An improved weak-form quadrature element (IWQE) method for static and dynamic analysis of non-homogeneous plane trusses

Abstract

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.