Reissner-Mindlin板壳无网格法的闭锁与灵敏度分析及优化的研究  

STUDY ON NUMERICAL LOCKING AND SENSITIVITY ANALYSIS AND OPTIMIZATION OF REISSNER-MINDLIN PLATE AND SHELL WITH MESHLESS METHOD

作　　者：龚曙光[1] 曾维栋[1] 张建平[1] 

机构地区：[1]湘潭大学机械工程学院,湖南湘潭411105

出　　处：《工程力学》2011年第4期42-48,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(50875223);湖南省教育厅重点项目(08A079);湖南省自科市州联合基金项目(09JJ9005)

摘　　要：该文利用罚函数法施加边界条件,建立了Reissner-Mindlin板壳无网格法的离散形式,通过数值锁死试验,探讨了EFG法、RPIM以及基于节点积分的无网格法在解决Reissner-Mindlin板壳闭锁问题中所存在的优缺点。所得结果表明,基于匹配近似场和节点积分方案的无网格法在处理剪切闭锁问题时具有优越性。然后以SCNI-MLS无网格法为基础,对Reissner-Mindlin板壳结构的尺寸、形状和轮廓设计进行了统一的设计灵敏度分析,结合约束变尺度序列二次规划法,完成了SCNI-MLS无网格法壳结构优化设计的算例,算例结果验证了所建立灵敏度分析的精度和优化方法的可行性。The meshfree discretization of a Reissner-Mindlin plate and shell is presented by using a Penalty function to impose the boundary conditions.Basing on a numerical locking test,the benefit and shortcoming of Element-free Galerkin（EFG） method,a radial point interpolation method（RPIM） and the Meshless with nodal integration for solving numerical locking are investigated.The result obtained show that the meshfree method with the matching approximation fields scheme and stabilized conforming nodal integration（SCNI） has its own superiority in solving locking problems.And then based on the SCNI-MLS meshfree method,a unified design sensitivity analysis for the Reissner-Mindlin plate and shell with respect to size,shape and configuration design variables is presented.The optimal design examples of a shell structure are achieved by integrating the SCNI-MLS with the sequential quadratic programming method.Numerical examples verified accuracy of the design sensitivity analysis and efficiency of the design optimization proposed.

关 键 词：无网格法 Reissner-Mindlin板壳 剪切锁死 灵敏度分析 优化设计 

分 类 号：TH123[机械工程—机械设计及理论] O241.82[理学—计算数学]