三维弹塑性问题的比例边界有限元法  

Scaled boundary finite element method for three-dimensional elastoplastic problems

作　　者：李云[1] 杜成斌[1] 江守燕[1] LI Yun;DU Chengbin;JIANG Shouyan(College of Mechanics and Engineering Science,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学力学与工程科学学院,江苏南京210098

出　　处：《河海大学学报（自然科学版）》2024年第4期47-55,共9页Journal of Hohai University(Natural Sciences)

基　　金：国家重点研发计划项目(2018YFE0122400);国家自然科学基金项目(51579084)。

摘　　要：为了研究三维复杂结构的非线性硬化问题,在考虑关联流动准则的Von Mises塑性屈服准则和各向同性/随动硬化准则的本构模型中,引入一致切线模量,并基于比例边界有限元方法和平衡八叉树算法对本构模型进行求解。采用Newton-Raphson迭代法求解位移和应力的非线性方程,为了减少计算量,仅在比例中心点执行并储存迭代过程的变量,同时采用Fortran语言编制了求解程序。两个算例计算结果表明,该模型的计算结果具有较高的准确性。In order to study the nonlinear hardening problem of three-dimensional complex structural materials,the consistent tangent modulus was introduced into the constitutive model considering the Von Mises plastic yield criterion and isotropic/kinematic hardening model,and the constitutive model was solved based on the scaled boundary finite element method(SBFEM)and balanced octree algorithm.The Newton Raphson iteration method was used to solve the elastic-plastic increment of displacement and stress.In order to reduce the computational complexity,the variables of the iteration process were only executed and stored at the proportional center point of the subdomain.At the same time,a solution program was developed using Fortran language.Two application examples show that the calculation results of the model have high accuracy.

关 键 词：三维比例边界有限元法 八叉树网格 弹塑性 屈服准则 硬化问题 

分 类 号：O346[理学—固体力学]