Download or read book Antiplane Elastic Systems written by Louis M. Milne-Thomson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term antiplane was introduced by L. N. G. FlLON to describe such problems as tension, push, bending by couples, torsion, and flexure by a transverse load. Looked at physically these problems differ from those of plane elasticity already treated * in that certain shearing stresses no longer vanish. This book is concerned with antiplane elastic systems in equilibrium or in steady motion within the framework of the linear theory, and is based upon lectures given at the Royal Naval College, Greenwich, to officers of the Royal Corps of Naval Constructors, and on technical reports recently published at the Mathematics Research Center, United States Army. My aim has been to tackle each problem, as far as possible, by direct rather than inverse or guessing methods. Here the complex variable again assumes an important role by simplifying equations and by introducing order into much of the treatment of anisotropic material. The work begins with an introduction to tensors by an intrinsic method which starts from a new and simple definition. This enables elastic properties to be stated with conciseness and physical clarity. This course in no way commits the reader to the exclusive use of tensor calculus, for the structure so built up merges into a more familiar form. Nevertheless it is believed that the tensor methods outlined here will prove useful also in other branches of applied mathematics.
Download or read book Anti plane Elastic Systems I written by Louis Melville Milne-Thomson and published by . This book was released on 1960 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plane Elastic Systems written by Louis M. Milne-Thomson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stability and Oscillation of Elastic Systems written by I︠A︡kov Gilelevich Panovko and published by . This book was released on 1973 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems such as jumps in elastic systems, problems of aeroelasticity, problems of frictional self-oscillations, and self-synchronization are discussed. The stability of equilibrium shapes of elastic systems is examined. Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces.
Download or read book The Stability of Elastic Systems written by S. J. Britvec and published by Elsevier. This book was released on 2014-07-03 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stability of Elastic Systems presents some of the most important aspects of the stability and the non-linear behavior at finite deformations of several types of structural elastic systems, which are important for a more precise understanding of the static performance of such systems. This book is divided into eight chapters that aim to complete parts of classical, eigenvalue, theories of buckling and to demonstrate the important role played by finite deformations in the theoretical analyses of stability. Other chapters discuss the properties of prismatic members and the post-buckling behavior of plane frameworks. A chapter describes the elastic buckling and stability of statically determinate space frameworks. The remaining chapters cover the elastic buckling of statically indeterminate pin-jointed systems and space frameworks. These chapters also examine the non-conservative aspects of structural systems. This book will be of great value to practicing engineers and students.
Download or read book Government wide Index to Federal Research Development Reports written by and published by . This book was released on 1965 with total page 1654 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics of Pre Strained Bi Material Elastic Systems written by Surkay D. Akbarov and published by Springer. This book was released on 2015-02-11 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
Download or read book Elasticity written by J. R. Barber and published by Springer Nature. This book was released on 2023-02-23 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes engineering applications of elasticity. This is a first-year graduate textbook in linear elasticity. It is written with the practical engineering reader in mind, dependence on previous knowledge of solid mechanics, continuum mechanics or mathematics being minimized. Examples are generally worked through to final expressions for the stress and displacement fields in order to explore the engineering consequences of the results. This 4th edition presents new and revised material, notably on the Eshelby inclusion problem and anisotropic elasticity. The topics covered are chosen with a view to modern research applications in fracture mechanics, composite materials, tribology and numerical methods. Thus, significant attention is given to crack and contact problems, problems involving interfaces between dissimilar media, thermoelasticity, singular asymptotic stress fields and three-dimensional problems.
Download or read book Plane elastic systems written by and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1964-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer. This book was released on 2013-12-20 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Linearized Theory of Elasticity written by William S. Slaughter and published by Springer Science & Business Media. This book was released on 2002 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical framework behind the theory is developed in detail, with the assumptions behind the eventual linearization made clear, so that the reader will be adequately prepared for further studies in continuum mechanics, nonlinear elasticity, inelasticity, fracture mechanics and/or finite elements. Prior to linearization, configurations and general measure of strain and stress are discussed. A modern treatment of the theory of tensors and tensor calculus is used. General curvilinear coordinates are described in an appendix.
Download or read book Rock Anisotropy and the Theory of Stress Measurements written by Bernard Amadei and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any undisturbed rock mass is subject to natural stresses inclu ding gravitational stresses due to the mass of the overburden and possibly tectonic stresses due to the straining of the earth's crust and remanent stresses due to past tectonism. Knowledge of the in situ stress field must be integrated into any rock engineering design along with general rock mass characteristics such as de for mability, strength, permeability and time dependent behavior. For example, the choice of optimum orientation and shape of deep underground caverns or complex underground works will be controlled by the orientation and the magnitude of the in situ stress @ield if it is necessary to minimize stress concentration problems. Long term variation of the in situ stress field may also help to evaluate the potential hazard of earthquake occurences. The magnitude and orientation of the stress field ata point within a rock mass can be measured but there is no known method by which the state of stress at a point can be accurately determined by instruments located remotely. In general, measurements are made inside boreholes, on outcrops or on the internal surfaces of under ground cavities. Most of the measuring techniques intentionally disturb the state of stress in the rock and then measure consequent strains and displacements. Measured strains or displacements are then related to the stresses through assumptions of material behavior. A common procedure is to assume that the rock mass is linearly elastic, isotropic, continuous and homogeneous.
Download or read book Anisotropic Elasticity written by Thomas C. T. Ting and published by Oxford University Press. This book was released on 1996-02-15 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.
Download or read book Handbook of Complex Analysis written by Reiner Kuhnau and published by Elsevier. This book was released on 2004-12-09 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Download or read book Mechanics Today written by S. Nemat-Nasser and published by Elsevier. This book was released on 2013-10-22 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics Today, Volume 4 focuses on solid mechanics and applied mathematics. This book is divided into six chapters. Chapter I provides a general description of the basic features and relevant concepts of mixed boundary-value problems in mechanics. The problem of crack extension in a solid under arbitrary loads is discussed in Chapter II, emphasizing the crack growth that leads from a planar to a nonplanar configuration. The third chapter reviews various methods of solving the scattering of elastic waves by inclusions. The interactions of electromagnetic field with deformable bodies in motion are elaborated in Chapter IV, while problems involving solids carrying high electric currents or being placed in high magnetic fields are deliberated in Chapter V. The last chapter concentrates on the implications of the second law of thermodynamics, and consequences of thermodynamic material stability and its corresponding restrictions on the evolutionary equations for internal variables. This publication is useful to specialists, but is also beneficial to non-experts with sufficient background in applied mechanics.
Download or read book Analytic Methods in Geomechanics written by Kam-tim Chau and published by CRC Press. This book was released on 2018-10-08 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multidisciplinary field, encompassing both geophysics and civil engineering, geomechanics deals with the deformation and failure process in geomaterials such as soil and rock. Although powerful numerical tools have been developed, analytical solutions still play an important role in solving practical problems in this area. Analytic Methods in Geomechanics provides a much-needed text on mathematical theory in geomechanics, beneficial for readers of varied backgrounds entering this field. Written for scientists and engineers who have had some exposure to engineering mathematics and strength of materials, the text covers major topics in tensor analysis, 2-D elasticity, and 3-D elasticity, plasticity, fracture mechanics, and viscoelasticity. It also discusses the use of displacement functions in poroelasticity, the basics of wave propagations, and dynamics that are relevant to the modeling of geomaterials. The book presents both the fundamentals and more advanced content for understanding the latest research results and applying them to practical problems in geomechanics. The author gives concise explanations of each subject area, using a step-by-step process with many worked examples. He strikes a balance between breadth of material and depth of details, and includes recommended reading in each chapter for readers who would like additional technical information. This text is suitable for students at both undergraduate and graduate levels, as well as for professionals and researchers.
