基于S-R和分解定理的无网格法在功能梯度板中的应用

doi:10.12066/j.issn.1007-2861.2266

上海大学学报(自然科学版) ›› 2022, Vol. 28 ›› Issue (4): 702-714.doi: 10.12066/j.issn.1007-2861.2266

• 研究论文 • 上一篇

基于S-R和分解定理的无网格法在功能梯度板中的应用

宋彦琦(), 石博康, 李向上

中国矿业大学(北京) 力学与建筑工程学院, 北京 100083

收稿日期:2020-01-22 出版日期:2022-08-30 发布日期:2020-10-21
通讯作者: 宋彦琦 E-mail:songyq@cumtb.edu.cn
作者简介:宋彦琦(1969—), 女, 教授, 博士, 博士生导师, 研究方向有限变形力学理论及应用. E-mail: songyq@cumtb.edu.cn
基金资助:
国家重点研发计划资助项目(2018YFC0808402)

Application of a meshless method based on the S-R decomposition theorem in functionally graded plates

SONG Yanqi(), SHI Bokang, LI Xiangshang

School of Mechanics & Civil Engineering, China University of Mining an Technology(Beijing), Beijing 100083, China

Received:2020-01-22 Online:2022-08-30 Published:2020-10-21
Contact: SONG Yanqi E-mail:songyq@cumtb.edu.cn

摘要/Abstract

摘要：

为了研究功能梯度板的非线性变形问题, 以 S-R 和分解定理为基础, 从虚功率原理出发, 结合更新拖带坐标系法、无网格 Galerkin 法, 推导出用于求解三维几何非线性问题的离散方程. 利用 MATLAB 编写无网格法程序, 对功能梯度板的非线性弯曲问题进行求解, 并研究板的体积分数指数和宽厚比对板弯曲的影响. 将计算结果与已有成果进行了比较, 验证了三维 S-R 无网格法求解功能梯度板大变形问题的合理性.

关键词: S-R 和分解定理, 几何非线性问题, 无网格 Galerkin 法, 功能梯度板

Abstract:

To study the nonlinear deformation problem of functionally graded plates, this study uses the S-R decomposition theorem combined with the updated comoving coordinate system method and meshless Galerkin method to derive a discrete equation for solving three-dimensional geometric nonlinear problems. The meshless method is programmed by MATLAB. The nonlinear bending problem of the functionally graded plate is first solved, and the effects of the volume fraction index and width-thickness ration on the bending of plates are studied. Results are compared with existing results, and the rationality of solving the large deformation problem of functionally graded plates using the three-dimensional S-R meshless method is verified.

Key words: S-R decomposition theorem, geometrically nonlinear problem, meshless Galerkin method, functionally graded plates

中图分类号:

O347

宋彦琦, 石博康, 李向上. 基于S-R和分解定理的无网格法在功能梯度板中的应用[J]. 上海大学学报(自然科学版), 2022, 28(4): 702-714.

SONG Yanqi, SHI Bokang, LI Xiangshang. Application of a meshless method based on the S-R decomposition theorem in functionally graded plates[J]. Journal of Shanghai University（Natural Science Edition）, 2022, 28(4): 702-714.

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基于S-R和分解定理的无网格法在功能梯度板中的应用

Application of a meshless method based on the S-R decomposition theorem in functionally graded plates

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