基于多重多级动力子结构的瞬态分析方法

提出利用多重多级子结构技术与Newmark算法求解结构动力学方程的高精度算法.该算法利用静凝聚技术列式简单,在凝聚过程中并不引入任何近似的优点,采用子结构周游树技术,分别对每个子结构求解Newmark等效平衡方程,最后通过回代求解得到整体结构的响应.由于该算法考虑了子结构内部自由度对整体求解的贡献,算法实施不受子结构划分方式的限制,因此可以得到系统高阶模态对响应分析的影响.该算法计算精度与传统的全结构求解相当,计算效率高,消耗计算机资源少,且可构造为统一的多重多级子结构综合分析算法框架.数值算例验证了该算法的正确性和有效性.

Transient analysis method based on multi-level dynamic substructures

A combined method based on multi-level substructural technique and Newmark algorithm is proposed for solving dynamical equations of structures.By employment of Newmark algorithm,the dynamical equations can be converted to be equivalent equilibrium equations and then the global equations are formed by static condensation method for each substructure,and finally response of overall structure is solved by backward substitution.Substructural tree travelling and static condensation techniques are used in the solution process.Its advantages are simple and accurate (without any approximation).In transient analysis,higher modes of response can be obtained,because the contribution of all internal DOFs of each substructures to overall structure can be taken into account.Furthermore,the partition scheme of substructures does not affect numerical precision,and this algorithm can be used to construct a unified algorithmic framework for general-purpose multi-level substructural analysis.Numerical results validate the correctness and efficiency.