Showing papers on "Finite element limit analysis published in 1987"

A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems

Abstract: An SUPG-type finite element method for linear symmetric multidimensional advective-diffusive systems is described and analyzed. Optimal and near optimal error estimates are obtained for the complete range of advective-diffusive behavior.

Finite Element Models for Bond Problems

Abstract: In the finite element analysis of reinforced concrete structures the modeling of bond‐slip between the reinforcement and concrete requires the use of special elements. In the past, various elements have been developed for this purpose. The behavior of the elements and the quality of the results are influenced mainly by the displacement function of the elements, the density of the element mesh, and the bond stressslip relations. In this paper the effects of different approaches for the displacement function and the bond stress‐slip relation are investigated.

Finite Element Approach to Rotor Blade Modeling

Abstract: The static and dynamic behavior of helicopter blades is investigated using a fmite element approach. This paper focuses on the development of an accurate geometric and structural model of the blade as a first step toward the complete analysis of the aeroelastic problem. A three-dimensional isaparametrie beam element including shear and waroine deformations of a thin-walled beam made of anisotropic material is formulated far arbitrarily . large deflections and rotations. Rotating and non-rotating frequencies far small amplitude vibrations are also presented. The predictions of this model are found in good agreement with experimentally measured deflections and vibration frequencies. Specific advantages of this finite element solution procedure are as follows: the formal derivation of the com~lex nonlinear equations of motion of the problem is not required, all the nonlinear terms are dealt with in a rational fashion bypassing the need for an ordering scheme, the complex struchrral behavior of the blade is accurately modeled, and finally both the undeformed and deformed geometry of the blade as well as other specific details of the rotor configuration are taken into account in a natural fashion.

A simple error estimator in the finite element method

Abstract: Recently, a new class of error indicators and estimators for the finite element methods has been introduced which is particularly easy to implement into existing finite element codes. This paper proves that the new indicators are equivalent to those analysed earlier by Babuska, thus showing that the rigorous mathematical results for the well-known jump indicator apply also for the new ones.

Simulation of contaminant transport in three dimensions: 1. The alternating direction Galerkin Technique

Abstract: The alternating direction Galerkin technique for the simulation of advective-dispersive transport in three dimensions is developed. The technique is designed for high efficiency in handling the large and detailed grids that are often required in simulations of natural groundwater systems. It is comparable to an alternating direction finite difference scheme, except for two advantages: first, the capability to handle certain curvilinear grids that may conform to either a flow net geometry or a natural stratigraphy and, second, the option to enhance solution accuracy through a choice between a finite difference or a finite element representation of the time derivative. Criteria for controlling numerical dispersion and accuracy can be applied easily. Three options for the time-stepping algorithm are developed and analyzed for stability, and their accuracy is investigated for simple flow systems. The technique is shown to be far more efficient than a conventional three-dimensional finite element model. In a companion paper, an application to a field-scale contaminant transport problem is described.

Adaptive finite element methods for high‐speed compressible flows

Abstract: An adaptive finite element algorithm for solving the unsteady Euler equations is described. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. A general version of the method which can be applied to moving grids with sliding interfaces is given, and results for a transient supersonic calculation of rotor-stator interaction are presented.

Nonlocal Finite Element Analysis of Strain‐Softening Solids

Abstract: A two-dimensional finite element formulation for imbricate nonlocal strain-softening continum is presented and numerically demonstrated. The only difference from the usual, local finite element codes is that certain finite elements are imbricated, i.e., they regularly overlap while skipping the intermediate mesh nodes. The element imbrication is characterized by generating proper integer matrices that give the numbers of the nodes for each finite element and the numbers of the imbricate elements overlapping each local element. The number of unknown displacements remains the same as for a local finite element code, while the number of finite elements approximately doubles. Numerical results show that stable two-dimensional strain-softening zones of multiple-element width can be obtained, and that the solution exhibits proper convergence as the mesh is refined. The convergence is demonstrated for the load-displacement diagrams, for the strain profiles across the strain-softening band, and for the total energy dissipated by cracking. It is also shown that the local formulations exhibit incorrect convergence; they converge to solutions for which the energy dissipation due to failure is zero, which is physically unacceptable. Stability problems due to strain-softening are avoided by making the loading steps so small that no two mutually nonoverlapping elements may enter the strain-softening regime within the same load step.

Optimal L ∞ -error estimates for nonconforming and mixed finite element methods of lowest order

Abstract: For second order linear elliptic problems, it is proved that theP 1-nonconforming finite element method has the sameL ∞-asymptotic accuracy as theP 1-conforming one. This result is applied to derive optimalL ∞-error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.

Numerical analysis of dynamic quasi-bifurcation

Abstract: A simple finite element approach to problems of dynamic structural instability under step loading is discussed. The method proposed is believed to yield important information about the structural behaviour in the non‐linear range. Incorporation of the method into existing finite element codes is straightforward.

A New Approach for the Thermomechanical Analysis of Tires by the Finite Element Method

Abstract: A new approach for the complete thermomechanical analysis of a pneumatic tire to estimate cyclic changes in the stresses and strains and obtain the pseudo‐steady state temperature profile in a tire rolling under a load is described. The approach uses a commercially available finite element code and involves a simplified two‐dimensional representation of the tire geometry to reduce computation time. The analysis includes three stages: inflation analysis, contact analysis, and temperature analysis. To handle the large deformations resulting from the inflation and contact loadings, the load is applied in small increments and a linearly elastic deformation is assumed in each increment. The structural and temperature analyses can be coupled through an iterative process to reflect the effect of temperature changes on material properties. Results obtained indicate that in spite of the simplifying assumptions made to reduce computation time, useful approximations to the solution of this complex problem c...

Towards accurate and consistent force calculation in finite element based computational magnetostatics

Abstract: Force calculations based on numerical field solutions represent an important step in the design of many electro-magneto-mechanical devices. Ensuring that the calculated forces are as accurate as possible for a given field solution is a requirement for any viable design system. This paper is concerned with the errors encountered in numerical force calculation and methods which avoid them.

Coupled thermoelastic-plastic stress analysis of solids by finite-element method

Abstract: This paper presents a finite-element formulation of a coupled thermoelastic-plastic stress analysis of solid structures. The formulation is based on a selected phenomenological energy dissipation model and elastic-plastic constitutive equations for both isotropic and kinematic hardening schemes. Numerical illustrations involving this coupling effect on a uniaxially loaded solid rod and on a thick-walled cylinder subject to internal pressure are included, using assumed values of dissipation factors. Temperature rises induced by one mechanical load cycle in both cases were computed. Numerical results indicate that the maximum effective strain in the solids from an uncoupled analysis can be as much as 10% larger than that from a coupled analysis under the same mechanical load. Coupled thermomechanical analysis is thus considered to be significant. The present method may readily be incorporated into a thermoelastic-plastic finite-element analysis and used to predict the healing of machine components produced ...

Finite Element Analysis of a Steady‐State Rotating Tire Subjected to Point Load or Ground Contact

Abstract: A radial automobile tire undergoing steady‐state rotation is analyzed by a finite element method. A special formulation is used which allows the finite element equations to be solved as a quasi‐static problem using static analysis solution procedures, rather than as a dynamic problem requiring solution in the time domain. This is accomplished through a transformation of variable that changes time derivatives, present through inertia, to spatial derivatives. Solution time for the analysis is thereby shortened. The tire is modeled first as a two‐dimensional ring on an elastic foundation, then in its full three‐dimensional geometry. Rotational speeds are those at which resonance occurs so that the dynamics can be easily visualized and the response easily verified. The models are subjected to point load excitation or ground contact. Point load is used to predict resonance responses of the undamped tire. Results agreed well with experimental measurements. The effect of inertia components and damping o...

Some Finite Element Methods for Linear Thin Shell Problems

Abstract: This paper is essentially based upon some of our works on numerical analysis of thin shell problems according to Koiter’s equations.

Power flow as a complement to statistical energy analysis and finite element analysis

Abstract: Present methods of analysis of the structural response and the structure-borne transmission of vibrational energy use either finite element (FE) techniques or statistical energy analysis (SEA) methods. The FE methods are a very useful tool at low frequencies where the number of resonances involved in the analysis is rather small. On the other hand SEA methods can predict with acceptable accuracy the response and energy transmission between coupled structures at relatively high frequencies where the structural modal density is high and a statistical approach is the appropriate solution. In the mid-frequency range, a relatively large number of resonances exist which make finite element method too costly. On the other hand SEA methods can only predict an average level form. In this mid-frequency range a possible alternative is to use power flow techniques, where the input and flow of vibrational energy to excited and coupled structural components can be expressed in terms of input and transfer mobilities. This power flow technique can be extended from low to high frequencies and this can be integrated with established FE models at low frequencies and SEA models at high frequencies to form a verification of the method. This method of structural analysis using power flo and mobility methods, and its integration with SEA and FE analysis is applied to the case of two thin beams joined together at right angles.

Computational Aspects of the h, p and h-p Versions of the Finite Element Method.

Abstract: : This paper discusses computational complexity of various versions of the finite element method in relation to the achieved accuracy of the finite element solution.

A New Justification of Finite Dynamic Element Methods

Abstract: Finite dynamic element methods were introduced by Premieniecki [11] and were studied by Paz and Dung [10], K.K. Gupta [5, 67, 8, 9], Fricker [2], A.K. Gupta [4] among others.

Combined Finite Difference/Finite Element Analysis for Soil Structure Interaction

Abstract: A method for the analysis of buried structures subjected to stress transients is presented. The method combines the finite difference and finite element techniques to provide the analyst with the capability to model the complete effects of soil-structure interaction, including material and geometric nonlinearities. The method and its computer implementation are briefly described and the results of two example analyses are presented.

The integration of geometric modelling with finite element analysis for the computer-aided design of castings

Abstract: This paper considers the problem of interfacing geometric modelling with finite element analysis in the numerical simulation of the casting process. It is shown that geometrical modellers are capable of describing uniquely the shape of the most complex cast object and that finite element meshes may be constructed within the component. However, such a mesh is defined by the geometry of the object and, hence, may not be the ideal for subsequent simulations. This difficulty is overcome by the use of an adaptive mesh created during the finite element analysis on the basis of information provided by the current solution. The fundamental background to adaptive mesh generation is presented together with the details of its implementation. The method is then applied to the calculation of the flow into a mould cavity from which the accuracy and efficiency of the method is demonstrated. It is concluded that the technique is viable for use with computer-aided design tools for the foundry industry.