任意壳线性弯曲与自由振动分析的最小二乘无网格法

陈卫1,杨健生1,韦冬炎1,谌亚菁1,彭林欣1,2,3

振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 125-134.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (16) : 125-134.
论文

任意壳线性弯曲与自由振动分析的最小二乘无网格法

  • 陈卫1,杨健生1,韦冬炎1,谌亚菁1,彭林欣1,2,3
作者信息 +

Bending and vibration analysis of an arbitrary shell by the moving-least square meshfree method

  • CHEN Wei1,YANG Jiansheng1,WEI Dongyan1,SHEN Yajing1,PENG Linxin1,2,3
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摘要

提出了一种求解任意壳结构线性弯曲与自由振动的最小二乘无网格法。利用映射技术并结合Mindlin板壳理论将三维任意壳参数化曲面转换成二维无网格模型。基于移动最小二乘法近似和一阶剪切变形理论求出其位移场,利用最小势能原理及Hamilton原理分别得到其弯曲及自由振动控制方程。由于该方法不能直接施加本质边界条件,故采用完全转换方法引入本质边界条件。文末以几种典型的不同形状壳结构算例表明,该研究的解与理论解或ABAQUS有限元解吻合良好,证明了该方法在计算任意壳的线性弯曲与自由振动的有效性及准确性。
关键词:映射技术;任意壳;移动最小二乘;无网格法;完全转换法

Abstract

A moving-least square meshfree method for linear bending and free vibration of arbitrary shell structures is proposed in this paper. By using the mapping technology in conjunction with the Mindlin’s theory of plates and shells, the 3D arbitrary shell parametric surface is converted into a 2D meshfree model. Based on the moving-least square (MLS) approximation and the first-order shear deformation theory, the displacement field of arbitrary shell is obtained, and the bending and free vibration control equations are obtained by using the minimum potential energy principle and Hamilton principle, respectively. Because the essential boundary conditions cannot be imposed directly, the full transformation method is used to introduce the essential boundary conditions. At the end of this paper, several examples of different shape shell structures show that the solutions in this paper are in good agreement with the theoretical solutions or ABAQUS finite element solutions, which validate the effectiveness and accuracy of this method in calculating the linear bending and free vibration of arbitrary shells.
Keywords: mapping technology; arbitrary shells; moving-least squares; meshfree method; full transformation method

关键词

映射技术 / 任意壳 / 移动最小二乘 / 无网格法 / 完全转换法

Key words

mapping technology / arbitrary shells / moving-least squares / meshfree method / full transformation method

引用本文

导出引用
陈卫1,杨健生1,韦冬炎1,谌亚菁1,彭林欣1,2,3. 任意壳线性弯曲与自由振动分析的最小二乘无网格法[J]. 振动与冲击, 2022, 41(16): 125-134
CHEN Wei1,YANG Jiansheng1,WEI Dongyan1,SHEN Yajing1,PENG Linxin1,2,3. Bending and vibration analysis of an arbitrary shell by the moving-least square meshfree method[J]. Journal of Vibration and Shock, 2022, 41(16): 125-134

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