杂交型无网格有限体积法及其应用

从有限体积法基本思想出发,采用移动最小二乘近似方案实现有限体积法与无网格法的结合,从而使有限体法摆脱网格的约束,在此基础上,提出杂交型无网格有限体积法,所谓杂交是指对位移和应力都分别进行独立插值,这样可避免在子域积分过程中被积函数出现形函数的偏导数。至于应力和位移之间的协调关系则通过配点法强制实现,采用修正配点法施加本质边界条件。算例结果表明,该方法具有很高的精度和计算效率。

A HYBRID MESHLESS FINITE VOLUME METHOD AND ITS APPLICATION

To avoid mesh restriction,the finite volume method(FVM) is combined with the meshless method based on the moving least squares(MLS) approximation.A hybrid meshless finite volume method(MFVM) is presented.Here,"hybrid" has the same meaning as the hybrid finite element.By the hybrid technique,both the displacement and the stress are independently interpolated.In this way,the derivatives of shape functions in integrand on the process of sub-domain integration will disappear.Then,the stress-displacement compatibility is implemented by the collocation method.Essential boundary conditions are imposed using a modified collocation technique.Numerical results in the case studies show that the presented method has higher accuracies and computational efficiencies.