梯形单元及其显式分析

Trapezoid Element and Its Explicit Analysis

本文介绍一种具有显式单刚的梯形元,它既是线性元,又能较方便拟合直线边界,且能直接获得单刚对结点座标的解析导数式,从而可推得位移应力等约束敏度,不必使用数值积分和差分求导,大大节省了机时,使有限元分析能与高效的优化算法有机结合。文中对比了几种其他类型的单元的计算,并给出了在重力坝分析上的应用情况。示例证明本文导出的显式刚度矩阵及其敏度公式正确无误,计算效率高,结果合理可信,能供工程实际应用。

The Paper presents a linear trapezoid element for 2-D finite element analysis. It has an explicit form of element stiffness matrix, and can easily fit any arbitrary linear boundary. Especially,it can provide analytical derivatives of element stiffness matrix with respect to nodal coordinates. So,formulations of sensitivity analysis for stress or displacement constraints can be formed explicitly without using numerical integration and the finite difference method. As a result, computational efforts reduce drastically and the FEM wil be able to combine with efficient optimum algorithms in structural optimization. A gravity concrete dam has been analyzed by the trapezoid elements. The comparison with several other types of element has also been tabulated at the end of the paper. Results strongly show that these formulas derived here are correct, efficient and reliable, and can be applied to practical engineering problems.