A Novel Weak-Form Space Quadrature Element Method and Application in Analysis of Non-Homogeneous Truss Structure

Abstract

This work proposes an improved weak-form quadrature element (IWQE) method for analyzing non-homogeneous space truss structures. The present method combines the high accuracy of the traditional WQE method with the universality of the standard finite element (FE) method. In the analysis, the structure is divided into a series of non-homogeneous elements with large sizes, and discrete function values are used to describe unknown mechanical properties in an element. Chebyshev–Lobatto differential quadrature and Gauss–Lobatto integral quadrature are used to deal with the energy variation of the element. Therefore, the endpoints of the element are included in the quadrature points, resulting in symmetric and positive definite stiffness matrix and diagonal mass matrix that represent internal point displacements by its endpoints in advance, significantly reducing order. All the elements can be easily and conveniently implemented as in FE. Both displacement and force boundary conditions are considered, leading to easier element assembly and smaller global matrices than traditional WQE while maintaining higher accuracy than FE. A non-homogeneous space truss composed of 40 bars is taken as an example to demonstrate the merits of the proposed method in accuracy, efficiency and robustness. The order of the global matrix equation is only 51 in present method.