Node-by-node meshless approach and its applications to structural analyses

The meshless method is expected to become an e!ective procedure for realizing a CAD/CAE seamless system for analyses ranging from modelling to computation, because time-consuming mesh generation processes are not required. In the present study, a new meshless approach, referred to as the Node-By-Node Meshless method is proposed, in which only nodal data is utilized to discretize the governing equations, which are derived using either the principle of virtual work or the Galerkin method. In this method, three key methodologies are utilized: (i) nodal integration using stabilization terms, (ii) interpolation by the Moving Least-Squares Method, and (iii) a node-by-node iterative solver. This paper presents the formulation of the proposed method along with numerical results obtained for two-dimensional elastostatic and eigenvalue problems. Copyright ( 1999 John Wiley & Sons, Ltd