数值流形方法无自锁和沙漏问题的一种单点积分策略  

A single point integration rule for numerical manifold method without locking and hourglass issues

作　　者：张宁 郑宏 杨亮 王熠琛 武文安 Ning Zhang;Hong Zheng;Liang Yang;Yichen Wang;Wenan Wu(School of Civil Engineering,Qinghai University Qinghai 810016,China;Key Laboratory of Urban Security and Disasier Engineering,Ministry of Education,Beijing University of Technology,Beijing100124,China;Agiletech Engineering Consulants Co.,Lid,Bejing 100037,China;National Engineering Lab for Green and Safe Construction Technology in Urban Rail Transit,Beijing 100037,China)

机构地区：[1]School of Civil Engineering,Qinghai University Qinghai 810016,China [2]Key Laboratory of Urban Security and Disasier Engineering,Ministry of Education,Beijing University of Technology,Beijing100124,China [3]Agiletech Engineering Consulants Co.,Lid,Bejing 100037,China [4]National Engineering Lab for Green and Safe Construction Technology in Urban Rail Transit,Beijing 100037,China

出　　处：《Acta Mechanica Sinica》2023年第9期100-113,共14页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.52130905,52079002,12202024).

摘　　要：凭借切割运算,数值流形方法(NMM)可通过最简单的规则网格处理任意形状的问题域然而,这通常会生成很多低阶的、形状不规则的单元。因此NMM不但需要大量积分点,而且在几乎不可压缩和弯曲变形占优时常常存在自锁现象.为解决上述问题,本研究将建立一个数值稳定的单点积分策略.通过单元的矩,该策略将单元虚功分解为零阶主项和高阶稳定项,进一步通过修正高阶稳定项中的球应变部分和剪切应变部分,达到克服体积自锁和剪切自锁的目的,并用始终非零的稳定项克服沙漏变形.除了积分点更少外,新方法不存在体积自锁、剪切自锁和沙漏模式,因而也具有更高精度.文中数值算例验证了新规则的鲁棒性和精度提升.Due to the salient feature of cutting operation,the numerical manifold method(NMM)can deal with an any-shaped problem domain by the simplest regular grid.However,this usually creates many irregularly shaped lower-order manifold elements.As a result,the NMM not only needs lots of integration points,but also encounters severe locking issues on nearly incompressible or bending-dominated conditions.This study shows a robust single-point integration rule to handle the above issue in the twodimensional NMM.The essential idea is to separate the virtual work of an element in terms of moments to the center,so that a zero-order main term and higher-order stabilizing terms are obtained.Further,the volumetric locking and the shearing locking are avoided by modifications to the spherical part and shearing part of the stabilizing terms,and hourglass deformation is overcome since stabilizing terms are always non-zero.Consequently,in addition to fewer integration points,the rule improves accuracy since it is free from locking or hourglass issues.Numerical examples verify the robustness and accuracy improvement of thenewrule.

关 键 词：自锁现象 数值流形方法 规则网格 沙漏模式 剪切应变 精度提升 积分点 

分 类 号：O3[理学—力学]