Based on the static theorem of shakedown analysis,a novel numerical method is developed to perform lower bound shakedown analysis by means of meshless local Petrov-Galerkin method(MLPG) with the Voronoi cells and the reduced-basis technique.

Examples show the local Petrov-Galerkin method is effective for large deformation analysis.

The meshless local Petrov-Galerkin method(MLPG) is used to numerically find the solutions of a crack of finite specimen under a impact load.

The meshless local Petrov-Galerkin method, which is based on the Voronoi cells and natural neighbour interpolations, is presented for solving the planar elasticity problem in this paper.

A local Petrov-Galerkin (MLPG) method for the stability analysis of anisotropic thin plate;

A modified meshless local Petrov-Galerkin (MLPG) method is presented for solving the plane stress problems of the incompressible hyperelastic materials.

An h-adaptive analysis based on the meshless local Petrov-Galerkin method was presented.

The thin beam on a nonlinear foundation was analysed by meshless local Petrov-Galerkin method.

Petrov-Galerkin method for the circular arch problem;

Petrov-Galerkin method is employed to obtain the optimal error estimates of GKdV equations.