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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.

This paper aims to investigate the performance of two novel numerical methods, the face-based smoothed finite element method (FS-FEM) and the edge-based smoothed finite element method (ES-FEM), which employ linear tetrahedral elements, for the purpose of strength assessment of a high-speed train hollow axle.

The calculation of stress for the wheelset, comprising an axle and two wheels, is facilitated through the application of the European axle strength design standard. This standard assists in the implementation of loading and boundary conditions and is exemplified by the typical CRH2 high-speed train wheelset. To evaluate the performance of these two methods, a hollow cylinder cantilever beam is first used as a benchmark to compare the present methods with other existing methods. Then, the strength analysis of a real wheelset model with a hollow axle is performed using different numerical methods.

The results of deflection and stress show that FS-FEM and ES-FEM offer higher accuracy and better convergence than FEM using linear tetrahedral elements. ES-FEM exhibits a superior performance to that of FS-FEM using linear tetrahedral elements, showing accuracy and convergence close to FEM using hexahedral elements.

This study channels the novel methods (FS-FEM and ES-FEM) in the static stress analysis of a railway wheelset. Based on the careful testing of FS-FEM and ES-FEM, both methods hold promise as more efficient tools for the strength analysis of complex railway structures.

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.

This paper focuses on the study of finite element (FE) analysis reliability of non‐linear planar structural problems (large strains and plasticity). In this first part, some error estimators of the flux projection type have been developed over the strain power density concept. Spatial, temporal and global error estimators are proposed. From this point, the authors analyse the behaviour of different discretization error components as a function of parameters such as load step or the number of degrees of freedom of the FE model. In the second part of this work, several properties of these estimators are checked with the application to some numerical examples.

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.

This paper presents a new approach for estimating the discretization error of finite element analysis of generalized eigenproblems. The method uses smoothed gradients at nodal points to derive improved element‐by‐element interpolation functions. The improved interpolation functions and their gradients are used in the Rayleigh quotient to obtain an improved eigenvalue. The improved eigenvalue is used to estimate the error of the original solution. The proposed method does not require any re‐solution of the eigenproblem. Results for 1‐D and 2‐D C° eigenproblems in acoustics and elastic vibrations are used as examples to demonstrate the accuracy of the proposed method.

Structures in seismic areas, during their service lifetime, are subjected to numerous seismic loads that certainly affect their structural integrity. The degradation of these structures, to a great extent, depends on the scale of seismic events, the steel mechanical performance on reversal loads and its resistance to corrosion phenomena. The paper aims to discuss these issues.

Based on the experimental results of seismic steel behavior S400 (BSt III), which was widely used in the past years, a prediction study of seismic steel behavior was conducted in the current study. This prediction on behavior of both reference and corroded steel was succeeded through a simulation of experimental low cycle fatigue conditions (LCF – strain controlled).

At the same time, the present study analyses fatigue factors (ef, a, f_SR, ed, ep, R, b) that define their inelastic relation between tension – strain and a prediction model on behavior of both reference and corroded steel rebar, in seismic loads conditions (LCF), is proposed.

Moreover, this study dealt with the synergy of corrosion factor and the existence of superficial ribs (ribbed and smoothed) in seismic behavior of steel bar S400 (BSt420). The S-N curves that are exported can be resulted in a first attempt of prediction of anti-seismic behavior on reinforced concrete structures with this the same steel class.

The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures.

In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF).

In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness.

An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method.

An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

The purpose of this paper is to investigate the formation process of linear‐shaped charge jet using the smoothed particle hydrodynamics (SPH). Different material yield models are embed to test the performance of SPH method in the simulation of explosive driven metal liner. The effects of different ignition model to the formation of metal jet have also been studied.

The SPH method is used with the correction of artificial viscosity and penalty force to simulate the formation process of linear‐shaped charge jet, which includes the process of explosion and interaction between explosive gas and metal liner. The numerical results which got by SPH method are compared with these obtained by mesh‐based method. Different material yield models are implemented in the numerical examples to show the effect of material model to the formation process of metal jet. The single point and two point ignition models are used to study the effect of ignition models to the process of explosion and formation of metal jet.

Compared with the original mesh‐based method, the SPH method can simulate the physical process of linear‐shaped charge jet naturally, as well as the capturing of explosive wave propagation. The implementation of different material yields models to obtain the same formation tendency of metal jet, but some numerical difference exists. In two‐point ignition model the explosive pressure is superimposed at the location that two detonation waves intersect. Compared with two ignition models, the two point ignition model can form the metal jet faster and get the higher velocity metal jet.

There are a few references that address the application of SPH to simulate shaped charge explosion process. The feasibility of the SPH method to simulate the formation process of linear shaped charged jet is tested and verified in this paper. From the results which compared with mesh‐based method, it is shown that the SPH method has the advantage in tracking the large deformation of material and capturing the explosive wave propagation. The SPH method can be selected as a good alternative to traditional mesh‐based numerical methods in simulating similar explosively driven metal material problems which can be referenced from this paper.

The purpose of this paper is to improve knowledge of the water impact phenomenon from both the experimental and numerical points of view.

A drop test campaign on water was carried out on semi‐cylindrical steel structures. Therefore, an experimental database for validation purpose was generated. Subsequently, a finite element model was developed in LS‐DYNA in order to reproduce the tests. The behaviour of water was modeled by using the smoothed particle hydrodynamics (SPH) methods. Numerical simulations were compared to experimental data and the influence of some numerical parameters on the simulations was investigated.

The FE model was found to be able to reproduce the tests, at least in terms of acceleration peak and distribution of plastic deformation. Acceptable prediction was also found for the pressure peak in soft areas.

In case of low velocity impact, the water model was found to be too rigid and the acceleration peaks were over‐predicted by the simulations. Further investigations are needed to adjust the water model in order to obtain better results also in the case of low velocity impact.

The experimental database could be very useful to the crashworthiness community to validate their numerical models. Moreover, the present paper provides guidelines to modelling the water impact correctly.