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 cri...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.展开更多
基金was supported by the National Natural Science Foundation of China(Grant No.10672032)
文摘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.
