MESHLESS LOCAL STRONG-WEAK (MLSW) METHOD FOR IRREGULAR DOMAIN PROBLEMS

The meshless local Petrov-Galerkin (MLPG) method is a representative meshless method, and is widely applied in computational mechanics. But, this method is necessary to execute the boundary integral operation, and it is always difficult to solve irregular domain problems. In order to remove this kind of limitation of the MLPG method, a meshless local strong-weak (MLSW) method is presented. The proposed method uses the MLPG method for domain discretization, adopts the meshless intervention-point (MIP) method for imposing the natural boundary conditions, and employs a collocation method for imposing the essential boundary conditions. Thus, the boundary integral is completely eliminated, and it favours to solve all kinds of irregular domain problem. Theoretically, the MLSW method deduced by coupling algorithm, not only has inherited the advantage of the MLPG method, which is always stable and accurate for numerical solution, but also has attained the superiority of the collocation-type method, which is naturally simple and flexible to cope with the domain of complex structure. Thereby, the method realizes advantageous complementarities of the weak-form method and the strong-form method. In addition, the MLSW method uses a moving least squares core (MLSc) approximation for constructing meshless shape function, which is an improvement for the traditional moving least squares (MLS) approximation. By replacing common basis function with core basis function, MLSc approximation is more stable and accurate, and also realizes a simple calculation for derivatives approximation. Early results with numerical tests have showed that the proposed new method is easy for numerical implementation, is accurate and stable for numerical solution, and is promising for engineering application.