A Four-Node Hybrid-Trefftz Plane Elasticity Element with Fundamental Analytical Solutions

2011 ◽  
Vol 279 ◽  
pp. 194-199
Author(s):  
Ke Yong Wang
Keyword(s):  
Analytical Solutions ◽  
Displacement Field ◽  
Plane Elasticity ◽  
Element Formulation ◽  
Airy Stress Function ◽  
Numerical Examples ◽  
Variational Functional ◽  
Elasticity Problems ◽  
Element Boundary ◽  
Fundamental Analytical Solutions

A new four-node hybrid-Trefftz element is developed for plane elasticity problems. From the Airy stress function, the fundamental analytical solutions of the governing equation are derived as Trefftz functions for the intra-element (Trefftz) displacement field. Together with an independent frame displacement field along the element boundary, the element formulation is then constructed following the modified variational functional. Several numerical examples indicate that the proposed element exhibits good performance.

A Thick/Thin Plate Element Based on the Area Coordinate Analytical Trial Functions

2013 ◽  
Vol 790 ◽  
pp. 341-346
Author(s):  
Li Wang ◽  
Yu Lin Lu ◽  
Hao Ran Lou ◽  
Jia Wei ◽  
Min Zhu
Keyword(s):  
Coordinate System ◽  
Thin Plate ◽  
Analytical Solutions ◽  
Plate Theory ◽  
Good Precision ◽  
Shear Locking ◽  
Plate Element ◽  
Governing Equations ◽  
Numerical Examples ◽  
Fundamental Analytical Solutions

In this paper, a generalized conforming thick/thin plate element based on the quadrilateral area coordinate system called AATF-PQ4 is developed. Based on the governing equations of Mindlin-Reissner plate theory, the fundamental analytical solutions are first derived, then using this trial functions to formulate element AATF-PQ4. In the case of thin plate, this thick/thin plate element is degraded into corresponding thin plate element automatically and is free from shear locking. Numerical examples show that the proposed element, AATF-PQ4, has a good precision for thick and thin plate.

8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh

2017 ◽  
Vol 34 (8) ◽  
pp. 2731-2751 ◽  
Author(s):  
Changsheng Wang ◽  
Yang Wang ◽  
Caixia Yang ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Element Mesh ◽  
Content Type ◽  
Mesh Model ◽  
Distorted Mesh ◽  
New Strategy ◽  
Discrete Methods ◽  
Element Boundary ◽  
Fundamental Analytical Solutions

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

scholarly journals A new strain-based finite element for plane elasticity problems

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Djamal Hamadi ◽  
Ashraf Ayoub ◽  
Toufik Maalem
Keyword(s):  
Design Methodology ◽  
Internal Node ◽  
Plane Elasticity ◽  
Numerical Examples ◽  
Type Design ◽  
Static Condensation ◽  
Elasticity Problems ◽  
General Plane ◽  
Numerical Performance ◽  
Plane Linear Elasticity

Purpose In this paper, a new quadrilateral strain-based element is developed. The element has five nodes, four at the corners as well as an internal node. Design/methodology/approach Through the introduction of the internal node, the numerical performance of the element proved to be superior to existing elements in the literature, even though a static condensation is required. Findings From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The proposed element can be used to solve general plane linear elasticity problems resulting in excellent results. Originality/value The results obtained are comparable with those given by the robust element Q8.

Solution of plane elasticity problems with Mathematica

1995 ◽  
Vol 55 (2) ◽  
pp. 229-236 ◽  
Author(s):  
N.I. Ioakimidis ◽  
G.T. Anastasselos
Keyword(s):  
Plane Elasticity ◽  
Elasticity Problems

scholarly journals An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

2021 ◽  
Vol 2002 (1) ◽  
pp. 012028
Author(s):  
Zhizhen Jiang ◽  
Rui Zhang ◽  
Shiyu Gong ◽  
Jiahui Hou ◽  
Xiaoqing Jin
Keyword(s):  
Analytical Method ◽  
Plane Elasticity ◽  
Elasticity Problems
Sign in / Sign up

Export Citation Format

Share Document