Author
N. I. Muskhelishvili
Bio: N. I. Muskhelishvili is an academic researcher. The author has contributed to research in topics: Cauchy principal value & Elasticity (economics). The author has an hindex of 4, co-authored 5 publications receiving 10559 citations.
Papers
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01 Jan 1958
TL;DR: In this article, the union of a finite number of contours or arcs which do not intersect one another and are of finite length is assumed to be a smooth line (for a generalization of the results to the case in which L is piecewise smooth see Appendix 2).
Abstract: In what follows, L is assumed to be a smooth line (for a generalization of the results to the case in which L is piecewise smooth see Appendix 2), i.e., the union of a finite number of contours or arcs which do not intersect one another and are of finite length.
3 citations
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TL;DR: In this paper, the authors present a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discuss the results obtained thereby, and the object of the theory is the study of the equilibrium of solids in the presence of cracks.
Abstract: Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.
4,677 citations
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
3,276 citations
TL;DR: In this paper, a pair of Gauss-Chebyshev integration formulas for singular integrals are developed and a simple numerical method for solving a system of singular integral equations is described.
Abstract: In this paper a pair of Gauss-Chebyshev integration formulas for singular integrals are developed. Using these formulas a simple numerical method for solving a system of singular integral equations is described. To demonstrate the effectiveness of the method, a numerical example is given. In order to have a basis of comparison, the example problem is solved also by using an alternate method.
1,300 citations
TL;DR: In this article, the main overall elastic moduli of fiber composites with transversely isotropic phases are connected by simple universal relations which are independent of the geometry at given concentration.
Abstract: The main overall elastic moduli of fibre composites with transversely isotropic phases are shown to be connected by simple universal relations which are independent of the geometry at given concentration. Exact values of the moduli themselves are found when the phases have equal transverse rigidities. Otherwise, upper and lower bounds are obtained in terms of phase properties and concentrations. It is proved that these are the best possible without taking account of the detailed geometry.
1,008 citations