asymptotical mechanics of thin walled structures foundations of engineering mechanics

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Asymptotical Mechanics Of Thin Walled Structures

Author : Igor V. Andrianov
ISBN : 3540408762
Genre : Mathematics
File Size : 89. 62 MB
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In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and its applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

Nonlinear Mechanics Of Thin Walled Structures

Author : Yury Vetyukov
ISBN : 9783709117774
Genre : Technology & Engineering
File Size : 25. 51 MB
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This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.

Mechanics Of Structural Elements

Author : Vladimir Slivker
ISBN : 9783540447214
Genre : Technology & Engineering
File Size : 33. 63 MB
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The book systematically presents variational principles and methods of analysis for applied elasticity and structural mechanics. The variational approach is used consistently for both, constructing numerical procedures and deriving basic governing equations of applied mechanics of solids; it is the derivation of equations where this approach is most powerful and best grounded by mathematics.

Mechanics Of Non Holonomic Systems

Author : Sh.Kh Soltakhanov
ISBN : 9783540858478
Genre : Technology & Engineering
File Size : 45. 41 MB
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A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. The system of equations of motion in the generalized coordinates is regarded as a one vector relation, represented in a space tangential to a manifold of all possible positions of system at given instant. The tangential space is partitioned by the equations of constraints into two orthogonal subspaces. In one of them for the constraints up to the second order, the motion low is given by the equations of constraints and in the other one for ideal constraints, it is described by the vector equation without reactions of connections. In the whole space the motion low involves Lagrangian multipliers. It is shown that for the holonomic and nonholonomic constraints up to the second order, these multipliers can be found as the function of time, positions of system, and its velocities. The application of Lagrangian multipliers for holonomic systems permits us to construct a new method for determining the eigenfrequencies and eigenforms of oscillations of elastic systems and also to suggest a special form of equations for describing the system of motion of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as programming constraints such that their validity is provided due to the existence of generalized control forces, which are determined as the functions of time. The closed system of differential equations, which makes it possible to find as these control forces, as the generalized Lagrange coordinates, is compound. The theory suggested is illustrated by the examples of a spacecraft motion. The book is primarily addressed to specialists in analytic mechanics.

Modeling Of Creep For Structural Analysis

Author : Konstantin Naumenko
ISBN : 9783540708391
Genre : Technology & Engineering
File Size : 29. 67 MB
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This book develops methods to simulate and analyze the time-dependent changes of stress and strain states in engineering structures up to the critical stage of creep rupture. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications. It also aims to extend the collection of available solutions of creep problems by new, more sophisticated examples.

Stressed Composite Structures

Author : A.G. Kolpakov
ISBN : 3540407901
Genre : Mathematics
File Size : 47. 73 MB
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The basic concepts of traditional mechanics of stressed structures are suitable for classical uniform structures made of homogeneous materials but not for complex structures such as a network plate or structures made of composite materials. In this book a new approach to stressed inhomogeneous structures is presented, leading to significant changes in the classical concepts of stressed bodies, especially plates, membranes, rods and beams. The approach is based on the rigorous mathematical asymptotic homogenization method and its newly elaborated modifications. It can be applied to the analysis, mechanical design and optimization problems of composite structures, including buckling problems.

Research And Applications In Structural Engineering Mechanics And Computation

Author : Alphose Zingoni
ISBN : 9781315850788
Genre : Science
File Size : 86. 31 MB
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Research and Applications in Structural Engineering, Mechanics and Computation contains the Proceedings of the Fifth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2013, Cape Town, South Africa, 2-4 September 2013). Over 420 papers are featured. Many topics are covered, but the contributions may be seen to fall

Structural Mechanics In U S S R 1917 1957

Author : Isaak M. Rabinovič
ISBN : UOM:39015053573625
Genre : Building
File Size : 35. 30 MB
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Advances In Mechanics Of Solids

Author :
ISBN : 9812568670
Genre : Science
File Size : 31. 15 MB
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"The contributions in this volume are written by well-known specialists in the fields of mechanics, materials modeling and analysis. They comprehensively address the core issues and present the latest developments in these and related areas. In particular, the book demonstrates the breadth of current research activity in continuum mechanics. A variety of theoretical, computational, and experimental approaches are reported, covering finite elasticity, vibration and stability, and mechanical modeling. The coverage reflects the extent and impact of the research pursued by Professor Haseganu and her international colleagues."--BOOK JACKET.

Thin Walled Laminated Structures

Author : Gennadi I. Mikhasev
ISBN : 3030127591
Genre : Science
File Size : 59. 32 MB
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This book presents a theoretical approach that allows the analysis of structures with magnetorheological and electrorheological layers, and shows, with the help of examples, how the mechanical behaviour of thin-walled laminated structures can be influenced. It consists of six chapters: Chapter 1 presents a brief overview of derivation approaches for theories of thin-walled structures, modelling of composites and modelling of laminated and sandwich structures. Chapter 2 describes the equivalent single layer model for thin laminated cylindrical shells, including the special cases of plates and beams. In addition to the classical mechanical properties, it also considers the electrorheological and magnetorheological properties. Chapter 3 presents the elastic buckling of laminated beams, plates, and cylindrical shells, discussing various problems, such as the influence of the boundary conditions, external loading and magnetic fields. It also suggests different approximations for asymptotic methods. Chapter 4 focuses on the free vibrations of elastic laminated beams, plates and cylindrical shells, investigating the influence of the boundary conditions and other factors. Chapter 5 presents the latest results concerning vibration of laminated structures composed of smart materials and discusses in detail the influence of electric and magnetic fields on smart structures. These results provide insights into the optimal design of these structures. Lastly, Chapter 6 features a short appendix presenting asymptotic estimates and series.

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