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The numerical quadrature of the stiffness matrices and force vectors is a major factor in the accuracy and efficiency of the finite element methods. Even in the analysis of linear problems, the use of too many quadrature points results in a phenomenon called locking whereas the use of insufficient quadrature points results in a phenomenon called spurious singular mode. Therefore, efficient numerical quadrature schemes for structural dynamics are developed. It is expected that these improved finite elements can be used more reliably in many structural applications. The proposed developed quadrature schemes for the continuum and shell elements are straightforward and are modularized so that many existing finite element computer codes can be easily modified to accommodate the proposed capabilities. This should prove of great benefit to many computer codes which are currently used in structural engineering applications.

This article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.

This paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.

On the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.

This study provides an accurate and efficient meshfree method for simulating crack growth.

A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities.

A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation.

Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency.

Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

A simple triangular shell element which incorporates the effects of coupling between membrane and flexural behaviour and avoids membrane locking is described. The element uses a discrete Kirchhoff bending formulation and a constant strain membrane element. For the purpose of permitting inextensional modes and thus avoiding membrane locking, a decomposition technique, which can also be viewed as a strain projection method, is used. The method is illustrated first for a beam element and then for a triangular shell element. Results are presented for a variety of linear static problems to illustrate its accuracy and some highly non‐linear problems to indicate its applicability to collapse analysis.

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described.

The proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step.

This approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods.

This research is limited to shape optimization of two‐dimensional electric structures, however, the work can be extended to 3D ones too.

The implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described.

The main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

This paper aims to investigate the application of adaptive integration in element-free Galerkin methods for solving problems in structural and solid mechanics to obtain accurate reference solutions.

An adaptive quadrature algorithm which allows user control over integration accuracy, previously developed for integrating boundary value problems, is adapted to elasticity problems. The algorithm allows the development of a convergence study procedure that takes into account both integration and discretisation errors. The convergence procedure is demonstrated using an elasticity problem which has an analytical solution and is then applied to accurately solve a soft-tissue extension problem involving large deformations.

The developed convergence procedure, based on the presented adaptive integration scheme, allows the computation of accurate reference solutions for challenging problems which do not have an analytical or finite element solution.

This paper investigates the application of adaptive quadrature to solid mechanics problems in engineering analysis using the element-free Galerkin method to obtain accurate reference solutions. The proposed convergence procedure allows the user to independently examine and control the contribution of integration and discretisation errors to the overall solution error. This allows the computation of reference solutions for very challenging problems which do not have an analytical or even a finite element solution (such as very large deformation problems).

The aim of this paper is to extend the Element Free Galerkin method (EFGM) in order to perform the elasto‐plastic analysis of isotropic plates.

The EFGM shape‐function construction is briefly presented. The Newton‐Raphson method and the elasto‐plastic algorithm adapted to the EFGM, are described. Several plate bending non‐linear material problems are solved and the obtained solutions are compared with available finite element method (FEM) solutions.

The paper finds that the developed EFGM approach is a good alternative to the FEM for the solution of non‐linear problems, once the obtained results with the EFGM show a high similarity with the obtained FEM results.

Comparing the FEM and the EFGM there are some drawbacks for the EFGM. The computational cost of the EFGM is higher, the imposition of the essential boundary conditions is more complex and there is a high sensitivity of the method in what concerns the choice of the influence domain and the choice of the weight function.

The knowledge that the EFGM formulation can be treated almost as the FEM formulation once the EFGM parameters are calibrated and optimized.

The extension of the EFGM to the elasto‐plastic analysis of isotropic plates.

The aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.

The cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.

When compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.

This work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

This paper demonstrates the capability of staggered solution procedure for coupled fluid‐structure interaction problems. Three possible computational paths for coupled problems are described. These are critically examined for a variety of coupled problems with different types of mesh partitioning schemes. The results are compared with the reported results by continuum mechanics priority approach—a method which has been very popular until recently. Optimum computational paths and mesh partitionings for two field problems are indicated. Staggered solution procedure is shown to be quite effective when optimum path and partitionings are selected.