Locking and Robustness in the Nite Element Method for Circular Arch Problem
نویسنده
چکیده
In this paper we discuss locking and robustness of the nite element method for a model circular arch problem. It is shown that in the primal variable (i.e., the standard displacement formulation), the p-version is free from locking and uniformly robust with order p ?k and hence exhibits optimal rate of convergence. On the other hand, the h-version shows locking of order h ?2 , and is uniformly robust with order h p?2 for p > 2 which explains the fact that the quadratic element for some circular arch problems suuers from locking for thin arches in computational experience. If mixed method is used, both the h-version and the p-version are free from locking. Furthermore, the mixed method even converges uniformly with an optimal rate for the stress.
منابع مشابه
Locking and Robustness in The Finite
In this paper we discuss locking and robustness of the nite element method for a model circular arch problem. It is shown that in the primal variable (i.e., the standard displacement formulation), the p-version is free from locking and uniformly robust with order p ?k and hence exhibits optimal rate of convergence. On the other hand, the h-version shows locking of order h ?2 , and is uniformly ...
متن کاملPENALTY METHOD FOR UNILATERAL CONTACT PROBLEM WITH COULOMB’S FRICTION FOR LOCKING MATERIAL
In this work, we study a unilateral contact problem with non local friction of Coulombbetween a locking material and a rigid foundation. In the first step , we present the mathematicalmodel for a static process, we establish the variational formulation in the form of a variationalinequality and we prove the existence and uniqueness of the solution. In the second step, usingthe penalty method we...
متن کاملhp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates
There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...
متن کاملImpact of Integration on Straining Modes and Shear-Locking for Plane Stress Finite Elements
Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectang...
متن کاملB-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems
In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.
متن کامل