微分求积法在立方准晶矩形薄板的应用  

Application of differential quadrature method to cubic quasicrystal rectangular thin plate

作　　者：赵延军 周彦斌[1] 刘官厅[1] ZHAO Yan-jun;ZHOU Yan-bin;LIU Guan-ting(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,Inner Mongolia,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《宝鸡文理学院学报（自然科学版）》2022年第4期7-13,20,共8页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：内蒙古自然科学基金项目(2020LH01011);内蒙古师范大学高层次人才引进科研项目(2019YJRC005)。

摘　　要：目的 研究三维立方准晶矩形薄板在两侧具有非线性分布的余弦压缩载荷作用下的应力分布。方法 通过使用微分求积法,把求解微分方程问题转化为求解线性方程组问题。结果 求解方程组得到声子场和相位子场在立方准晶矩形薄板各位置的应力分量。结论 通过数值结果得到声子场和相位子场的应力变化趋势图,对三维立方准晶薄板的屈曲分析具有一定的指导意义。Purposes-To investigate the stress distribution of three-dimensional cubic quasicrystal rectangular thin plate under cosine compression loading with nonlinear distribution on both sides. Methods-The differential quadrature method is used to transform the problem of solving differential equations into the one of solving linear equations. Results-The stress components of phonon field and phason field in cubic quasicrystal rectangular thin plate are obtained by solving the equations. Conclusions-The stress trend diagram of phonon field and phason field is obtained by numerical results, which has certain guiding significance for the buckling analysis of three-dimensional cubic quasicrystal thin plate.

关 键 词：余弦载荷分布 立方准晶 微分求积法 应力分布 

分 类 号：O343[理学—固体力学]