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Peter Bettess

Bio: Peter Bettess is an academic researcher from Durham University. The author has contributed to research in topics: Finite element method & Plane wave. The author has an hindex of 25, co-authored 63 publications receiving 4001 citations.


Papers
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Journal ArticleDOI
TL;DR: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems and boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits as mentioned in this paper.
Abstract: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.

711 citations

Journal ArticleDOI
TL;DR: In this article, an analytical study of a soil layer subject to a periodic surface force is presented, and the results of the analysis are given in a non-dimensional, generally valid, form and should find practical application in assessing the type of approximation that is applicable in new problems.
Abstract: The behaviour of saturated, porous media under dynamic or quasi-static loads was first formulated by Biot (1941, 1960). For dynamic problems a simplification was recently proposed by one of the Authors. As the two formulations must coincide over a range of problems and as for slow transients both must be adequately represented by pure consolidation theory, this Paper examines the respective ranges of validity by an analytical study of a soil layer subject to a periodic surface force. The analysis also indicates under what conditions such extremes as undrained or quasi-static assumptions can be safely used. Results of the analysis are given in a non-dimensional, generally valid, form and should find practical application in assessing the the type of approximation that is applicable in new problems. Le comportement des milieux poreux satures soumis a des charges dynamiques ou quasi statiques a ete analyse pour la premiere fois par Boit (1941, 1960). Pour les problemes dynamiques, une simplification a ete re...

549 citations

Journal ArticleDOI
TL;DR: In this article, the wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined, and appropriate boundary conditions are described, for finite and infinite boundaries.
Abstract: The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.

428 citations

Journal ArticleDOI
TL;DR: In this article, a new, improved infinite element based on mapping is proposed for modelling unbounded domain problems, which is ideally suited for the analysis of infinite domain static problems in two and three dimensions.
Abstract: A new, improved infinite element based on mapping is proposed for modelling unbounded domain problems. Mapping has previously been used in such problems, not only for the entire domain, but also for the infinite element itself. The novelty of the present approach is the simplicity of the mapping, and the retention of standard integration abscissae and weights. The implementation of these elements is very straightforward, and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions.

365 citations

Journal ArticleDOI
TL;DR: In this article, two general approaches used in the soluation of coupled structures and fluid systems in which effects of large scale flow are excluded are presented. But the numerical problems posed, discretization methods used and possible simplifications are discussed.
Abstract: The paper presents an introduction to two general approaches used in the soluation of coupled structures and fluid systems in which effects of large scale flow are excluded. In the first approach, the Lagrangian, the fluid is simply treated as a ‘solid’ with a negligible shear modulus. In the second method, Eulerian, a single pressure variable is used in the fluid. The numerical problems posed, discretization methods used and possible simplifications are discussed.

299 citations


Cited by
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Journal ArticleDOI
TL;DR: A new approach to structural topology optimization that represents the structural boundary by a level set model that is embedded in a scalar function of a higher dimension that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation.

2,404 citations

Journal ArticleDOI
TL;DR: An algorithmic approach to the boundary design of elastic structures which allows one to rapidly solve the two-dimensional Lam� equations in arbitrary domains and compute, for example, the stresses, and to develop a systematic way of modifying the design to optimize chosen properties.

987 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.

976 citations

Book
19 May 2005
TL;DR: In this article, the authors present a detailed review of liquid sloshing dynamics in rigid containers, including linear forced and non-linear interaction under external and parametric excitations.
Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

920 citations