Plane Elastic Systems
Plane Elastic Systems

Author: Louis M. Milne-Thomson

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 220

ISBN-13: 3642878709

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In an epoch-making paper entitled "On an approximate solution for the bending of a beam of rectangular cross-section under any system of load with special reference to points of concentrated or discontinuous loading", received by the Royal Society on June 12, 1902, L. N. G. FlLON introduced the notion of what was subsequently called by LovE "general ized plane stress". In the same paper FlLO~ also gave the fundamental equations which express the displacement (u, v) in terms of the complex variable. The three basic equations of the theory of KoLOsov (1909) which was subsequently developed and improved by MUSKHELISHVILI (1915 and onwards) can be derived directly from Filon's equations. The derivation is indicated by FlLO)!E~KO-BoRODICH. Although FILO)! proceeded at once to the real variable, historically he is the founder of the modern theory of the application of the complex variable to plane elastic problems. The method was developed independently by A. C. STEVEXSOX in a paper received by the Royal Society in 1940 but which was not published, for security reasons, until 1945.

Chemistry and Physics of Fracture
Chemistry and Physics of Fracture

Author: R.M. Latanision

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 726

ISBN-13: 9400936656

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For many years it has been recognized that engineering materials that are-tough and ductile can be rendered susceptible to premature fracture through their reaction with the environment. Over 100 years ago, Reynolds associated hydrogen with detrimental effects on the ductility of iron. The "season cracking" of brass has been a known problem for dec ades, but the mechanisms for this stress-corrosion process are only today being elucidated. In more recent times, the mechanical properties of most engineering materials have been shown to be adversely affected by hydrogen embrittlement or stress-corrosion cracking. Early studies of environmental effects on crack growth attempted to identify a unified theory to explain the crack growth behavior of groups of materials in a variety of environments. It is currently understood that there are numerous stress-corrosion processes some of which may be common to several materials, but that the crack growth behavior of a given material is dependent on microstructure, microchemistry, mechanics, surface chemistry, and solution chemistry. Although the mechanism by which various chemical species in the environment may cause cracks to propagate in some materials but not in others is very complex, the net result of all environmentally induced fracture is the reduction in the force and energy associated with the tensile or shear separation of atoms at the crack tip.

Complex Variable Methods in Plane Elasticity
Complex Variable Methods in Plane Elasticity

Author: Jian-Ke Lu

Publisher:

Published: 1995

Total Pages: 0

ISBN-13: 9789812831347

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Ch. I. General theory. 1. Basic concepts and formulas -- 2. Stress functions -- 3. The stresses and displacements under transformation of coordinate system -- 4. Complex expressions for certain mechanical quantities -- 5. Boundary conditions of fundamental problems: the case of bounded and simply connected regions -- 6. The case of bounded and multi-connected regions -- 7. The case of unbounded regions -- 8. Modified second fundamental problems under general relative displacements -- ch. II. General methods of solution for fundamental problems. 9. First fundamental problems for bounded and simply connected regions -- 10. First fundamental problems for the infinite plane with a hole -- 11. First fundamental problems for multi-connected regions -- 12. The general method of solution for second fundamental problems -- 13. The method of solution for modified second fundamental problems -- ch. III. Methods of solution for various particular problems. 14. The case of circular region -- 15. The case of infinite plane with a circular hole -- 16. The case of circular ring region -- 17. Applications of conformal mapping -- 18. The case of half-plane -- 19. The case of cyclic symmetry -- 20. The methods of solution for cyclically symmetric problems -- ch. IV. Problems with compound boundary conditions. 21. Mixed boundary problems -- 22. First fundamental problems of welding -- 23. Second fundamental problems of welding -- 24. Welding in the whole plane, some examples -- ch. V. Fundamental crack problems. 25. General expressions of complex stress functions -- 26. First fundamental problems for the infinite plane with cracks -- 27. Second fundamental problems for the infinite plane with cracks -- 28. Collinear or co-circular cracks in the infinite plane -- 29. Crack problems for bounded regions -- 30. Simplification of the method of solution for first fundamental problems -- ch. VI. Fundamental crack problems of composite materials. 31. Fundamental crack problems of composite materials in the infinite plane -- 32. The welding problem for a circular plate with a straight crack -- 33. The welding problem for two half-planes with cracks -- 34. Fundamental crack problems of composite materials for a bounded region

Boundary Integral Equations in Elasticity Theory
Boundary Integral Equations in Elasticity Theory

Author: A.M. Linkov

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 286

ISBN-13: 9401599149

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by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.

Defects, Fracture and Fatigue
Defects, Fracture and Fatigue

Author: G. Sih

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 480

ISBN-13: 9400968213

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The Second International Symposium on Defects, Fracture and Fatigue took place at Mont Gabriel, Quebec, Canada, May 30 to June 5, 1982, and was organized by the Mechanical Engineering Department of McGill University and Institute of Fracture and Solid Mechanics, Lehigh University. The Co-Chairmen of the Sympo sium were Professor G.C. Sih of Lehigh University and Professor J.W. Provan of McGill University. Among those who served on the Organizing Committee were G.C. Sih (Co-Chairman), J.W. Provan (Co-Chairman), H. Mughrabi, H. Zorski, R. Bullough, M. Matczynski, G. Barenblatt and G. Caglioti. As a result of the interest expressed at the First Symposium that was held in October 1980, in Po land, the need for a follow-up meeting to further explore the phenomena of mate rial damage became apparent. Among the areas considered were dislocations, per sistent-slip-bands, void creation, microcracking, microstructure effects, micro/ macro fracture mechanics, ductile fracture criteria, fatigue crack initiation and propagation, stress and failure analysis, deterministic and statistical crack models, and fracture control. This wide spectrum of topics attracted researchers and engineers in solid state physics, continuum mechanics, applied mathematics, metallurgy and fracture mechanics from many different countries. This spectrum is also indicative of the interdisciplinary character of material damage that must be addressed at the atomic, microscopic and macroscopic scale level.