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A localized MAPS using polynomial basis functions for the fourth-order complex-shape plate bending problems
Archive of Applied Mechanics ( IF 2.8 ) Pub Date : 2020-06-23 , DOI: 10.1007/s00419-020-01718-y
Zhuo-Chao Tang , Zhuo-Jia Fu , C. S. Chen

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.

中文翻译:

使用多项式基函数的局部MAPS用于四阶复杂形状板的弯曲问题

本文提出了一种基于多项式基函数的近似特定解的局部化方法,以解决复杂区域的板弯曲问题。可以将四阶微分方程的闭式特殊解简化为亥姆霍兹方程和修正的亥姆霍兹方程的特定解的线性组合。为了减轻使用局部配置方法解决超定四阶板弯问题的难度,引入了计算域之外的其他重影点以提高稳定性和准确性。说明了三个示例,以验证所提出的本地化MAPS的可行性。
更新日期:2020-06-23
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