Meshless Local Boundary Element Method For 2D Elastic And Elastoplastic Problems

Meshless methods which overcome the drawbacks of FEM and BEM are newly numerical methods. Meshless local boundary element method is a true meshless method with the advantages of EFG, FEM and BEM.In the paper, the local boundary integral equation is developed, its shape function is constructed by the moving least square approximation. The integral singularities caused by the companion solution is handled, without introducing CPV integral, its validity of the method is proved by numerical examples which show the high accuracy of the equations. The influence of the size of local domain and parameters in weight functions are studied, some effective advice is given. Strain norm and stress norm are used to evaluate the computing accuracy. At last, the numerical examples demonstrate the algorithm's effectiveness and reliability.Based on the above research, the method is applied to solve elastoplastic problems, the related equations are proposed, and the computing flow chart is given. Finally, a summary is made and the outlook for application and development of the method are prospected.