General Finite Element Model Research Articles

GENERALIZED COUPLED TRANSIENT THERMOELASTIC PROBLEM OF A SQUARE CYLINDER WITH ELLIPTICAL HOLE BY LAPLACE TRANSFORM/FINITE-ELEMENT METHOD

A general finite-element model is proposed to deal with dynamic transient response in a square cylinder with an elliptical hole by generalized coupled thermoelastic theory, especially for a long transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the finite-element method and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, the transient solutions at any time can be evaluated directly. Some numerical results, which demonstrate the accuracy, efficiency, and versatility of the proposed method, are presented. Moreover, the effects of the thermoelastic coupling term, inertia term, and relaxation times on solutions are investigated and discussed.

A finite element model for the shape development of irregular planar cracks

This paper describes a general finite element model used to calculate opening mode stress intensity factors ( K I ) along the front of an irregular planar crack. Local advance is calculated as a function of K I and a new profile defined. The finite element mesh is automatically reconfigured to the new profile and the process repeated to follow crack shape development. Quality checks against known solutions are presented and the effect of constrained and unconstrained corners on developing crack profiles is examined.

Coupled transient thermoelastic response in an axi-symmetric circular cylinder by Laplace transform-finite element method

A powerful general finite element model is proposed to deal with the transient response in an axi-symmetric infinitely long elastic circular cylinder subjected to arbitrary thermal loadings over a finite band of the cylindrical surface by generalized coupled thermoelastic theory, especially for longer transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the finite element method and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, transient solutions at any time could be evaluated directly. Some numerical results, which demonstrate the accuracy, efficiency and versatility of the proposed method, are presented. Moreover, the effects of the thermoelastic coupling term, inertia term, and relaxation times on long-term transient solutions are investigated and discussed.

Computer graphics aided geometric modeling and mesh generation schemes for preprocessing and finite element analysis

The paper describes automated generation and editing schemes together with the development of computer-aided geometric models for general applications. For the construction of general finite element models of complex shapes, conventional approaches typical of wireframe, surface, or solid modeling cannot be effectively utilized for generating continuum solid models as well as discrete models simultaneously. In view of these facts, features to generate and model two-dimensional as well as threedimensional continuum and discrete models by isoparametric mapping/solid geometrical modeling techniques via a common interactive processor are described. The proposed scheme is demonstrated for modeling structural, thermal, or flow networks that are commonly encountered in engineering applications. In a research environment, the techniques addressed in this paper should prove to be very useful in providing flexibility and thereby significantly reducing the work load of frequent CAD users.

Generalized Coupled Transient Thermoelastic Plane Problems by Laplace Transform/Finite Element Method

A general finite-element model is proposed to deal with dynamic theromelastic problems especially with longer transient period. The method consists of formulating and solving the problem in the Laplace transform domain by the Finite Element Method (FEM) and then numerically inverting the transformed solution to obtain the time-domain response. Therefore, the transient solutions at any time could be evaluated directly. A number of examples are presented which demonstrate the accuracy, efficiency, and versatility of the proposed method, and show the effects of relaxation times, inertia, and thermoelastic coupling terms.

On the design of large flexible space structures (LFSS)

For a general finite-element model of an LFSS, a strictly passive compensator results in an exponentially stable feedback system when actuators and sensors are colocated. In the general case (no colocation) we state necessary and sufficient conditions on the parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> for stabilizing a certain number of modes. We give conditions for robust stability and show that feedback does not destabilize the unmodeled modes under certain conditions.

Combined finite element-transfer matrix method based on a mixed formulation

Combined finite element-transfer matrix (FE-TM) methods are an efficient technique for the dynamic analysis of chain-like structures. They offer the advantages of an automatic reduction in the size of the eignvalue problem and of a straightforward means of dynamic substructuring. This paper presents a new approach to FE-TM methods which is based on a mixed finite element formulation utilizing the Reissner functional. This new approach permits the extension of the FE-TM method to more general finite element models with rectangular transfer matrices. Application of the method to two specific element types is considered.

Finite Element Analysis of Dynamic Coupled Thermoelasticity Problems With Relaxation Times

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.

A general finite element model for shells of arbitrary geometry

Abstract A finite element formulation is developed for the large displacement analysis of arbitrary shells. Formulation is based on a convected coordinate system and a tensorial approach is followed. The strain-displacement relationships used do not reflect the Kirchhoff hypothesis and Love's approximations. Isoparametric interpolation is used for the discretization of the problem, and the number of nodal points is variable. The numerical examples include the buckling analysis of cylindrical shells as well as two problems to test the convergence and accuracy of the algorithm.