无额外自由度广义有限元的近不可压弹-塑性分析
Nearly Incompressible Elasto-Plastic Analysis of Extra-DOF-Free Generalized Finite Elements
马今伟 1段庆林2
作者信息
- 1. 大连理工大学 工业装备结构分析优化与CAE软件全国重点实验室,辽宁 大连 116024
- 2. 大连理工大学 大连理工大学白俄罗斯国立大学联合学院,辽宁 大连 116024
- 折叠
摘要
研究了常规有限元方法在近不可压弹-塑性分析中的体积自锁问题,并在广义有限元框架下引入无额外自由度的强化函数对此问题进行了改进.一方面,插值函数在引入强化函数后获得了更加丰富的近似空间,提高了在体积近似不变约束下正确反映结构变形的能力;另一方面,强化函数的建立不依赖额外自由度,从而消除了传统广义有限元方法中的线性相关性问题.分析并验证了常规有限元在线弹性、超弹性和塑性分析中的体积自锁问题具有不同的触发条件和表现形式.3 个典型的数值算例表明,无额外自由广义有限元能有效地缓解体积自锁并得到准确合理的计算结果.
Abstract
The volumetric locking of the conventional finite element method(FEM)was investigated through the nearly incompressible elasto-plastic analysis,and the extra-DOF-free reinforcement function was introduced in the framework of the generalized finite element method(GFEM)for improvement of this problem.Through the introduction of the reinforcement function,a richer approximation space was obtained for the interpolation function,of which the ability of correctly reflecting structural deformations was promoted under the approxi-mate volumetric invariance constraint.Furthermore,the construction of the reinforcement function is independ-ent of the extra degrees of freedom,which eliminates the linear dependency in the traditional GFEM.Different triggering conditions and manifestations of volumetric locking of the conventional FEM were found in linear e-lastic,hyperelastic,and plastic analyses.Three classical numerical examples show that,the extra-DOF-free GFEM can effectively alleviate the volumetric locking in all analyses,and obtain accurate and reasonable re-sults.
关键词
广义有限元/额外自由度/近不可压/体积自锁/弹塑性/超弹性Key words
generalized finite element/extra degree of freedom/nearly incompressible/volumetric locking/elastoplasticity/hyperelasticity引用本文复制引用
基金项目
中央高校基本科研业务费(DUT21GF304)
科学挑战专题(TZ2018002)
出版年
2024
国家科技期刊平台
NSTL
万方数据