In this paper, we discuss an adaptive hybrid stress finite element method on quadri- lateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new tr...In this paper, we discuss an adaptive hybrid stress finite element method on quadri- lateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5- node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lam~ constant A. We introduce~ for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.展开更多
This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation.This element was originally proposed by Choi and Park[Computers and Structures,32(1989),pp.295–304 and Thin-Wall...This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation.This element was originally proposed by Choi and Park[Computers and Structures,32(1989),pp.295–304 and Thin-Walled Structures,28(1997),pp.1–20]for the analysis of Mindlin plates.We show the consistency error of this element is only O(h^(1/2))over the transition edges of the quadrilateral subdivision.By modifying the shape functions with respect to mid-nodes,we get an improved version of the element for which the consistency error is O(h).Numerical examples are provided to verify the theoretical results.展开更多
文摘In this paper, we discuss an adaptive hybrid stress finite element method on quadri- lateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5- node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lam~ constant A. We introduce~ for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.
基金supported by Natural Science Foundation of China(10771150)the National Basic Research Program of China(2005CB321701)the Program for New Century Excellent Talents in University(NCET-07-0584).
文摘This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation.This element was originally proposed by Choi and Park[Computers and Structures,32(1989),pp.295–304 and Thin-Walled Structures,28(1997),pp.1–20]for the analysis of Mindlin plates.We show the consistency error of this element is only O(h^(1/2))over the transition edges of the quadrilateral subdivision.By modifying the shape functions with respect to mid-nodes,we get an improved version of the element for which the consistency error is O(h).Numerical examples are provided to verify the theoretical results.
