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.

这项工作提出了一种改进的弱形式正交单元（IWQE）方法来分析非均匀空间桁架结构。本方法结合了传统WQE方法的高精度和标准有限元(FE)方法的普适性。分析时，将结构划分为一系列大尺寸的非齐次单元，并用离散函数值来描述单元中未知的力学性能。采用Chebyshev-Lobatto微分求积法和Gauss-Lobatto积分求积法来处理单元的能量变化。因此，单元的端点包含在求积点中，从而得到对称且正定的刚度矩阵和对角质量矩阵，提前通过其端点表示内部点位移，从而显着降低了阶数。所有元素都可以像在 FE 中一样轻松方便地实现。同时考虑了位移和力边界条件，与传统 WQE 相比，单元组装更容易，全局矩阵更小，同时保持比 FE 更高的精度。以由40根杆组成的非均质空间桁架为例，证明了该方法在准确性、效率和鲁棒性方面的优点。本方法中全局矩阵方程的阶数仅为51。