Showing papers on "Extended finite element method published in 1983"

Finite Elements for Electrical Engineers

Abstract: 1. Finite elements in one dimension 2. First-order triangular elements for potential problems 3. Electromagnetics of finite elements 4. Simplex elements for the scalar Helmholtz equation 5. Differential operators in ferromagnetic materials 6. Finite elements for integral operators 7. Curvilinear, vectorial and unbounded elements 8. Time and frequency domain problems in bounded systems 9. Unbounded radiation and scattering 10. Numerical solution of finite element equations References Appendices Index.

Error Estimate Procedure in the Finite Element Method and Applications

Abstract: Statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models The error on constitutive law for these fields yields an expression of the finite element error Moreover, the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis

Abstract: This is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second-order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates on the p-convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.

Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods

Abstract: The notion of a generalized finite element method is introduced. This class of methods is analyzed and their relation to mixed methods is discussed. The class of generalized finite element methods offers a wide variety of computational procedures from which particular procedures can be selected for particular problems. A particular generalized finite element method which is very effective for problems with rough coefficients is discussed in detail.

A methodology for the determination of global electromechanical quantities from a finite element analysis and its application to the evaluation of magnetic forces, torques and stiffness

Abstract: The paper will present two general methods for the deduction of global information from the final result of the finite element computation of an electromagnetic device. The first one, called the local jacobian derivative, may be used for evaluation of the derivative of any integral quantity versus the parameter of motion of a rigid body. Typically, this method when applied to electromagnetic systems, can be used for the computation of magnetic force or torque by virtual-work principle. Compared with the popular Maxwell's tensor method, this procedure is easier to implement in a finite element package especially for 3D problems. The second method which is based on a stationary property of the field solution, allows the evaluation of a second order derivative of any integral quantity. For instance, computation of the stiffness of a magnetic system (derivative of a force or a torque) may be achieved as the second order derivative of the magnetic energy. It may be pointed out that this method requires the field computation once for a linear problem as well as for a non-linear one.

A Modified Quadtree Approach To Finite Element Mesh Generation

Abstract: By allowing the use of quadrants with cut corners, this modeling technique overcomes some of the drawbacks of standard quadtree encoding for finite element mesh generation.

Finite elements for the dynamic analysis of fluid‐solid systems

Abstract: Several new finite elements are presented for the idealization of two- and three-dimensional coupled fluid-solid systems subjected to static and dynamic loading. The elements are based on a displacement formulation in terms of the displacement degrees-of-freedom at the nodes of the element. The formulation includes the effects of compressible wave propagation and surface sloshing motion. The use of reduced integration techniques and the introduction of rotational constraints in the formulation of the element stiffness eliminates all unnecessary zero-energy modes. A simple method is given which allows the stability of a finite element mesh of fluid elements to be investigated prior to analysis. Hence, the previously encountered problems of ‘element locking’ and ‘hour glass’ modes have been eliminated and a condition of optimum constraint is obtained. Numerical examples are presented which illustrate the accuracy of the element. It is shown that the element behaves very well for non-rectangular geometry. The optimum constraint condition is clearly illustrated by the static solution of a rigid block floating on a mesh of fluid elements.

Clinical Science Stress Analysis of the Human Tooth Using a Three-dimensional Finite Element Model

Abstract: A three-dimensional finite element model has been developed for the purpose of analyzing the stress distribution in a human mandibular right first molar. The model takes into account the non-symmetric geometry and loading, and the material inhomogeneities of the tooth. Comparisons with existing two-dimensional analyses are given.

A non‐conforming piecewise quadratic finite element on triangles

Abstract: It is shown in this paper that non-conforming finite elements on the triangle using second-degree polynomials can be easily built and used. Indeed they appear as an ‘enriched’ version of the standard piecewise quadratic six-node element. This work is divided into two parts. In the first we present the basic properties of the element, namely how it can be built and basic error estimates. We also show that this element exhibits a very peculiar regularity property. In the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials.

Magnetic field computation using Delaunay triangulation and complementary finite element methods

Abstract: A two-dimensional finite element analysis package is described which automatically generates optimal finite element meshes for magnetic field problems. The system combines the concept of Delaunay triangulation with variational principles to provide a grid which adapts to the characteristics of the solution. In this procedure, two different approximate solutions to the magnetic field are derived, the difference between the two approximate solutions providing an element by element measure of the accuracy of the solution. By refining those elements having the largest errors and recomputing the solution iteractively, finite element meshes having a uniforrn error density are obtained. The system is menu oriented and utilizes multiple command and display windows to create and edit the object description interactively. Matrix solution is by means of a rapid pre-conditioned conjugate gradient algorithm, and a wide variety of post-processing operations are supported. Application of the mesh generator to a variety of problems in magnetic field design shows it to be one of the most powerful and easy to use systems yet devised.

An analysis of thep-version of the finite element method for nearly incompressible materials

Abstract: In this paper we analyze the behavior of the so-calledp-version of the finite element method when applied to the equations of plane strain linear elasticity. We establish optimal rate error estimates that are uniformly valid, independent of the value of the Poisson ratio,v, in the interval ]0, 1/2[. This shows that thep-versiondoes not exhibit the degeneracy phenomenon which has led to the use of various, only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material.

Anisotropic elasto-plastic finite element analysis of thick and thin plates and shells

Abstract: An elasto-plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three-dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine-node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber-Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.

Stability of finite elements under divergence constraints

Abstract: A finite dimensional stability test for checking velocity/pressure finite element trial spaces is presented. Applications are made to a new class of element pairs proposed in this paper as well as to existing spaces.

Finite element techniques for modeling groundwater flow in fractured aquifers

Abstract: A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual-porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual-porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one-dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element-convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture-matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.

Finite Element Analysis of Dynamic Coupled Thermoelasticity Problems with Relaxation Times

Abstract: A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Green and Lindsay’s dynamic thermoelasticity model is selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. Time integration of the semidiscrete finite element equations is achieved by using an implicit-explicit scheme proposed by Hughes, et al. The procedure proves to be most effective and versatile in thermal and stress wave propagation analysis. A number of examples are presented which demonstrate the accuracy and versatility of the proposed model, and the importance of finite thermal propagation speed effects.

On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions

Abstract: Second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered. The behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.

The boundary element method applied to two-dimensional contact problems

Abstract: Contact problems and the study of the load transfer in mechanical assemblages are of great importance in mechanical engineering. Since Hertz1 published his famous work on normal contact between elastic bodies, a century of research work has been performed in this area. The work has been analytical, experimental and numerical. Until now, theoretical results for contact problems have been presented, see Persson2, Kalker3, Sundelius4, Gladwell5, etc. that are of great importance for understanding the nature of contact problems.