用微分求积法求解梁的弹塑性问题

ELASTO-PLASTIC ANALYSIS OF BEAMS BY DIFFERENTIAL QUADRATURE METHOD

根据梁塑性弯曲的工程理论,采用微分求积法进行了梁的弹塑性平面弯曲分析。微分求积法是一种直接求解微分方程(组)的数值方法,不依赖于变分原理,且能以较少的网格点求得微分方程的高精度数值解。与有限元分析结果的比较,表明了微分求积法求解梁的弹塑性问题的计算效率和精度。微分求积法的计算结果不受荷载步长的限制,也不需要迭代求解,特别对于承受非线性分布荷载作用的梁的弹塑性分析具有很大的优越性。通过选用不同的网格点数目,分析了微分求积法的稳定性和收敛性。

According to the engineering theory of plastic bending, the elasto-plastic bending analysis of a beam is conducted using differential quadrature method. Differential quadrature method is a numerical approach for directly solving the governing differential equations of a problem and it is not based on variation principles. Numerical solutions with high accuracy are often obtained with fewer grid points in the method. Numerical results from this approach are compared with those obtained from finite element method and the calculating efficiency and precision are assessed. It is shown that the solutions are not affected by the length of load steps and iteration is avoided. Especially for the elasto-plastic analysis of beams subjected to a distributed load of nonlinearly varying intensity, differential quadrature method has more advantages over finite element method. The stability and convergence of differential quadrature method are also studied.