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发展了一种三维粘弹性摄动随机有限元法(VPSFEM),并对固体火箭发动机药柱进行了随机分析。以不可压和近似不可压粘弹性有限元方法为基础,采用一阶随机摄动技术处理结构分析参数的随机性,推导了三维粘弹性摄动随机有限元方法的递归方程组,并给出了结构响应统计特征的求解方法。推导过程中同时考虑了材料力学性能和载荷环境参数的随机性。算例分析中对典型载荷作用下的固体火箭发动机药柱结构进行了三维随机分析,结果表明三维粘弹性摄动随机有限元方法效率高,且精度能够满足工程需要。
A three-dimensional viscoelastic perturbation stochastic finite element method (VPSFEM) was developed. The solid rocket motor pellets were stochastically analyzed. Based on the incompressible and approximate incompressible viscoelastic finite element method, the randomness of structural analysis parameters is solved by the first-order stochastic perturbation technique, and the recursive equations of the three-dimensional viscoelastic perturbation stochastic finite element method are deduced. Solution Method of Structural Response Statistical Characteristics. The derivation process takes into account both the mechanical properties of the material and the randomness of the environmental parameters of the load. Three-dimensional random analysis of the solid rocket motor grain structure under typical loads is carried out in the case study. The results show that the three-dimensional viscoelastic perturbation stochastic finite element method is highly efficient and can meet the engineering requirements.