Plate Bending Problems, Meshless Local Boundary Integral Equation Method

Local boundary integral equation method (LBIE) developed recently is a new efficient and flexible numerical method. LBIE, based on the local boundary equation, adopts the traditional moving least squares (MLS) approximation which depends on only the values of the nodes in the domain of the problem or along its boundary. The whole process of integration is carried on over a local domain or its local boundary centered at the node in question. The local boundary equation can be rewritten to represent the values of the unknown function at the point of interest, and the essential boundary conditions can be directly and easily enforced by using the Green formula and the characters of the Dirac function. So, no mesh is required either for purposes of interpolation of the solution variables, or for the integration of the energy, it is a real meshless method.In this paper, firstly, the theory and the discretization schemes of LBIE and the concepts of MLS and GMLS are introduced; secondly, LBIE method is applied to solve the thin plate-bending problems and four typical examples are given to demonstrate the applicability and validity of the method. The results obtained from numerical examples agree well with the exact solutions and have an excellent rate of convergence. Then, several conclusions and discussions are made. At the end of the paper, a computer program by the language MATLAB is provided and the functions of sub-routines are presented.