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The Finite Element Method in Structural and Continuum Mechanics

TL;DR: In this paper, a mathematical reference record was created on 2004-09-07, modified on 2016-08-08, and used for modelisation of mathematical reference records for the Mathematique Reference Record.
Abstract: Keywords: Modelisation ; Mathematique Reference Record created on 2004-09-07, modified on 2016-08-08
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Journal ArticleDOI
TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.

1,573 citations


Cites methods from "The Finite Element Method in Struct..."

  • ...The general framework supplied by variational crystal plasticity formulations provides an attractive vehicle for developing a comprehensive theory of plasticity that incorporates existing knowledge of the physics of deformation processes [8–10] into the computational tools of continuum mechanics [11,12] with the aim of developing advanced and physically based design methods for engineering applications [13]....

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Book
01 Jan 1972
TL;DR: In this article, the method of Weighted Residuals is used to solve boundary-value problems in heat and mass transfer problems, and convergence and error bounds are established.
Abstract: Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.

1,367 citations

Journal ArticleDOI
TL;DR: In this article, a simple extension is made which allows the element to be economically used in all situations by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties.
Abstract: The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced. In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations. The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.

1,336 citations

Journal ArticleDOI
TL;DR: In this paper, a fractional calculus is used to construct stress-strain relationships for viscoelastic materials and these relationships are used in the finite element analysis of damped structures and closed-form solutions to the equations of motion are found.
Abstract: Fractional calculus is used to construct stress-strain relationships for viscoelastic materials. These relationships are used in the finite element analysis of viscoelastically damped structures and closed-form solutions to the equations of motion are found. The attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions.

1,041 citations