用局部Petrov-Galerkin方法求解不可压超弹性材料问题

用一种修正的无网格局部Petrov-Galerkin方法求解了不可压超弹性材料平面应力问题。在建立求解方程过程中,采用径向基函数耦合多项式构造近似函数,并以Heaviside分段函数作为加权函数简化了刚度矩阵的域积分,引入平面应力假设避免了材料不可压引起的数值求解困难。数值算例表明:该文方法求解不可压超弹性材料平面应力问题具有稳定性好、精度高的特点。

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR SOLVING INCOMPRESSIBLE HYPERELASTIC PROBLEMS

A modified meshless local Petrov-Galerkin (MLPG) method is presented for solving the plane stress problems of the incompressible hyperelastic materials. To develop the proposed method, trial functions are constructed using the radial basis function (RBF) coupled with a polynomial basis function when the governing equations are established, and a simple Heaviside test function is chosen to simplify the domain integral of the stiffness matrix in the MLPG method. Moreover, the plane stress hypothesis is employed to overcome the numerical difficulties induced by the incompressibility in the plane stress problems. Examples show that the proposed method possesses high stability and reasonable accuracy for solving the plane stress problems of the incompressible hyperelastic materials.