種別 paper
主題 The One-Point Integration Rule in Nonlinear Finite Element Analysis
副題
筆頭著者 Guo-xiong Yu(Nagoya University)
連名者1 Hiro-ya. Nagashima(Nagoya University)
連名者2 Tada-aki Tanabe(Nagoya University)
連名者3
連名者4
連名者5
キーワード
16
2
先頭ページ 117
末尾ページ 122
年度 1994
要旨 1. INTRODUCTION
Analysis of the localization,the phenomenon that large strains concentrate into a thin band without affecting the other portions of the structure, is thought to be a major challenge in computational mechanics. Many methods in finite element with a discontinuous field have beert proposed to successflly solve this problem.No matter Which method is used, the one point quadraiure scheme is considered to be the most efficient one.
It has been known for long time that one-point quadrature scheme provides tremendous benefits in nonlinear algorithms because the number of evaluations of the semidiscretized gradient operator, commonly know as the [B] matrix, and the constitutive equations, is reduced substantially.
However, the use of one-point quadrature scheme results in certain hourglass modes, or zero-energy modes. If a mesh is consistent with a global pattern of these modes, they will quickly dominate and destroy the solution. Some methods have been proposed to deal with this phenomenon. Those include the one proposed by Kosloff and Frazier, Flanagan and Belytschko. The method proposed by Kosloff and Frazier has been thought to be the most effective and the easiest to understand particularly for rectilinear elements.
In the paper written by Kosloff and Frazier, their hourglass control method was proven to be correct and effective in the elastic analysis, but nothing was included in the scope of nonlinear analysis. In this paper, a method to control the hourglass modes in nonlinear calculation is developed. A modified scheme iS proposed to obtain the accurate response of the structure in nonlinear region. The discussions of this paper are confined within the rectangular linear element. The research for a more general case will be presented in future publications.
8. CONCLUSIONS
A method was developed to eliminate hourglass instabilities in four-node rectangular elements in nonlinear problems. A modified scheme has been presented to obtain accurate nonlinear element flexural response. Through numerical calculations, it has been proven that this modified scheme can give as accurate results as the Q6 incompatible element and consume less time.
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