A Lagrangian Uniform-Mesh Finite Element Method Applied to Problems Governed by Poisson’s Equation

2007 ◽  
Author(s):  
Linxia Gu ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Lagrangian Formulation ◽  
Uniform Mesh ◽  
Interpolation Function ◽  
Step Functions ◽  
Surface Integration ◽  
Interpolation Functions ◽  
Element Method

A method is presented for the solution of Poisson’s Equations using a Lagrangian formulation. The interpolation functions are the Lagrangian operation of those used in the classical finite element method, which automatically satisfy boundary conditions exactly even though there are no nodes on the boundaries of the domain. The integration is introduced in an implicit way by using approximated step functions. Classical surface integration terms used in the weak form are unnecessary due to the interpolation function in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplified the connection between the mesh and the solid structures, thus providing a very easy way to solve the problems without a conforming mesh.

LQG Control and Robustness Study for a Prestressed Membrane With Bimorph Actuators

2014 ◽  
Author(s):  
Ipar Ferhat ◽  
Cornel Sultan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Nominal System ◽  
Order Form ◽  
Lqg Control ◽  
Bimorph Actuators ◽  
Element Method

Linear Quadratic Gaussian (LQG) control is developed for a prestressed square membrane with bimorph actuators attached to it. The membrane is modeled using the finite element method and the membrane is assumed to be clamped on all edges. After obtaining the mass, damping, stiffness and input matrices in second order form using the weak form Finite Element Method (FEM), the problem is represented in first order form to develop the LQG controller. To study the robustness of the system, the control and observer gain matrices developed for the nominal system are applied to systems obtained from the nominal system by modifying material properties and prestress.

scholarly journals Cover interpolation functions and h-enrichment in finite element method

2017 ◽  
Vol 2 (1) ◽  
pp. 72-79
Author(s):  
H. Arzani ◽  
E. Khoshbavar rad ◽  
M. Ghorbanzadeh ◽  
◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Functions ◽  
Element Method

Analysis of the Large Plastic Deformation Involved in Wear Processes Using the Finite Element Method With an Updated Lagrangian Formulation

1987 ◽  
Vol 109 (2) ◽  
pp. 330-337 ◽  
Author(s):  
Nobuo Ohmae
Keyword(s):  
Finite Element Method ◽  
Plastic Deformation ◽  
Finite Element ◽  
Equivalent Stress ◽  
Lagrangian Formulation ◽  
The Finite Element Method ◽  
Large Plastic Deformation ◽  
Updated Lagrangian Formulation ◽  
Updated Lagrangian ◽  
Element Method

Large plastic deformation caused by friction for high purity copper was investigated using the finite element method with an updated Lagrangian formulation. The phenomenological background of this large plastic deformation was studied with a scanning electron microscope, and the nucleation of voids similar to those obtained for copper rolled to over 50 percent reduction was observed. Void nucleation was found to correlate with the agglomeration of over-saturated vacancies formed under high plastic strains. The computer-simulation analyzed such heavy deformation with an equivalent stress greater than the tensile strength and with an equivalent plastic strain of 0.44. Crack propagation was discussed by computing the J-integrals.

An Investigation of the Implementation of the p-Version Finite Element Method

1995 ◽  
Author(s):  
Simon D. Campion ◽  
John L. Jarvis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Function Method ◽  
Jacobian Matrix ◽  
P Elements ◽  
Load Vector ◽  
Geometry Mapping ◽  
Selection Of ◽  
Interpolation Functions ◽  
Element Method

Abstract The use of the p-version finite element method has become more widespread over the last five years or so, as witnessed by the addition of p-elements to a number of well known commercial codes. A review of the keynote papers on the p-version method is presented which focusses on the use of the hierarchical concept and the selection of the interpolation functions. The importance of accurate geometry mapping is also discussed, and the use of the blending function method is presented. Details of implementation of the p-version method are discussed in the light of the authors efforts to develop a program for solving two-dimensional elastostatic problems. Topics covered include the rules for numerical integration for the p-method, the possible use of numerical rather than explicit differentiation for determining the Jacobian matrix, and the programming of the load vector for the p-method. The lessons learnt are illustrated by simple examples, and will be of benefit to those wishing to program p-elements for other applications.

PARAMETER-UNIFORM FINITE ELEMENT METHOD FOR TWO-PARAMETER SINGULARLY PERTURBED PARABOLIC REACTION-DIFFUSION PROBLEMS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250047 ◽  
Author(s):  
M. K. KADALBAJOO ◽  
ARJUN SINGH YADAW
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reaction Diffusion ◽  
Rectangular Domain ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Spatial Direction ◽  
Small Parameters ◽  
Diffusion Problems ◽  
Element Method

In this paper, parameter-uniform numerical methods for a class of singularly perturbed one-dimensional parabolic reaction-diffusion problems with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and finite element method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(N-2( ln N)2 + Δt). Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.

A Gradient Weighted Finite Element Method (GW-FEM) for Static and Quasi-Static Electromagnetic Field Computation

2019 ◽  
Vol 17 (06) ◽  
pp. 1950017 ◽  
Author(s):  
Bingxian Tang ◽  
She Li ◽  
Xiangyang Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Weak Form ◽  
Electromagnetic Problems ◽  
Tetrahedral Elements ◽  
Field Computation ◽  
Analytical Results ◽  
Element Method

This paper presented a Gradient Weighted Finite Element Method (GW-FEM) for solving electromagnetic problems. First, the analysis domain is discretized into a set of triangular or tetrahedral elements which are easy to automatically generate. Then, Gradient Weighted influence domains are further constructed by the center element with all the adjacent elements. The Galerkin Weak form is evaluated based on these influence domains. The GW-FEM is employed here for the solution of static and quasi-static electromagnetic problems by using linear triangular or tetrahedral elements. All the properties of GW-FEM are proved theoretically and analyzed in detail. Consistency between four benchmark results is obtained by GW-FEM and analytical results verify the accuracy, stability, and potential of this method. It turns out that GW-FEM possesses potentials in the applications of electromagnetic problems.

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