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The purpose of this paper is to propose a new explicit time integration algorithm for solution to the linear and non-linear finite element equations of structural dynamic and wave propagation problems.

The algorithm is completely explicit so that no linear equation system requires solving, if the mass matrix of the finite element equation is diagonal and whether the damping matrix does or not. The algorithm is a single-step method that has the simple starting and is applicable to the analysis with the variable time step size. The algorithm is second-order accurate and conditionally stable. Its numerical stability, dissipation and dispersion are analyzed for the dynamic single-degree-of-freedom equation. The stability of the multi-degrees-of-freedom non-proportional damping system can be evaluated directly by the stability theory on ordinary differential equation.

The performance of the proposed algorithm is demonstrated by several numerical examples including the linear single-degree-of-freedom problem, non-linear two-degree-of-freedom problem, wave propagation problem in two-dimensional layer and seismic elastoplastic analysis of high-rise structure.

A new single-step second-order accurate explicit time integration algorithm is proposed to solve the linear and non-linear dynamic finite element equations. The algorithm has advantages on the numerical stability and accuracy over the existing modified central difference method and Chung-Lee method though the theory and numerical analyses.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

Two kinds of time integration methods; the dynamic explicit method and the static implicit method, have been compared, especially with emphasis on the shell formulations and the stress integration methods. Two methods have been applied to the benchmark problem named the S‐rail stamping process, provided by NUMISHEET’96 committee, in order to compare their numerical results with each other and with the average values of the experiments as well. Based on the comparisons, it is shown that both time integration methods can be successfully applied to industrial sheet metal stamping simulations. In detail, the static implicit method is advantageous over the dynamic explicit method in terms of accuracy, while the latter is known to be more efficient than the former in terms of computation efficiency.

The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

The purpose of this paper is to propose two linear solid-shell finite elements, a six-node prismatic element denoted SHB6-EXP and an eight-node hexahedral element denoted SHB8PS-EXP, for the three-dimensional modeling of thin structures in the context of explicit dynamic analysis.

These two linear solid-shell elements are formulated based on a purely three-dimensional (3D) approach, with displacements as the only degrees of freedom. To prevent various locking phenomena, a reduced-integration scheme is used along with the assumed-strain method. The resulting formulations are computationally efficient, as only a single layer of elements with an arbitrary number of through-thickness integration points is required to model 3D thin structures.

Via the VUEL user-element subroutines, the performance of these elements is assessed through a set of selective and representative dynamic elastoplastic benchmark tests, impact-type problems and deep drawing processes involving complex non-linear loading paths, anisotropic plasticity and double-sided contact. The obtained numerical results demonstrate good performance of the SHB-EXP elements in the modeling of 3D thin structures, with only a single element layer and few integration points in the thickness direction.

The extension of the SHB-EXP solid-shell formulations to large-strain anisotropic plasticity enlarges their application range to a wide variety of dynamic elastoplastic problems and sheet metal forming simulations. All simulation results reveal that the numerical strategy adopted in this paper can efficiently prevent the various locking phenomena that commonly occur in the 3D modeling of thin structural problems.

Because of the unrealistic demand of computer resources in terms of memory and CPU times for the direct numerical simulation of practical peen forming processes, a two‐stage combined finite/discrete element and explicit/implicit solution strategy is proposed in this paper. The procedure involves, at the first stage, the identification of the residual stress/strain profile under particular peening conditions by employing the combined finite/discrete approach on a small scale sample problem, and then at the second stage, the application of this profile to the entire workpiece to obtain the final deformation and stress distribution using an implicit static analysis. The motivation behind the simulation strategy and the relevant computational and implementation issues are discussed. The numerical example demonstrates the ability of the proposed scheme to simulate a peen forming process.

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.

Recent progress in element technology in large scale explicit finite element codes has opened the way for the solution of elastoplastic shell problems of unprecedented complexity. This new capability has focused attention on the numerical issues involved in the implementation of elastoplastic material models for shells, particularly when vectorizable algorithms are required for supercomputer applications. This paper reviews four algorithms currently in the literature for plane stress and shell plasticity. First, each of the four methods is described in detail. Next, an accuracy analysis is presented for each algorithm for perfectly plastic, linear kinematic hardening, and linear isotropic hardening cases. Finally, a comparison is made of the relative computational efficiency of the four algorithms, and the importance of vectorization is illustrated.

The purpose of this paper is to propose a numerical prediction method of buckling loads for shell structures under axial compression and thermal loads based on vibration correlation technique (VCT).

VCT is a non-destructive test method, and the numerical realization of its experimental process can become a promising buckling load prediction method, namely numerical VCT (NVCT). First, the derivation of the VCT formula for thin-walled structures under combined axial compression and thermal loads is presented. Then, on the basis of typical NVCT, an adaptive step-size NVCT (AS-NVCT) calculation scheme based on an adaptive increment control strategy is proposed. Finally, according to the independence of repeated frequency analysis, a concurrent computing framework of AS-NVCT is established to improve efficiency.

Four analytical examples and one optimization example for imperfect conical-cylindrical shells are carried out. The buckling prediction results for AS-NVCT agree well with the test results, and the efficiency is significantly higher than that of typical numerical buckling methods.

The derivation of the VCT formula for thin-walled shells provides a theoretical basis for NVCT. The adaptive incremental control strategy realizes the adaptive adjustment of the loading step size and the maximum applied load of NVCT with Python script, thus establishing AS-NVCT.