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微分求积法(DQ法)是一种高精度,高计算效率的微分方程数值求解方法。该文采用微分求积法进行了结构弹塑性地震反应分析。针对结构弹塑性地震反应分析的特点,对于采样周期内地震加速度记录的增量分布做了线性假定,采用了一种新型的不等距的时间网格并在新的网格上实施DQ算法。对于拐点的处理则提出了一种简单的迂回处理方法,可以方便地利用现有研究成果来完成DQ方案中拐点的处理。数值算例的结果表明:采用微分求积法求解结构弹塑性地震反应可以达到较高的计算精度并且可以从两个方面提高计算效率。
The differential quadrature method (DQ method) is a numerical solution method of differential equations with high precision and high computational efficiency. In this paper, the structure elastic-plastic seismic response analysis is carried out by using differential quadrature method. Aiming at the characteristics of structural elastoplastic seismic response analysis, a linear assumption is made for the incremental distribution of seismic acceleration records during the sampling period. A new type of time grid with non-equidistant distance is used and the DQ algorithm is implemented on the new grid. For the treatment of inflection points, a simple detouring method is proposed, which can easily use the existing research results to complete the inflection point processing in the DQ scheme. Numerical examples show that using differential quadrature method to solve elasto-plastic seismic response of structures can achieve high computational accuracy and improve computational efficiency in two aspects.