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.