�ֱ�����˽Ӵ������MLPG(Meshless Local Petrov-Galerkin)�����㷨�����ۻ������Ƶ�����ع�ʽ�����������ֵ��ͽӴ�״̬�Ķ���������ʹ�ö�ά���Ի�����������������������Ȩ������ͨ���ƶ���С���˷���ֵ����MLPG�����㷨���õ��Ӵ������У�ʹ�÷���������ӱ��ʱ߽��������Զ�ά���ԽӴ�����ĽӴ����̽���ģ�⣬���������õ���ʵ�ĽӴ������������һ���µ�Ӧ����λ�Ʒ�������ѧ���ģ�ͣ�����Ŵ��㷨��ʵ�ʹ��̽Ӵ��������������Ż��������Ż������Ŀ�꺯���仯���ߣ��������������Ƚϣ���֤�˸÷�������Ч��.
The theory of contact problem and meshless local Petrov-Galerkin(MLPG) mixed collocation method was introduced, the correlative formula was conducted, and the definite condition of two typical contact state was presented. The MLPG mixed collocation method was used in contact analysis through two-dimension linear basis function, cubic spline weight function and moving least square shape function. The essential boundary condition was imposed by penalty function method, the contact process of two-dimension elastic contact problem was simulated, real contact state was received by iteration, and a new stress-displacement non-linear mathematics solution model was proposed, engineering contact problem was solved and optimized with genetic algorithm, the optimization result and the change curve of objective function was presented. Numerical examples show that the proposed method is effective.