摘要
论文将广义有限差分法用于数值计算Kirchhoff板和Winkler板的弯曲问题.广义有限差分法是基于最小二乘原理的一种区域型无网格方法.相比于传统的网格类数值解法,广义有限差分法无需网格生成且无需数值积分.通过数值实验结果表明,广义有限差分法可以有效地求解两类薄板在不同横向荷载作用下的弯曲问题.
A newly-developed domain-type meshless collocation method,the generalized finite difference method（GFDM）,is applied to solve the Kirchhoff and Winkler plate bending problems under different types of loading and varied boundary conditions.In comparison with the traditional finite difference method,the GFDM is free form mesh generation and numerical integration,which can be more flexible when the shape of the computational domain is irregular.Besides,the GFDM keeps the merits of simplicity and wide applicability in the classical finite difference method.In this study,the Kirchhoff and Winkler plate bending problems are governed by the fourth-order partial differential equations under Kirchhoff and Winkler assumptions,respectively.To solve these thin-plate bending problems,the moving least squares theory and fourth-order Taylor series expansion are used to construct the GFDM approximation formulation.Then the derivatives at each node in the computational domain are expressed by the linear combinations of nearby function values and weighting coefficients.The quartic spline is adopted as the weighting coefficient function in the GFDM.Several numerical examples have been tested to verify the accuracy and efficiency of the proposed GFDM.It is found that the generalized finite difference method with fewer discretization nodes provides accurate numerical results for solving Kirchhoff and Winkler plate bending problems under different types of transverse loading（e.g.,uniformly distributed loading,hydrostatic pressure loading,exponential-function type loading and periodic-function type loading）and varied boundary conditions（e.g.,simply-supported BC,clamped BC and free BC）in various computational domains（e.g.,square domain,sectoral domain and parallelogram plate）.The convergence analysis shows that the GFDM has a rapid convergence rate of solving thin-plate bending problems.In comparison with the boundary particle method（BPM）and the COMSOL software（the finite element method）,the results of the GFDM ar
作者
汤卓超
傅卓佳
范佳铭
Zhuochao Tang;Zhuojia Fu;Chiaming Fan(College of Mechanics and Materials,Hohai University,Center for Numerical Simutlation Software in Engineering ＆ Sciences,Nanjing,211100;Department of Harbor and River Engineering,Taiwan Ocean University,Keelung,20224)
出处
《固体力学学报》
CAS
CSCD
北大核心
2018年第4期419-428,共10页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金(11772119)
中国博士后科学基金(2014M561565,2015T80492)
中央高校基本科研基金(2016B06214)
江苏省青蓝工程项目资助
