A localized MAPS using polynomial basis functions for the fourth-order complex-shape plate bending problems

摘要

In this paper, the localized method of approximate particular solutions using polynomial basis functions is proposed to solve plate bending problems with complex domains. The closed-form particular solutions of fourth-order differential equations can be reduced to the linear combination of the particular solutions of Helmholtz and modified Helmholtz equations. To alleviate the difficulty of solving overdetermined fourth-order plate bending problems using the localized collocation method, additional ghost points outside the computational domain are introduced to improve the stability and accuracy. Three examples are illustrated to validate the feasibility of the proposed localized MAPS.