M. Kaminski. Perturbation-based stochastic finite element method using polynomial response function for the elastic beams. Mechanics Research Communications, 2009, 36: 381-390.
Theoretical Inference of the Dynamic Stochastic Finite Element Method Based on the Virtual Displacement Principle
虚位移原理, 摄动技术, 八节点四边形对称等参单元, 动态随机有限元
Virtual Displacement Principle; Perturbation Technology; Axisymmetric Isoparametric Quadrilateral Element with Eight-Nodes; Dynamic Stochastic Finite Element
《Advances in Applied Mathematics》, Vol.2 No.2, 2013-05-23
对偏微分方程弱解的积分形式——虚位移原理进行较详细的研究，并构造出八节点四边形轴对称等参单元。然后从虚位移原理出发，给出轴对称动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动态随机有限元方程，提出了基于虚位移原理的动态随机有限元方法，该方法为研究工程对象的动态响应特性提供了一种新的解决途径。Virtual displacement principle which is the weak solution integral form of partial differential equations was researched in detail, and axisymmetric isoparametric quadrilateral element with eight-nodes was constructed. Then, based on the virtual displacement principle, the static equilibrium equation of the axisymmetric dynamic problems and the equivalent integral weak form under the boundary conditions of the force were derived, combined with perturbation technology, the dynamic stochastic finite element equation of the axisymmetric isoparametric quadrilateral element with eight-nodes was derived, and the dynamic stochastic finite element method based on the principle of the virtual displacements principle was put forward, the method provides a new solution for researching dynamic response characteristics of engineering objects.