An improved weak-form quadrature element (IWQE) method for static and dynamic analysis of non-homogeneous plane trusses
An improved weak-form quadrature element (IWQE) method for static and dynamic analysis of non-homogeneous plane trusses
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DOI：
10.1016/j.engstruct.2022.115410
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发表时间：
2023-02
影响因子：
5.5
通讯作者：
Kai Wang;C. Feng;D. Zhou
中科院分区：
文献类型：
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作者：
Kai Wang;C. Feng;D. Zhou
基于Chebyshev插值和Gauss-Lobatto正交，结合变分原理，提出了一种改进的弱形式正交单元法（IWQE），并对其进行了进一步定制。与采用拉格朗日插值和高斯正交的现有WQE方法相比，该方法对具有大量正交点的元素具有鲁棒性。与有限元法的单元刚度矩阵为正半确定相比，IWQE法的单元刚度矩阵总是正半确定的。因此，元素内部节点的位移只能通过使用其结束节点的值来唯一地表示。因此，组装矩阵的大小仅取决于末端节点的数量，整个结构的组装矩阵的顺序可以大大降低。这些属性可以大大提高计算效率。为验证所建立的IWQE方法，以非均质平面桁架结构为例进行了静动力分析。与微分正交元（DQE）、微分正交元（WQE）和有限元方法相比，本文提出的微分正交元方法具有更好的收敛性、精度和鲁棒性，为分析非齐次结构提供了更有效、更强大的数值工具。
Based on Chebyshev interpolation and Gauss-Lobatto quadrature together with the variational principle, an improved weak-form quadrature element (IWQE) method is developed and further customized for analyzing plane truss structures. Compared to existing WQE method which adopts Lagrange interpolation and Gauss quadrature, this developed IWQE method has demonstrated robustness for elements with a large number of quadrature points. Compared to finite element (FE) method whose stiffness matrix of an element is positive and semi-definite, the stiffness matrix of the IWQE method of an element is always positive and definite. Therefore, the displacements of an element's internal nodes can be uniquely expressed by using the values of its end nodes only. Accordingly, the sizes of the assembled matrices only depend on the number of end nodes and the orders of the assembled matrices for the whole structure can be greatly reduced. Such attributes can substantially increase the computational efficiency. To validate the developed IWQE method, the static and dynamic analysis of a plane truss structure with non-homogeneous properties are taken as an example for case study. Compared to the other numerical methods, such as differential quadrature element (DQE), WQE and FE, this IWQE method developed in present work demonstrates better convergence, accuracy and robustness, providing a more efficient and powerful numerical tool for analyzing structures with non-homogeneous attributes.