基于边光滑有限元法的剪切变形板几何非线性分析  

Geometric nonlinear analysis on shear deformation plates using edge-based smoothed finite element method

作　　者：崔向阳[1] 李光耀[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《计算机辅助工程》2011年第1期155-162,共8页Computer Aided Engineering

基　　金：国家自然科学基金(11002053);国家重点基础研究发展计划("九七三"计划)(2010CB328005);汽车车身先进设计制造国家重点实验室资助课题;中央高校基本科研业务费项目

摘　　要：为改善在计算板的几何非线性问题时有限元法系统过硬的数值缺陷,提高计算精度,在考虑剪切变形的von Karman假设下,基于全拉格朗日描述方法,将边光滑有限元法应用于板的几何非线性分析.计算公式基于1阶剪切变形理论,并采用离散剪切间隙有效地消除剪切自锁.在三角形单元的基础上进一步形成边界光滑域,在每个光滑域内对应变进行光滑操作并进行数值积分,并通过光滑Galerkin弱形式得到离散方程.数值算例的结果表明:基于边的光滑操作在一定程度上软化数值模型,改善传统有限元系统过刚的数值缺陷,提高数值解的精度.To overcome the over-stiff phenomenon in finite element method system and improve the calculation accuracy,the edge-based smoothed finite element method is applied to geometric nonlinear analysis on plates based on von Karman assumption which is in considering shear deformation and Total Lagrange description method.The formulations are based on the first order shear deformation theory and the shear locking is eliminated by using discrete shear gap.The edge-based smoothing domains are further formed based on the triangular elements,the strain smoothing operation and numerical integration are implemented and performed in each smoothing domain.And the discretized system equations are obtained using the smoothed Galerkin weak form.The results of numerical examples demonstrate that the edge-based smoothing operation can provide much needed softening effect to the numerical model to reduce the overly-stiff behavior of the finite element system and hence improve significantly the accuracy of the solution.

关 键 词：边光滑有限元法 非线性 有限元法 应变光滑 

分 类 号：O241.82[理学—计算数学] TB115.7[理学—数学]