Development of a CAE system based on the node-by-node meshless method

Abstract

The authors propose a node-by-node meshless method (NBNM), which discretizes the weak-formed governing equations of continuum mechanics using only distributed nodal data. This method uses the following three core methodologies: (i) interpolation using the moving least squares method (MLSM) (ii) estimation of stiffness by nodal integration with stabilization terms, and (iii) a node-by-node iterative solver. This paper discusses the effect of the stabilization term introduced to the NBNM and examines the convergence of the NBNM approximation. An error indicator for NBNM analysis is proposed, and the development of a prototype CAE system based on this method is outlined. Moreover, results of two-dimensional plane stress analysis with adaptation are shown. In conclusion, this paper will show that the NBNM is capable of utilizing CAD data easily and performing effective adaptation analyses, and therefore may be used as a convenient CAE tool.