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Variational Incremental And Energy Methods In Solid Mechanics And Shell Theory

Author: J. Mason
Publisher: Elsevier
ISBN: 1483289648
Size: 69.96 MB
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Studies in Applied Mechanics, 4: Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory covers the subject of variational, incremental, and energy methods in Solid Mechanics and Shell Theory from a general standpoint, employing general coordinates and tensor notations. The publication first ponders on mathematical preliminaries, kinematics and stress in three-dimensional solid continua, and the first and second laws of thermodynamics. Discussions focus on the principles of virtual displacements and virtual forces, kinematics of rigid body motions, incremental stresses, kinematics of incremental deformation, description of motion, coordinates, reference and deformed states, tensor formulas for surfaces, and differentials and derivatives of operators. The text then elaborates on constitutive material laws, deformation and stress in shells, first law of thermodynamics applied to shells, and constitutive relations and material laws for shells. Concerns cover hyperelastic incremental material relations, material laws for thin elastic shells, incremental theory and stability, reduced and local forms of the first law of thermodynamics, and description of deformation and motion in shells. The book examines elastic stability, finite element models, variational and incremental principles, variational principles of elasticity and shell theory, and constitutive relations and material laws for shells. The publication is a valuable reference for researchers interested in the variational, incremental, and energy methods in solid mechanics and shell theory.

Convex Models Of Uncertainty In Applied Mechanics

Author: Y. Ben-Haim
Publisher: Elsevier
ISBN: 1483290972
Size: 23.78 MB
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Recognition of the need to introduce the ideas of uncertainty in a wide variety of scientific fields today reflects in part some of the profound changes in science and engineering over the last decades. Nobody questions the ever-present need for a solid foundation in applied mechanics. Neither does anyone question nowadays the fundamental necessity to recognize that uncertainty exists, to learn to evaluate it rationally, and to incorporate it into design. This volume provides a timely and stimulating overview of the analysis of uncertainty in applied mechanics. It is not just one more rendition of the traditional treatment of the subject, nor is it intended to supplement existing structural engineering books. Its aim is to fill a gap in the existing professional literature by concentrating on the non-probabilistic model of uncertainty. It provides an alternative avenue for the analysis of uncertainty when only a limited amount of information is available. The first chapter briefly reviews probabilistic methods and discusses the sensitivity of the probability of failure to uncertain knowledge of the system. Chapter two discusses the mathematical background of convex modelling. In the remainder of the book, convex modelling is applied to various linear and nonlinear problems. Uncertain phenomena are represented throughout the book by convex sets, and this approach is referred to as convex modelling. This book is intended to inspire researchers in their goal towards further growth and development in this field.

Probabilistic And Convex Modelling Of Acoustically Excited Structures

Author: I. Elishakoff
Publisher: Elsevier
ISBN: 1483290352
Size: 18.26 MB
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This book summarises the analytical techniques for predicting the response of linear structures to noise excitations generated by large propulsion power plants. Emphasis is placed on beams and plates of both single-span and multi-span configurations, common in engineering structural systems. Since the natural frequencies and the associated normal modes play a central role in the random vibration analysis of a continuous dynamical system, rather detailed discussions are devoted to their determination. Material covered in the first chapter provides a useful reference for the subsequent discussion of multi-span structures. Also included in this volume is a hybrid probabilistic and convex-uncertainty modeling approach in which the upper and lower bounds of the cross-spectral densities of the acoustic excitation are obtained on the basis of measured data. The random vibration of a structure is treated, for the first time, as an "anti-optimization" problem of finding the least favourable value of the mean-square response.

Nonlinear Continuum Mechanics Of Solids

Author: Yavuz Basar
Publisher: Springer Science & Business Media
ISBN: 3662042991
Size: 13.41 MB
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The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

Problems Of Technological Plasticity

Author: Boris Abramovich Drui︠a︡nov
Publisher: Elsevier Science Limited
Size: 51.42 MB
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Beginning with the classical rigid-plastic model of deformed workpiece and the characteristic (slipline) method of analysis, classical results of the theory of plasticity are presented. Included are original analytical and numerical solutions obtained in Russia and unknown to Western readers.

Micromechanics Of Granular Materials

Author: Masao Satake
Publisher: Elsevier Science Ltd
ISBN: 9780444705235
Size: 28.85 MB
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This proceedings volume contains papers from researchers in Japan, the United States and England who have made fundamental contributions to the micromechanics of granular materials. The purpose of the seminar was to facilitate an exchange of ideas between scientists working with statistical and continuum theories, computer simulations and experiments on both static and dynamic behaviour. In describing the solid like behaviour of granular materials, many new ideas on the constitutive relations are introduced in this volume. As an application of the analysis, the mechanism of liquefaction is discussed. Computer simulations have become a vital tool in establishing the micromechanical approaches which otherwise would not be experimentally tested. In numerical simulations and theoretical analyses of rapid granular flow, various modifications on the nature of materials and boundaries are given. Possible applications of the techniques of the stereology and analysis based on geometrical statistics are also included. The papers collected in this volume signify that the promotion of a good understanding of the mechanics of granular materials has been and will continue to be valued in a variety of technical disciplines.