弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法

彭林欣1,2,3,谌亚菁1,覃霞1,杨健生1

振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 11-22.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 11-22.
论文

弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法

  • 彭林欣1,2,3,谌亚菁1,覃霞1,杨健生1
作者信息 +

Meshless method for static bending and free bending vibration analysis of  stiffened circular plates on elastic foundation

  • PENG Linxin1,2,3, SHEN Yajing1, QIN Xia1, YANG Jiansheng1
Author information +
文章历史 +

摘要

基于一阶剪切理论和移动最小二乘法,提出分析弹性地基圆形加肋板线性弯曲的静力和自由振动问题的无网格方法。对弹性地基采用文克勒地基模型,对圆形加肋板则将平板和肋条分开考虑,通过位移协调条件建立两者的参数转换方程。平板和肋条均采用一系列点来离散,用移动最小二乘法建立的形函数来分别描述两者的位移场,再分别通过最小势能原理和哈密顿原理导出弹性地基的静力弯曲和弯曲自由振动控制方程,最后采用完全转换法处理边界条件。以一系列不同基床系数、荷载、边界、肋条布置方式的弹性地基圆形加肋板为例,研究所提出方法的收敛性和稳定性,并将计算结果与有限元、文献对比。研究表明该方法可以有效分析弹性地基圆形加肋板线性弯曲的静力和自由振动问题,且肋条位置改变时,可避免网格重构。

Abstract

Based on the first-order shear deformation theory, a meshless method for bending analyses of stiffened circular plates in static and free vibrational state on elastic foundation is proposed. Winkler foundation is used to model the elastic foundation. The stiffened circular plate is modelled as a composite structure that consists of a flat circular plate and many stiffeners. A series of points are used to discretize the flat circular plate and stiffeners to obtain the mesh-free model. The moving least-squares approximation is used to construct the shape functions and to derive the displacement fields of the flat circular plate and stiffeners, respectively. The total potential energy and kinetic energy of the stiffened circular plate is obtained according to the compatibility condition between the flat circular plate and the stiffeners. The equations governing the bending behaviors of the stiffened circular plate in static and free vibrational state are derived according to the principle of Minimum Potential Energy and the Hamilton's Principle, respectively. The boundary conditions are enforced by the full transformation method. The convergence of the proposed method and the domain of influence that affects the calculated results are studied. Several numerical examples are calculated by the proposed method and compared with the results available in the literature or given by the finite element software ABAQUS. The results show that the proposed method frees the researchers from determining a nodal line on the plate along every stiffener, which is very beneficial for carrying out optimization studies on stiffeners’ locations.

关键词

弹性地基 / 圆形加肋板 / 线性弯曲 / 自由振动 / 无网格

Key words

elastic foundation / stiffened circular plate / linear bending / free vibration / meshless method

引用本文

导出引用
彭林欣1,2,3,谌亚菁1,覃霞1,杨健生1. 弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法[J]. 振动与冲击, 2022, 41(7): 11-22
PENG Linxin1,2,3, SHEN Yajing1, QIN Xia1, YANG Jiansheng1. Meshless method for static bending and free bending vibration analysis of  stiffened circular plates on elastic foundation[J]. Journal of Vibration and Shock, 2022, 41(7): 11-22

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