Finite element mesh control by integer programming

A novel technique is presented for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions. Target division numbers on the subregion edges are given as input. By allowing these numbers to vary, meshes can be found which satisfy both the subregion constraints imposed by the mesh patterns being employed, and the compatibility constraints on edges shared by two or more adjacent subregions. Among all such feasible solutions the optimal one is obtained by minimizing the changes to the division numbers, using an integer programming technique.     

Finite element methods for an optimal steady-state control problem

An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.     

Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing

A comparison between the recently developed Cosserat brick element (see [9]) and other standard elements known from the literature is presented in this paper. The Cosserat brick element uses a director vector formulation based on the theory of a Cosserat point. The strain energy for a hyperelastic element is split additively into parts for homogeneous and inhomogeneous deformations respectively. The kinetic response due to inhomogeneous deformations uses constitutive constants that are determined by analytical solutions of a rectangular parallelepiped to the deformation modes of bending, torsion and hourglassing. Standard tests are performed which typically exhibit hourglassing or locking for many other finite elements. These tests include problems for beam and plate bending, shell structures and nearly incompressible materials, as well as for buckling under high pressure loads. For all these critical tests the Cosserat brick element exhibits robustness and reliability. Moreover, it does not depend on user-tuned stabilization parameters. Thus, it shows promise of being a truly user-friendly element for problems in nonlinear elasticity.     

Finite element analysis on deflection control of plates with piezoelectric actuators

A finite element model for the deflection control of plates with piezoelectric actuators is presented. This model contains an actuator element, an adhesive interface element and an eight-node isoparametric plate element. The actuator element developed here is based on first-order shear deformation theory. An analytical solution is also derived in comparison with results using the finite element model. The analyses articulate separate response of the plate; actuators and the adhesive give the flexible meshing advantage of solving the- smart structure problem with any type of boundary conditions and geometry configuration.     

Hyperelasticity and physical shear buckling of a block predicted by the Cosserat point element compared with inelasticity and hourglassing predicted by other element formulations

This paper examines the response of 18 nonlinear “hyperelastic” elements which are available in the computer codes ABAQUS, ADINA, ANSYS and FEAP. Simulations are proposed to test inelasticity of element formulations caused by potential path-dependence of the external work done on the element. All elements tested based on full integration produce hyperelastic response for these simulations. Most modified elements produce inelastic response for these simulations and one generates energy. One incompatible mode element in ADINA and one enhanced strain element in FEAP exhibit hyperelastic response in these simulations. However, both of these elements predict unphysical hourglass buckling modes for plane strain compression of a block. The Cosserat point element has been proven analytically to be hyperelastic for all deformations. The example problems indicate that the Cosserat point element is robust, does not exhibit typical locking phenomena and predicts a physical shear buckling mode for plane strain compression of a block.     

Finite element analysis of engines

The basic principles are outlined by means of a simple example, some applications given and the way is explained in which finite element analysis is carried out.     

Finite element in adhesion analyses

Finite element computer programs have been used successfully for stress analysis of bodies with complex geometries and loads, and the use of these programs in cohesive fracture mechanics analysis is now widely accepted. Similar numerical procedures have been developed for use in adhesive fracture mechanics, but rather strong stress oscillations near the point of debonding have been shown to occur both analytically and numerically. This paper discusses the effect of these oscillations upon the calculation of the stress and strain energy, and demonstrates that in this potentially difficult problem, finite element codes can be used with sufficient precision for fracture analysis.

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Zusammenfassung Finite Komputerverfahren wurden erfolgreich angewandt zur Untersuchung der Spannungen in Körpern mit komplizierter Geometrie und Belastung, und der Gebrauch dieser Verfahren ist jetzt weitgehend angenommen im Gebiet der kohesiven Bruchmechanik.Ähnliche numerische Verfahren wurden für die adhesive Bruchmechanik ausgearbeitet, aber ziemlich starke Spannungsschwankungen nahe am Trennungspunkt wurden sowohl analytisch wie numerisch gefunden. Dieser Bericht befaßt sich mit dem Einfluß dieser Schwankungen auf die Berechnung der Spannungen und der Verformungsenergie, und beweist daß in diesem sehr schwierigen Gebiet die finite Verfahren mit genügend Genauigkeit zur Untersuchung des Bruches angewandt werden können.

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Résumé Les programmes de calcul par éléments finis ont été utilisés avec succès pour l'analyse des contraintes dans les pièces dont la géométrie ou la mise en charge est complexe, et l'emploi de ces programmes est à présent largement introduit dans l'analyse de la mécanique de la rupture par décohésion.Des procédures similaires ont été développées pour traiter de la mécanique de la rupture par décollement, mais on a constaté, tant sur le plan théorique que sur le plan expérimental, des oscillations prononcées de la contrainte au voisinage du point de décollement.Ce mémoire discute les effets que peuvent avoir ces variations sur le calcul de la contrainte et de l'énergie de déformation, et démontre que, dans ce problème difficile, les méthodes de calcul aux éléments finis peuvent néanmoins être utilisées avec une précision suffisante pour analyser les ruptures.

     

Finite dynamic element formulation for a plane triangular element

The higher order dynamic correction terms for the stiffness and inertia matrices associated with a triangular plane stress-strain finite dynamic element are developed in detail. Numerical results presented indicate that the adoption of these matrices along with a suitable quadratic matrix eigenproblem solver effects a significant economy in the free vibration solution of structures when compared with the analysis based on the usual finite element procedure. A FORTRAN IV computer program listing of the various relevant element matrices is also presented in the Appendix.     

Finite element modelling and vibration control study of active plate with debonded piezoelectric actuators

A finite element model for a piezoelectric plate with edge debonded actuators is presented. This model is employed to investigate the effect of edge debonding on actuation authority, natural frequencies and vibration control performance. The regions of the plate with the piezoelectric patches are modelled such that each layer undergoes rotation due to shear deformation independently. The necessary constraints for continuity of displacements at the interfaces of the layers are imposed. The plate with edge debonded actuators is idealized by dividing it into debonded regions and healthy regions. A finite element procedure for imposing the constraints regarding continuity of displacements at the interfaces of the adjacent regions is developed and is implemented using MATLAB. Experiments are conducted for finding the actuation authority and natural frequencies of the plate with debonded actuators. It has been found that the developed model has predicted the mechanics of actuator debonding properly. The investigations have revealed the fact that the edge debonding of actuators will result in considerable degradation in actuation authority and vibration control performance.     

Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem

The boundary control problem of optimal heating of an infinitely long slab with tempertue-dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods. In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co-ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.     

Finite element computation of Green's functions

Green's functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green's function of the problem to compute its numerical solution. However, Green's functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to calculate Green's functions for any linear homogeneous medium from a simple finite element model. The method relies on the theory of wave propagation in periodic media and requires the knowledge of the finite element dynamic stiffness matrix of only one period. Several examples are given to check the accuracy and the efficiency of the proposed numerical Green's function.     

钢煤斗结构的有限元分析

通过对一个钢筋混凝土和钢煤斗的混和结构进行有限元分析,参照结构的实际破坏特征,找出破坏的原因,提出对该类结构设计有益的结论。采用了两种有限元软件,将分析结果进行了比较。讨论在兼顾准确和简洁的前提下如何建模和分析。同时也比较了几种建模方法的优劣,提出对有限元分析有参考价值的建议。     

Finite element analysis of helicoidal waveguides

The purpose of the paper is to propose an efficient method to compute propagation modes in helicoidal waveguides. An helicoidal system of co-ordinates is introduced to define the structure and to set up the problem. These co-ordinates, albeit non-orthogonal, preserve the translational invariance in a way that allows a two-dimensional finite element model similar to that of classical straight waveguides     

Finite element approximation of piezoelectric plates

A Reissner–Mindlin‐type modellization of piezoelectric plates is here considered in a suitable variational framework. Both the membranal and the bending behaviour are studied as the thickness of the structure tends to zero. A finite element scheme able to approximate the solution is then proposed and theoretically analysed. Some numerical results showing the performances of the scheme under consideration are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element post-buckling analysis for frames

Presented in this paper is a direct method of analysis of the elastic non-linear behaviour of frames. Emphasis is given to the method's capability of tracing the post-buckling path from a bifurcation point although the method can also trace the non-linear behaviour of frames with eccentricities. The method is proposed as an alternative to the main methods currently in use, the perturbation method and the incremental method. Conditions for equilibrium and stability are developed from a variational approach to the total potential. A finite element approximation is made and an efficient solution technique for the resulting non-linear equations is developed. Results for three frames are given demonstrating good agreement with solutions generated from other approaches.     

Finite element analysis of wave motion

To estimate wave motion, the finite element method is presented based on the linear interpolation function and two-step explicit numerical integration in time. For the determination of free surface position, the two-step scheme based on the Eulerian technique is usefully employed. Travel and run-up of solitary wave have been analysed and compared with the analytical solution. Both results are reasonably well in agreement. This method is applied to estimate the wave force on the practical breakwater to show the validity of the method.