A time-domain POD approach based on numerical implicit and explicit Green?s functions for 3D elastodynamic analysis

被引:3
|
作者
Souza, Y. P. [1 ]
Loureiro, F. S. [2 ]
Mansur, W. J. [1 ]
Ferreira, W. G. [3 ]
Camargo, R. S. [3 ]
机构
[1] Univ Fed Rio de Janeiro, Dept Civil Engn, COPPE, Rio De Janeiro, RJ, Brazil
[2] Univ Fed Sao Joao del Rei, Dept Thermal & Fluid Sci, Sao Joao Del Rei, MG, Brazil
[3] Univ Fed Espirito Santo, Dept Civil Engn, Vitoria, ES, Brazil
关键词
Direct time integrations; Numerical Green?s functions; Proper orthogonal decomposition; Elastodynamics; PROPER ORTHOGONAL DECOMPOSITION; PHYSICAL INTERPRETATION; INTEGRATION ALGORITHMS; STRUCTURAL DYNAMICS; MARCHING PROCEDURES; ORDER REDUCTION; FAMILY; SCHEME; DISSIPATION; SYSTEMS;
D O I
10.1016/j.compstruc.2022.106921
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This paper is concerned with the development of time integration methods based on numerical Green's functions applied in conjunction with the proper orthogonal decomposition (POD) technique to solve three-dimensional elastodynamic problems discretized by the FEM. The convolution integral in the veloc-ity expression of these methods is firstly carried out through integration by parts, and then approximated numerically, resulting in a simpler and more accurate convolution than that reported in the literature. To compute the solution samples, required by the POD technique, the Implicit Green's functions Approach (ImGA)-Newmark method rewritten in terms of the ultimate spectral radius is employed. The proposed ImGA scheme is truly self-starting and easy to implement with just one free parameter. To solve the reduced-order model, a new highly accurate time integration scheme based on the Explicit Green's func-tions Approach (ExGA)-Runge-Kutta method is proposed, considering the Gauss-Lobatto-Legendre (GLL) points to perform both the time integration of the Green's functions and the approximation of the con-volution integrals. To verify the accuracy and efficiency of the proposed formulation, the numerical results are compared with those from the full-order model. Moreover, undamped solution samples are utilized to build a reduced-order model that can take into account a Rayleigh damping matrix.(c) 2022 Elsevier Ltd. All rights reserved.
引用
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页数:18
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