动态应力解空间谱元离散的关键时间点识别方法

Critical Time Points Identification Method for Solution Space of Dynamic Stress Based on Spectral Element

针对结构动态响应优化过程中动态分析的复杂性和高耗时性,提出动态应力解空间谱元离散的关键时间点识别方法。通过模态叠加法,获得结构动态应力解空间,将其在高斯-勒让德-罗巴托点谱元离散,构造时间点与其对应的动态应力解空间矩阵,应用Lagrange插值,得到高精度的近似函数。调用区域细分全局优化算法找到动态应力的绝对极大值点,即关键时间点。通过对动载荷作用下的124杆桁架结构和悬臂梁进行关键时间点识别,说明了提出方法的可行性和有效性。

According to the complexity and high-cost character of dynamic analysis in the processing of structural dynamic optimization, the critical time points identification method for solution space of dynamic stress based spectral element is proposed. The solution space of the structural dynamic stress is obtained by using the modal superposition method. And then, it is discretized as the spectral points about Gauss-Legendre-Lobatto. The matrices of time points and their corresponding solution space values of dynamic stress are constructed. The Lagrange interpolation techniques are applied in the solution space domain to get dynamic stress function of high precision. The absolute maximum point, which is the critical time point, is found by executing the global optimizer named Dividing RECTangles. Two examples of 124-member plane truss and the cantilever are used to illustrate the feasibility and validity of the proposed method.