基于虚位移原理的随机有限元方法研究  

On the Stochastic Finite Element Method Based on the Virtual Displacement Principle

作　　者：周宗和[1] 尹喜庆[1] 

机构地区：[1]海军驻武汉四三八厂军事代表室,武汉430060

出　　处：《石河子大学学报（自然科学版）》2013年第2期242-248,共7页Journal of Shihezi University(Natural Science)

基　　金：装备预研基金项目(9140A27050106JB11)

摘　　要：为研究工程对象的响应特性提供一种新的解决途径,本文根据虚位移原理得出弹性体轴对称静态问题的平衡方程以及力的边界条件下的等效积分"弱"形式,结合摄动技术推导出八节点四边形轴对称等参单元的静态随机有限元方程,提出了基于虚位移原理的随机有限元方法,最后考虑汽轮机转子的物性参数和载荷参数的随机性,利用这种方法对汽轮机转子的静态随机响应特性进行计算和分析,并与直接Monte-Carlo模拟仿真法的计算结果相对比,验证了该方法的正确性和有效性。Based on the virtual displacement principle,the static equilibrium equation of the elastomer axisymmetric problems and the equivalent integral weak form under the boundary conditions of the force were derived. Combined with perturbation technol-ogy,the static stochastic finite element equation of the axisymmetric isoparametric quadrilateral element with eight-nodes was derivcd,and the stochastic finite element method based on the principle of the virtual displacements principle was put forward. Then, considering the randomness of the physical parameters and the load parameters of the steam turbine rotor, using the pro- posed method to calculate and analyze the static random response characteristics of the steam turbine rotor, and comparing with the calculated results through direct Monte-Carlo simulation method. This study proves the correctness and effectiveness of the method,which provides a new solution for researching response characteristics of engineering objects.

关 键 词：虚位移原理 摄动技术 八节点四边形轴对称等参单元 汽轮机转子 随机有限元 

分 类 号：O242[理学—计算数学]