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In this work, an SFEM is proposed for solving acoustic problems by redistributing the entries in the mass matrix to “tune” the balance between “stiffness” and “mass” of discrete equation systems, aiming to minimize the dispersion error. The paper aims to discuss this issue.

This is done by simply shifting the four integration points’ locations when computing the entries of the mass matrix in the scheme of SFEM, while ensuring the mass conservation. The proposed method is devised for bilinear quadratic elements.

The balance between “stiffness” and “mass” of discrete equation systems is critically important in simulating wave propagation problems such as acoustics. A formula is also derived for possibly the best mass redistribution in terms of minimizing dispersion error reduction. Both theoretical and numerical examples demonstrate that the present method possesses distinct advantages compared with the conventional SFEM using the same quadrilateral mesh.

After introducing the mass-redistribution technique, the magnitude of the leading relative dispersion error (the quadratic term) of MR-SFEM is bounded by (5/8), which is much smaller than that of original SFEM models with traditional mass matrix (13/4) and consistence mass matrix (2). Owing to properly turning the balancing between stiffness and mass, the MR-SFEM achieves higher accuracy and much better natural eigenfrequencies prediction than the original SFEM does.

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems is generalized to two dimensions, using quadrilateral elements. Its performance is compared with that of conventional local smoothing techniques and of direct differentiation of the finite‐element solution, on finite‐element approximations to analytically known polynomial and transcendental functions on a quadrilateral second‐order finite‐element mesh. The new method appears to be reliable and more stable than local smoothing, and to provide better accuracy than direct differentiation, at low computational cost.

Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness.

This novel approach is based on the newly developed G space and weakened weak (w²) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells.

Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies.

The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems.

It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study.

First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully.

First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system.

The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

The gradient recovery method proposed by Zhu and Zienkiewicz for one‐dimensional problems and extended to two dimensions by Silvester and Omeragi? is generalized to three‐dimensional solutions based on rectangular prism (brick) elements. The extension is not obvious so its details are presented, and the method compared with conventional local smoothing and direct differentiation. Illustrative examples are given, with an extensive experimental study of error. The method is computationally cheap and provides better accuracy than conventional local smoothing, but its accuracy is position dependent.

This paper aims to propose a new smoothed particle hydrodynamics (SPH)-finite element (FE) algorithm to study fluid–structure interaction (FSI) problems.

The fluid domain is discretized based on the theory of SPH), and solid part is solved through FE method, similar to other SPH-FE methods in the previous studies. Instead of master-slave technique, the interpolating (kernel) functions of immersed boundary method are implemented to couple fluid and solid domains. The procedure of modeling completely follows the classic IB framework where forces and velocities are transferred between interacting parts. Three benchmark FSI problems are simulated and the results are compared with those of similar numerical and experimental works.

The proposed SPH-FE algorithm with promising and acceptable results can be utilized as a reliable method to simulate FSI problems.

Contrary to most SPH-FE algorithms, the calculation of contact force is not required at interacting boundaries and no iterative process is proposed to calculate forces, velocities and positions at new time step.

The purpose of this paper is to confirm that the axisymmetric finite element and smoothed particle hydrodynamics (FE-SPH) adaptive coupling method is effective to solve explosion problem in concrete based on the experiments.

Axisymmetric FE-SPH adaptive coupling method is first presented to simulate dynamic deformation process of concrete under internal blast loading. Using calculation codes of FE-SPH coupling method, numerical model of explosion is approximated initially by finite element method (FEM), and distorted finite elements are automatically converted into meshless particles to simulate damage, splash of concrete by SPH method, when equivalent plastic strain of elements reaches a specified value.

In this paper, damage process and pressure curve of concrete around explosive are analyzed and buried depth of explosive in concrete influence on damage effect under internal blast loading are obtained. Numerical analyses show that FE-SPH coupling method integrates high computational efficiency of FEM and advantages of SPH method, such as natural simulation to damage, splash and other characteristics of explosion in concrete.

This work shows that FE-SPH coupling method has good performance to solve the explosion problem.

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.

The purpose of this paper is to achieve numerical simulation of discontinuous rock masses.

The extended finite element method (XFEM) was used. Discontinuities (such as joints, faults, and material interfaces) are contained in the elements, thus the mesh can be generated without taking into account the existence of discontinuities. When one element contains no discontinuity, the displacement function is degenerated into that of the conventional finite element. For the element containing discontinuities, the standard displacement‐based approximation is enriched by incorporating level‐set‐based enrichment functions that model the discontinuities, and an element subdivision procedure is used to integrate the domain of the element.

Mesh generation can be simplified considerably and high‐quality meshes can be obtained. A solution with good precision can also be achieved. It is concluded that the XFEM technique is especially suitable in simulating discontinuous rock masses problems.

Crack initiation and propagation should be considered in further studies.

The paper presents a very useful numerical method for a geotechnical engineering problem that has the ability to simulate the failure process of discontinuous rock masses. The method is expected to be used widely in the deformation and stability analysis of complicated rock masses.

The paper provides a new numerical method for discontinuous rock masses that is very convenient for pre‐processing.

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).

The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.

Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.

The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.