kinematic description of the beam is geometrically exact and employs rotation tensors associated with both cross-section rotation and the relative rotations of the cross-section walls in the cross-section plane. Moreover, arbitrary deformation modes, complying with Kirchhoff’s assumption, are also included, which makes it possible to capture local/distortional/global buckling phenomena. Load height effects associated with cross-section rotation/deformation are also included. The examples presented throughout the paper show that the proposed beam finite element leads to accurate solutions with a relatively small number of degrees-of-freedom (deformation modes and finite elements). [Copyright &y& Elsevier]

• Presents a new arc-length solution method for structural mechanics problems. • Allows equilibrium paths to be tracked in problems involving snap-back and snap-through. • Method has much wider application to other physical problems involving instability. Tracing load-displacement paths in structural mechanics problems is complicated in the presence of critical points of instability where conventional load- or displacement control fails. To deal with this, arc-length methods have been developed since the 1970s, where control is taken over increments of load at these critical points, to allow full transit of the load-displacement path. However, despite their wide use and incorporation into commercial finite element software, conventional arc-length methods still struggle to cope with non-zero displacement constraints. In this paper we present a new displacement-controlled arc-length method that overcomes these shortcomings through a novel scheme of constraints on displacements and reaction forces. The new method is presented in a variety of serving suggestions, and is validated here on six very challenging problems involving truss and continuum finite elements. Despite this paper's focus on structural mechanics, the new procedure can be applied to any problems that involve nonhomogeneous Dirichlet constraints and challenging equilibrium paths. [ABSTRACT FROM AUTHOR]

Abstract: This paper brings together the principles, equations, and applications of damage modelling and elastic waves propagation, both traditional and state-of-the-art in a review form. It begins with the relevant fundamentals of damage modelling, derives the basic equations of fracture mechanics and elastic wave propagations, and covers advanced topics and applications of Lamb waves that are at the forefront of today’s research. The results obtained indicate that the current approach is capable of detecting cracks and delaminations of very small size, even in the presence of considerable measurement errors. The sections are filled with case studies, worked examples and exercises that make this paper an outstanding resource. [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]

Abstract: In this paper we introduce an enhanced implicit algorithm for phenomenological plasticity based on nested surfaces for the description of multiaxial nonlinear hardening. The algorithm uses an implicit version of the Mróz translation rule. This rule is computed explicitly from the trial state and, as a result, the final stress state is obtained solving a nonlinear scalar equation. With the algorithm and the formulation introduced in this paper, there is no need for performing iterations in order to obtain the final active surface. This surface is determined in advance directly from the trial stress state and therefore the efficiency of the algorithm is greatly improved, specially when the number of surfaces describing the stress–strain curve is moderate to large. The algorithm has been implemented in the commercial code ADINA as a user subroutine. [Copyright &y& Elsevier]

A topology optimization technique for systematically designing contact-aided compliant mechanisms (CCM) is presented in this paper. A CCM is a single piece elastic body that uses intermittent contacts in addition to elastic deformation to transmit force and motion. Contact interactions give rise to interesting nonlinear and nonsmooth behaviors even under the small deflection assumption made in this work. The difficulties associated with the nondifferentiability inherent in the CCM systematic synthesis problem are circumvented by using a regularized contact model. This model uses a smooth approximation of the unilateral displacement constraints that are used to model contact interactions. The use of a regularized contact model in the underlying state problem makes it possible to use efficient smooth optimization algorithms for the systematic synthesis of CCMs. The formulation of the design problem for CCMs, sensitivity analysis, and solution methodology are presented. The paper includes CCM designs that exhibit nonsmooth motion and force transmission characteristics, which are not possible or practical with compliant mechanisms that do not use intermittent contact interactions. [Copyright &y& Elsevier]

This paper presents the initial-value solutions of static equilibrium differential equations of single-cell thin-walled composite-laminated box beams under bending loads with consideration of both shear lag and shear deformation. The initial-value solutions is used to establish the related element stiffness matrix and equivalent nodal forces vector, so that the analysis of shear lag and shear deformation effects in composite-laminated box girders is admitted into the program system of the finite beam element method. The procedure of this paper can be used to analyze effectively the mechanical behaviors of some complex composite structures (such as continuous laminated box girders, etc.). [Copyright &y& Elsevier]

In this paper, delamination progression in a composite laminate is modelled by interface elements within a geometrically non-linear FE analysis setting. With the assumption of small continuum deformations, a rotational interface formulation is obtained from a recently proposed formulation based on the concept of a regularised strong discontinuity, cf. [Int. J. Numer. Meth. Eng. 54 (2002) 473]. The degradation of the stress vector in the cohesive zone is described by a damage-plasticity coupling, which is calibrated analytically against experimental data of mixed-mode fracture energies. The paper is concluded by a couple of numerical examples that describe the predictive capabilities of the interface formulation. [Copyright &y& Elsevier]

This paper proposes a mesoscale approach for simulating moisture transport by capillary action in partly-saturated porous cementitious composites. The modeling approach explicitly accounts for moisture transport through a mesostructure composed of coarse aggregates, surrounding cementitious mortar and interfaces. These latter, namely interface transition zones (ITZs), allow to describe the interaction between aggregates and mortar, and may cause an alternative path for the internal moisture movements. Basic morphology effects of the ITZs are simulated using a ribbon approach. Random spatial distribution of cement particles are stacked in the meso-geometry. Aggregate particles are introduced as randomly perturbed polygons and the moisture transport is modeled as a diffusion problem and solved by means of the finite element method. The proposed constitutive models are based on a proper description of the permeability and pore size distribution which strongly affect the local moisture content. Numerical results at both macro- and mesoscale levels demonstrate the soundness and capability of the proposed approach. The integrated modeling results actually demonstrate the potential of the mesoscale approach and shows the role of the ITZs as an internal interconnected network. [ABSTRACT FROM AUTHOR]

This paper is devoted to shape optimization of constrained contact force problem. A linear relaxation model of contact force-clearance relation is developed. It is shown that such relaxation is essential to avoid zero sensitivity values of zero contact force with respect to design variables and to drive the satisfaction of contact force constraint at the specific contact region. In this work, both frictionless and frictional contact optimization problems are investigated by means of a gradient-based optimization algorithm. The optimization procedure including sensitivity analysis with relaxation model is implemented outside the structural contact analysis software to deal with non-smooth contact problems. The procedure is firstly validated by simple examples with analytical solutions and is finally applied to the design of an assembled aero-engine structure for leakproofness. [ABSTRACT FROM AUTHOR]

The performance of timber structures is governed by the nonlinear response at their connections, where high deformation levels and stress concentrations are developed, particularly when subjected to load reversals. To date, no constitutive model for wood under cyclic load exists which is able to incorporate its most important failure modes while considering plastic deformations and cyclic stiffness and strength degradation simultaneously. This paper presents the formulation and implementation of a plasticity-damage model with these characteristics within a continuum mechanics approach. The theoretical framework of both plasticity and damage models is described, and a detailed derivation of the constitutive equations required for their computational implementation and coupling as well as the return mapping and iterative algorithms for their integration are presented. The damage evolution process is handled by two independent scalar variables for tension and compression. A general orthotropic plasticity yield surface with isotropic hardening is employed to incorporate timber plastic flow in compression. A closed-form expression for the plasticity-damage consistent tangent operator is derived. It is demonstrated that the proposed constitutive model captures all the key characteristics required for an accurate modelling of timber under large deformation levels until failure. [ABSTRACT FROM AUTHOR]

This paper describes the development of a computational model for the hot rolling of steel in a continuous rolling mill. The solution procedure consists of slices aligned in the rolling direction. The deformation and heat flow are assumed to be only in the direction perpendicular to the rolling and the assumed behavior of the material is ideal plastic. The strongly coupled thermal and mechanical models are solved by a novel meshless, local radial basis function collocation method, based on subdomains with 5 nodes for the thermal, and 7 nodes for the mechanical model. Multiquadrics radial basis functions with first-order monomials are used for the shape functions. The rearrangement of the collocation nodes in this large deformation problem is based on elliptical node generation. The non-linear relations are coped with a direct iteration, where the material properties are linearized during each of the iterations. Verification is based on comparison with an analytical solution and results from the finite-element method. A complete rolling simulation with 5 rolling stands is presented. The results encompass the roll speed, the separating force and the torque. The displacement and temperature fields of the rolling from the square to the round profile are displayed. [ABSTRACT FROM AUTHOR]

Dealing with bifurcation points when solving large deformation finite element problems is not an easy task. Near such points, the Jacobian matrix becomes singular and the problem becomes difficult to solve numerically. In these situations, increasing heuristically the loading parameter during the simulation in order to follow the solution branch is not an option as this approach usually results in the divergence of the process. Efficient numerical techniques capable of handling the presence of bifurcation points are therefore necessary and continuation methods have proved to be powerful tools when dealing with these kind of issues. In Léger et al. (2015), a new implementation technique based on a Schur complement approach for the Moore-Penrose continuation method, which facilitates the detection of bifurcation points and enables branch following, was presented. This method has proved to perform well in most situations; however, in others (i.e. when mesh adaptation is added to the algorithm), some difficulties appear. In this paper, we therefore present an improved approach, which is much more robust, for the detection of bifurcation points in nonlinear finite element problems. Numerical examples will be presented to show the efficiency of the new approach. [ABSTRACT FROM AUTHOR]

The Material Point Method (MPM) uses a combined Eulerian-Lagrangian approach to solve problems involving large deformations. A problem domain is discretised as material points which are advected on a background grid. Problems are encountered with the original MPM when material points cross between grid cells, and this has been tackled by the development of the Generalised Interpolation MPM, where material points’ domains of influence extend beyond the currently occupied grid cell. In this paper, the Generalised Interpolation Material Point (GIMP) Method has been implemented implicitly in a manner that allows a global stiffness matrix to be constructed similar to that in the Finite Element Method (FEM) by combining contributions from individual elements on the background grid. An updated Lagrangian finite deformation framework has been used to ensure non-linear behaviour within each of the loadsteps. The weighting functions used for this which make the GIMP method different to standard MPM are presented and the implementation is explained. Specific details on computing the deformation gradient to be consistent with the updated Lagrangian framework and the updating of the material point influence domains are outlined, both of which are currently unclear in the published literature. It is then shown through numerical examples that for both small and large deformation elastic and elasto-plastic problems, the implicit GIMP method agrees well with analytical solutions and exhibits convergence properties between that of linear and quadratic FEM. [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 proposes a general finite-element procedure for the nonlinear analysis of cables based on a mixed variational formulation in curvilinear coordinates with finite deformations. The formulation accounts for nonlinear elasticity and inelasticity, overcoming the limitation of recent numerical approaches which integrate explicitly the global balance of linear momentum for a linear elastic material with infinitesimal deformations. The formulation uses a weak form of the catenary problem and of the strain-displacement relation to derive a new family of cable finite elements with a continuous or discontinuous axial force field. Several examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St. Venant-Kirchhoff elastic materials and neo-Hookean materials. These studies show that the proposed formulation captures the displacements and the axial force distribution with high accuracy using a small number of finite elements. [ABSTRACT FROM AUTHOR]

This paper explores the simulation of small deformation contact problems with a coupled isogeometric-meshless formulation, based on local maximum-entropy (LME) approximants. The framework of isogeometric analysis (IGA) is employed on a thin region close to the boundary of the domain and the meshless formulation in its interior. The method maintains the advantages of IGA in the simulation of contact and introduces a higher flexibility in the discretization of complex shapes. In addition, a new integration strategy is presented for the IGA-LME blending and its advantages respect to the original approach are discussed. [ABSTRACT FROM AUTHOR]

In this paper, the Analog Equation Method (AEM), a boundary element based method, is employed for the analysis of homogenous beams of arbitrary cross section (thin- or thick-walled) taking into account nonuniform warping and shear deformation effects (shear lag due to both flexure and torsion), considering a B-spline approximation for the fictitious loads of a substitute problem. The fictitious loads are established using a BEM-based technique and the solution of the original problem is obtained from the integral representation of the solution of the substitute problem. The beam is subjected to the combined action of arbitrarily distributed or concentrated axial and transverse loading, as well as to bending, twisting and warping moments. Its edges are subjected to the most general boundary conditions, including also elastic support. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions, which are obtained by solving corresponding boundary value problems, formulated exploiting the longitudinal local equilibrium equation. Ten one-dimensional boundary value problems are described by second-order differential equations. Integrating B-splines in the AEM technique, the computational cost is efficiently reduced while the results are highly accurate. [ABSTRACT FROM AUTHOR]

This paper presents a systematic analysis of localization properties of the anisotropic damage model proposed by Desmorat and coworkers. The general localization condition, based on the vanishing determinant of the second-order localization tensor, is converted into a specific criterion valid for the present model and dependent on the current state variables and model parameters. The localization properties are then described in terms of (i) the critical value of a parameter governing the damage growth, (ii) the critical ratio between the tangent and elastic moduli, (iii) the direction of a potential weak discontinuity plane and (iv) the discontinuity mode. For plane-stress and plane-strain states, these characteristics are investigated in detail and the differences between two- and three-dimensional analyses are explained and discussed. The theoretical results are verified by numerical simulations of a bar under uniform tension using a skewed finite element mesh, which allows localization into inclined bands of different directions. [ABSTRACT FROM AUTHOR]

A high accuracy finite strip for the buckling and post-buckling analysis of moderately thick symmetric cross-ply composite plates is presented in this paper by using first order shear deformation theory (FSDT). The presented method, which is designated by the name Full-analytical Finite Strip Method (F-a FSM), provides an efficient and extremely accurate buckling solution in which the Von-Karman’s equilibrium set of equations is solved exactly, and the out-of-plane mode shapes and critical loads are obtained. In the post-buckling stage, the Von-Karman’s compatibility equation is solved exactly with the assumption that the deflected form after buckling is a combination of obtained buckling modes (single or multiple mode shapes). The principle of minimum potential energy is invoked to solve for the unknown coefficients in the assumed out-of-plane deflection and rotations functions. [ABSTRACT FROM AUTHOR]

The design of coupling algorithms for partitioned fluid–structure interaction (FSI) simulations are typically validated on FSI problems involving large deformations of thin elastic structures with large added mass ratios. A large number of FSI problems may however feature additional internal non-linearities, examples of which include problems with free surface flow or FSI problems involving contact between two or more solid bodies. In this paper we aim to demonstrate the applicability of quasi-Newton methods when applied to these classes of problems. The analyses will focus on a comparison between two promising families of quasi-Newton methods, namely the ‘quasi-Newton least squares’ (QN-LS) family of methods and the ‘multi-vector iteratively updated quasi-Newton’ (MVQN) method. Both of these families of quasi-Newton methods construct approximations of the FSI system Jacobians using only iteratively obtained interface information, and can therefore be applied to black-box subdomain solvers. We will further attempt to quantify the ability of these QN methods to adequately approximate these additional non-linearities based on the form of the chosen interface equations. [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 new integral approximation of frictional contact problems under large deformations is presented. Impenetrability, friction and the relevant complementarity conditions are expressed through a non-smooth equation, considered in the continuous setting. A weak formulation of this non-smooth complementarity equation is discretized through a standard Galerkin procedure, is linearized consistently and incorporated in a generalized Newton solution process. The resulting integral handling of contact and friction complementarity conditions, previously implemented for small deformations only, is extended in the present paper to large deformations. In total, the proposed method is relatively simple to implement, while its robustness is illustrated through numerical examples. [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 discusses the similarity of meshless discretizations of Peridynamics and Smooth-Particle-Hydrodynamics (SPH), if Peridynamics is applied to classical material models based on the deformation gradient. We show that the discretized equations of both methods coincide if nodal integration is used. This equivalence implies that Peridynamics reduces to an old meshless method and all instability problems of collocation-type particle methods apply. These instabilities arise as a consequence of the nodal integration scheme, which causes rank-deficiency and leads to spurious zero-energy modes. As a result of the demonstrated equivalence to SPH, enhanced implementations of Peridynamics should employ more accurate integration schemes. [ABSTRACT FROM AUTHOR]

Abstract: This paper uses a multilayered shell element to compute the dynamic response of multilayered poroelastic structures such as car instrument panels, car floors, or car roofs. It is based on the P-order Shear deformation Theory with an added Zigzag function (ZPST). Biot’s theory is used to describe the poroelastic layer and standard couplings are realized between elastic and poroelastic layers. A method based on Padé approximants is also used in order to reduce the computation time. This acceleration technique enables to achieve fast frequency sweep computations compared to a standard direct method. Finally, numerical validations on plates and curved geometries are presented. [Copyright &y& Elsevier]

Abstract: Three-dimensional (3D) cyclic analysis and constitutive material model are needed to better understand the behavior of unreinforced masonry (URM) buildings under earthquake excitations. So far, most of the existing constitutive material models applied to the field of masonry structures have focused on two-dimensional modeling and monotonic loading. In addition, most of the studies have used implicit dynamic procedures in the time domain. Based on the inherent features of implicit formulations for nonlinear problems, a number of iterations are required at each time step to achieve convergence, which leads to intensive computations and lack of convergence in some cases such as cyclic loadings. In this paper, a 3D cyclic constitutive material model implemented within an explicit analysis procedure is proposed, which can be used to model large deformation behavior of masonry walls. A rigorous constitutive material model is proposed and validated with available experimental data from previous researches, and for the attributes for which experimental data is not readily available; a number of new experimental tests has been conducted by the authors. The material model is implemented in a user-defined subroutine and compiled with ABAQUS (VUMAT). The subroutine is then tested by several numerical examples on a single element under cyclic normal and transverse deformations to examine the behavior of the material model. Moreover, several analyses are conducted and the numerical results are compared with experimental data to assess the robustness and predictive capabilities of the proposed material model and the numerical solution algorithms. [Copyright &y& Elsevier]

Abstract: This paper proposes and validates a three degrees of freedom element formulation that accounts for torsion and transverse bending of three-dimensional curved elements in explicit numerical analyses methods such as Dynamic Relaxation. Using finite difference modeling, in-plane distortions and moments, the increment of twist (and hence torsion) and out-of-plane bending deformations are determined. Numerical stability and convergence limits of the element are discussed. Two sets of circular arc test cases validate the accuracy of the element against theoretical and six degrees of freedom finite-element results. This element is widely applicable and found in strained grid shells and spline stressed membranes. [Copyright &y& Elsevier]

Abstract: In the current paper, it is the first time that a dynamic stability analysis of moderately thick cylindrical panels made from FG materials is conducted by employing finite strip formulations based on a Reddy-type third order shear deformation theory (HSDT). Two versions of finite strip methods (FSM), namely semi-analytical and B-spline methods are developed. The mechanical properties of FGM are assumed to change in thickness direction according to a power-law function. The temperature effects are ignored. The strain terms are expressed in terms of the Koiter–Sanders theory of shallow shells. In order to demonstrate the capabilities of the developed methods in predicting parametric behavior of the subject structures, some representative results are obtained and compared with those in the literature wherever available. [Copyright &y& Elsevier]

Abstract: This paper presents a damage detection technique combining proper orthogonal decomposition (POD) with self-adaptive differential evolution algorithm for structural health monitoring considering environmental variability and measurement noises. The damage detection methodology consists of three stages. Identification of the exact time instant of damage and exact spatial location of damage using proper orthogonal modes constitutes the first two stages. The damage severity assessment is the third stage and is formulated as a constrained optimisation problem, solved using newly proposed self-adaptive differential evolution algorithm. Numerical simulation studies indicate that the proposed method is robust and can be used effectively in SHM applications. [Copyright &y& Elsevier]

Abstract: In Reinforced Concrete structures, the concrete damage configuration as well as the crack pattern distribution depend directly on bonding, and its implementation for numerical analysis is still complicated. In this work, a new thermodynamical non linear bond model is introduced taking into account tangential bond deterioration and coupling between tangential slip and normal decohesion/penetration. For FEM implementation, the model (based on a stress–strain relationship) is supported by a non-width interface element. The calibrated material parameters are grouped in four sets: elastic behavior; tangential degradation; crack friction and confinement; and normal behavior. Finally, some numerical examples are presented in this paper. [Copyright &y& Elsevier]

Abstract: A generalized constitutive model for describing the creep deformation and creep damage development in initially isotropic materials with characteristics dependent on the kind of the stress state has been implemented into the finite element analysis. This paper presents a number of benchmark creep damage tests and reference solutions to verify the finite element results taking into account the material tension–compression asymmetry and symmetry. The numerical results based on the ABAQUS finite element code in which a user subroutine CREEP is incorporated have been compared in the benchmark tests with the numerical results obtained by other authors or by other methods. [Copyright &y& Elsevier]

Abstract: This paper presents a curved beam model for the nonlinear electro-dynamic analysis of micro-beams with initial curvature, taking into account the nonlinear electric force and nonlinear deformation. The governing equations of motion and boundary conditions are derived in an arc coordinate system. Unlike previous studies based on von Karman nonlinearity or considering mid-plane stretching only, the present study does not involve any assumptions on nonlinear deformation. Differential quadrature method and Petzold–Gear BDF method are employed to obtain the nonlinear electro-dynamic behavior of curved micro-beams. The effects of nonlinear deformation, initial gap and initial rise on the nonlinear electro-dynamic characteristics are studied. [Copyright &y& Elsevier]

Abstract: Reported in this paper is the development and verification of a finite element model with the fewest solid elements that can predict the non-linear stiffness characteristics of adhesively bonded single lap-joints in vehicle bodies. This work was driven by the need to significantly reduce computing hardware resources and run times for whole body analyses, and to achieve this goal the lap-joint needs to be modelled by a ‘small’ number of shell elements. It is well-known that the deformation of bonded lap-joints is dependent on seven key parameters, and that it is impractical to have a comprehensive characterisation of these by physical testing alone. To gain further understanding of the influence of these parameters on joint stiffness, over a wider range of variables than could be practically achieved in the laboratory, the ANSYS finite element code is used to simulate the highly non-linear (geometric and material) response of bonded joints. The authors use the laboratory results for joint stiffness from nineteen batches of laboratory specimens to aid the development, and verification, of numerical derived stiffness curves from a solid element model. Initially, a very refined mesh is used. This model is developed to have a ‘coarse’ solid element mesh that minimises run times without the calculated joint stiffness deviating by more than 10% from the batch mean of 10 measurements from laboratory testing. Numerical results from many simulations using the ‘coarse’ solid mesh model are used to show that, for the shell modelling methodology (reported in Part 2 on this work) to be successful, a representative model must account for the four key parameters of: adherend stress–strain relationship, adherend thickness, bond line thickness, and the over lap length. The ANSYS results also confirm that stiffness is directly proportional to joint width. [Copyright &y& Elsevier]

Abstract: This paper uses the ZPST multilayered shell element developed by Sulmoni et al. to compute the dynamic response of multilayered viscoelastic structures such as windscreens or car bodyworks. It is based on the P-order shear deformation theory with an added zigzag function. The viscoelastic properties are taken into account with frequency dependent elastic moduli measured with a Dynamic Mechanical Thermal Analyzer. A method based on Padé approximant is also used to reduce the computation time. This acceleration technique enables to achieve fast frequency sweep computations compared to a standard direct method. Finally, validations are made on plates and cylindrical geometries. [Copyright &y& Elsevier]

Abstract: Although fibre reinforced polymers exhibit several advantages over traditional materials, their widespread acceptance is being delayed by the lack of appropriate design codes. In fact, additional and comprehensive experimental data are needed to assess the accuracy of recently developed analytical and numerical design tools. This work reports an experimental study on the first-order, buckling and post-buckling behaviours of I-section beams made of GFRP pultruded profiles. Tests were first carried out on small-scale (coupon) specimens, in order to determine the most relevant material mechanical properties. Full-scale tests were then conducted on (i) simply supported beams with spans varying from 1.0m to 4.0m under 3-point bending and (ii)cantilevers with spans ranging from 2.0 m to 4.0 m subjected to a tip point load applied at the end cross-section centroid or top/bottom flange mid-point. While the first series is aimed at investigating the flexural behaviour under service and failure conditions (including the local buckling of the top flange), the objective of the second series is to study the collapse behaviour stemming from lateral-torsional buckling. The results obtained confirm that, due to the GFRP low Young’s modulus and high strength, the beam structural integrity is often governed by excessive deformation and/or local and global buckling phenomena, rather than by material strength limitations. Moreover, the low shear-to-Young’s modulus ratio implies that the role played by the shear deformation is quite relevant, particularly in stocky beams. The experimental data presented here is used to validate and assess the accuracy of numerical simulations reported in a companion paper (Part 2). [Copyright &y& Elsevier]

Abstract: In this paper, the compressive, i.e. bucking and post-buckling, behavior of composite laminates with through-the-width and embedded delaminations is investigated analytically. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh–Ritz approximation technique. In the case of the multiple delaminations, the contact phenomenon has significant effects on the compressional behavior of the laminates. Thus, the contact between the delaminated sublaminates is also considered in the presented FSDT analytical method. The method can handle both local buckling of the delaminated sublaminates and global buckling of the whole plate. Also, the three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model. The agreement between the results is very good. [Copyright &y& Elsevier]

Abstract: The paper describes the modeling of thick composite laminate and sandwich plates and beams with linear viscoelastic treatments. A discrete laminate model (DLM) is described, validated and compared to numerical spectral finite elements method (SFEM), finite element method (FEM) and experimental results. The DLM approach assumes each layer as thick laminate with orthotropic orientation, rotational inertia and transversal shearing, membrane and bending deformations. First order shear deformation theory is used. The equation of motion is developed following a wave approach based on discrete layer description. It handles symmetrical and asymmetrical layouts of unlimited number of transversal incompressible layers. Next, dilatational (symmetric mode) motion along the core’s thickness is considered to complete the DLM solution when applied to the case of symmetric sandwich structures with soft and thick core. The model is compared to a second approach employing spectral finite elements. The latter handles composite laminated plates and beams with orthotropic orientation. It is shown that both approaches estimate accurately the propagating wave solutions of laminated structures. Using these solutions, the input mobility and the mechanical impedance are computed. The two models are successfully compared to classical finite elements as well as to experimental results for different boundary conditions. Moreover, the equivalent damping loss factor of composite laminate plates with viscoelastic treatment is addressed and the influence of the heading direction is discussed. [Copyright &y& Elsevier]

Abstract: This paper highlights the role of advanced structural analysis tools on the conception of high-performance earthquake-resistant structural systems. A new steel frame equipped with self-centering devices and viscoelastic dampers is described. A prototype building using this frame is designed and a detailed nonlinear analytical model for seismic analysis is developed. Seismic analyses results show the effectiveness of the proposed frame to enhance structural and non-structural performance by significantly reducing residual drifts and inelastic deformations, and by reducing drifts, total floor accelerations and total floor velocities. These results are the basis for further studies aiming to develop design methods and criteria for the proposed high-performance frame. [Copyright &y& Elsevier]

Abstract: This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes. [Copyright &y& Elsevier]