Penalty 4-Node Quadrilateral Element Formulation for Axisymmetric Couple Stress Problems

被引:0
作者
Jiang, Yongkang [1 ]
Shang, Yan [1 ]
机构
[1] Nanjing Univ Aeronaut & Astronaut, State Key Lab Mech & Control Aerosp Struct, Nanjing 210016, Peoples R China
基金
中国国家自然科学基金;
关键词
FEM; axisymmetric; size effect; couple stress theory; penalty element; FINITE-ELEMENT; MEMBRANE ELEMENT; ELASTICITY; VIBRATION; IMMUNE;
D O I
10.3390/ma17225486
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
To address the issue of size effects in axisymmetric deformation of small-scale solids, this work proposes a 4-node 12-DOF element for axisymmetric problems based on the consistent couple stress theory (CCST), following the framework of the unsymmetric finite element method. With the use of the penalty function method, an independently assumed rotational field is introduced into the virtual work principle to approximate the physical rotation, ensuring the satisfaction of the C1 continuity requirement of the CCST in a weak form. As a benefit, the enriched C0 isoparametric-based interpolation is employed to construct the test functions for displacement and rotation. Furthermore, the force-stress field that satisfies the equilibrium equations related to axisymmetric deformation is employed as the element's force-stress trial function. In order to circumvent locking issues, reduced integration is employed in the penalty stiffness integration process. The numerical results demonstrate that the new element exhibits high computational accuracy and convergence rate in both static and modal analysis problems, effectively capturing size-dependent phenomena.
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页数:20
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