Efficient Mesh-freee Methods for Plate Analysis

Abstract

Based on the existing foundation, the development of two mesh-free methods, namely LSFD method and LRBFDQ method, is advanced further in following aspects: (a)high order schemes of LSFD are introduced, (b)the chain rule for discretization of high order derivatives is proposed, (c)the LSFD and LRBFDQ formulations in terms of local (n, t)-coordination system at boundary are developed, (d)a practical approach for searching a proper value of the shape parameter in LRBFDQ is proposed. By making use of these new developments in conjunction with the property of local mesh-free approximation and the enforcement of all boundary conditions, following numerical difficulties have been overcome: (1)modeling of complex domain shapes, (2)accurate approximation of high order derivatives, (3)capturing of steep variations of functions and derivatives, and (4)implementation of multiple boundary conditions. In this thesis, a wide range of plate problems and other engineering problems with various complexities have been solved.