C^0 and C^1 theories and test functions for FEM patch test in microstructures

作     者：CHEN WanJi Institute for Structural Analysis of Aerocraft,Shenyang Aerospace University,Shenyang 110136,China 

作者机构：1. Institute for Structural Analysis of Aerocraft Shenyang Aerospace University Shenyang 110136 China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2010年第53卷第6期

页      面：1086-1093页

核心收录：

学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：was supported by the National Natural Science Foundation of China (Grant No. 10672032) 

主　　题：couple stress theory displacement-rotation dependent theory displacement-rotation independent theory finite element method for microstructures test function for patch test 

摘      要：Among many theories and categories in microstructures,rotation-displacement used as independent or dependent variables,is a noticeable topic. In FEM,it is called C0 and C1 theory. The convergence criteria of finite elements for microstructures are less mature than those for the conventional thin plate bending problem. In this paper,the patch test functions for assessing convergence of the C0 and C1 finite elements in microstructures is established based on the enhanced patch test theory. The author has further explored the C0 and C1 finite element theories and investigated the difference and correlation between their finite element formulations. Newly proposed finite element theories for microstructures are as follows:(1) the displacement-rotation dependent C1 element that requires the element function satisfying both C0 and C1 continuity;(2) the displacement-rotation independent C0 element which requires new convergence criteria,such as non-zero constant shear stress patch test and zero constant shear stress patch test for approximating C1 element.