准晶问题多项式应力函数及其在有限元中的应用  

Polynomial Stress Functions of Quasicrystal Problems and Their Applications in FEM

作　　者：赵颖涛[1] 杨宇威 章伟 ZHAO Yingtao;YANG Yuwei;ZHANG Wei(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Jiangxi Hongdu Aviation Industry Co.Ltd.,Nanchang,Jiangxi 330096,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]江西洪都航空工业集团有限责任公司,江西南昌330096

出　　处：《北京理工大学学报》2024年第9期887-894,共8页Transactions of Beijing Institute of Technology

基　　金：航空科学基金资助项目(20172972002)。

摘　　要：本文基于广义Lekhnitskii各向异性弹性理论,提出了一种确定准晶问题多项式应力函数的系统性方法,并将之应用于杂交应力函数(HSF)单元的构造.结果表明,对于准晶平面问题,任意齐n次多项式应力函数至多存在6个独立的多项式,且多项式应力函数的一般表达式可以显式地给出.所得的多项式作为解析试函数用于构造准晶问题的新型八节点HSF单元,与传统的有限元相比,HSF单元具有更高的精度和更优异的性能.In this paper,systematic approaches to determining polynomial stress functions for quasicrystal plane problems were presented based on the generalized Lekhnitskii’s anisotropic elasticity theory.The approaches were applied to develop hybrid stress function(HSF)finite elements.Results show that for quasicrystal plane problems,an arbitrary nth-degree homogeneous polynomial encompasses a maximum of six independent polynomials,and the general expression of the polynomial stress function can be explicitly expressed.The obtained polynomials are used as analytical trial functions to construct a novel 8-node hybrid stress function(HSF)element.In comparison with traditional numerical methods,HSF demonstrates higher accuracy and superior performance.

关 键 词：多项式应力函数 准晶 解析试函数 杂交应力函数(HSF)单元 

分 类 号：O347.3[理学—固体力学]