摘要
为了提高平面问题的求解精度,基于勒让德正交函数族引入泡状函数来增强映射关系的思想,构造Q8_Legendre单元。针对单元的位移场中含有泡状函数导致单元刚度矩阵规模变大的问题,在得到单元刚度矩阵后附加自由度凝聚,以减小整体刚度矩阵规模、节省计算机内存空间。算例表明,随着泡状函数项数的不断增加,Q8_Legendre单元能够通过分片试验,使得单元的位移精度得到改善,而应力精度保持相当。当出现畸变网格时,Q8_Legendre单元表现出抗畸变的性能,且不会出现闭锁现象。
In order to improve the solution precision of the plane problem,the Q8_Legendre element is constructed based on the idea of introducing Bubble function to enhance the mapping relationship based on Legendre orthogonal function.Because the displacement field of the element contains Bubble function,the size of the element stiffness matrix becomes larger.In order to reduce the size of the overall stiffness matrix and save the computer memory space,the additional degrees of freedom are condensed after the stiffness matrix of the element is obtained.Some numerical examples show that the Legendre element can pass the patch test,and the displacement accuracy of the element is improved with the increasing of Bubble function number,while the stress accuracy remains almost the same.When the distortion mesh is encountered,the Q8_Legendre element exhibits the performance of antidistortion ability,and locking phenomenon does not appear.
作者
乔海青
鲍四元
沈峰
QIAO Haiqing;BAO Siyuan;SHEN Feng(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)
出处
《中山大学学报（自然科学版）（中英文）》
CAS
CSCD
北大核心
2024年第3期163-171,共9页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
江苏省高校青蓝工程(2022GX05)
江苏省研究生科研创新与实践计划项目(KYCX23_3332)。
关键词
平面问题
泡状函数
位移修正模型
高斯积分
抗畸变
plane problem
Bubble function
displacement correction model
Gauss quadrature
antidistortion
