A direct formulation and numerical solution of the general transient elastodynamic problem. II
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1968-04-01 and is currently open access. It has received 461 citations till now. The article focuses on the topics: Transient (oscillation).read more
Citations
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Cracks in three dimensions: a dynamic dual
Abstract: In this paper the dual boundary element method is used to calculate dynamic stress intensity factors for three-dimensional cracked structures. The application of Laplace transforms to the time-dependent equations of elasticity reduce the problem to a static one in Laplace space. By applying the displacement integral equation on one of the crack surfaces and the traction boundary integral equation on the other, a general mixed-mode crack problem can be solved in a single region, in the same way as a static problem. Stress intensity factors in the time domain are obtained by the use of Durbin's inversion method. The accuracy of this method is demonstrated by its application to embedded elliptical cracks and edge cracks.
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Boundary element method with fourier eigen transform in elastodynamics
TL;DR: In this paper, the Fourier eigen transform to the boundary element method in elastodynamics is introduced and the new approach is very attractive in saving computer time, which is very useful in saving computational resources.
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Interruption of a seepage flow from a water source
F.M. Abdrabbo,M.A. Mahmoud +1 more
TL;DR: In this article, a drainage system consisting of an open surface drain, ditch, and lake with a potential head of water across the system was modelled and analyzed using the boundary element method.
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The Boundary Element Method in Elastostatics
TL;DR: In this article, the basic theory and numerical aspects of the boundary element method in elastostatics are introduced, which will be used later on as a numerical analysis tool for shape optimization.
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A dynamic program for two-dimensional fracture mechanics problems
TL;DR: In this paper, the theoretical and numerical fundamentals of boundary integral equations method techniques in real transformed dynamic are presented, and numerical results for impact problems with crack obtained by B.I.E. Method, through a dynamic program of general application, are shown.
References
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Book
A treatise on the mathematical theory of elasticity
TL;DR: Webb's work on elasticity as mentioned in this paper is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity.
Journal ArticleDOI
Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)
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An integral equation approach to boundary value problems of classical elastostatics
TL;DR: In this paper, a vector boundary formula relating the boundary values of displacement and traction for the general equilibrated stress state is derived, which is used to generate integral equations for the solution of the traction, displacement, and mixed boundary value problems of plane elasticity.