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 : 20. 41 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 : 71. 80 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 : 30. 97 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 : 25. 33 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.

Asymptotic Methods In Mechanics Of Solids

Author : Svetlana M. Bauer
ISBN : 9783319183114
Genre : Mathematics
File Size : 70. 8 MB
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The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic.

Stressed Composite Structures

Author : A.G. Kolpakov
ISBN : 3540407901
Genre : Mathematics
File Size : 87. 88 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 : 26. 11 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 into one of four broad themes of the conference, namely: (i) structural mechanics (dynamics, vibration, seismic response, statics, bifurcation, buckling, stability, impact response, contact mechanics, fluid-structure interaction, soil-structure interaction, etc); (ii) mechanics of materials (elasticity, plasticity, fracture, damage, fatigue, creep, shrinkage, etc); (iii) modelling and testing (finite-element modelling, numerical methods, numerical simulations, experimental methods, experimental testing); (iv) structural-engineering practice (planning, analysis, design, construction, maintenance, repair, retrofitting, decommissioning). Not only do the considerations cover many types of engineering structures (buildings, bridges, tunnels, towers, space frames, roofs, foundations, shells, plates, mechanical assemblies, etc), they also span a diversity of engineering materials ranging from the traditional to the novel: steel, concrete, timber, masonry, aluminium, special alloys, glass, composites, functionally-graded materials, smart materials, etc. Two versions of each paper are available. The printed book features 2-page versions of the papers, intended to be concise but sufficiently informative summaries of the full papers. Details may be seen in the full papers, which are carried on the accompanying CD-ROM. Research and Applications in Structural Engineering, Mechanics and Computation is of interest to civil, structural, mechanical, marine and aerospace engineers concerned with the modelling, analysis, design, construction and maintenance of engineering structures. Researchers, practitioners and academics in these discipines will find the book useful. The SEMC international conferences, inaugurated in 2001, aim at bringing together from around the world academics, researchers and practitioners in the broad fields of structural mechanics, associated computation and structural engineering, to review recent achievements in the advancement of knowledge and understanding in these areas, share the latest developments, and address the challenges that the present and the future pose.

Asymptotic Methods In The Buckling Theory Of Elastic Shells

Author : P. E. Tovstik
ISBN : 9789810247263
Genre : Technology & Engineering
File Size : 32. 73 MB
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This book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff-Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes.The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the buckling of which has some specific features. The buckling modes localized near the weakest lines or points on the neutral surface are constructed, including the buckling modes localized near the weakly supported shell edge. The relations between the buckling modes and bending of the neutral surface are analyzed. Some of the applied asymptotic methods are standard; the others are new and are used for the first time in this book to study thin shell buckling. The solutions obtained in the form of simple approximate formulas complement the numerical results, and permit one to clarify the physics of buckling.

Insights And Innovations In Structural Engineering Mechanics And Computation

Author : Alphose Zingoni
ISBN : 9781317280637
Genre : Technology & Engineering
File Size : 41. 73 MB
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Insights and Innovations in Structural Engineering, Mechanics and Computation comprises 360 papers that were presented at the Sixth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2016, Cape Town, South Africa, 5-7 September 2016). The papers reflect the broad scope of the SEMC conferences, and cover a wide range of engineering structures (buildings, bridges, towers, roofs, foundations, offshore structures, tunnels, dams, vessels, vehicles and machinery) and engineering materials (steel, aluminium, concrete, masonry, timber, glass, polymers, composites, laminates, smart materials). Some contributions present the latest insights and new understanding on (i) the mechanics of structures and systems (dynamics, vibration, seismic response, instability, buckling, soil-structure interaction), and (ii) the mechanics of materials and fluids (elasticity, plasticity, fluid-structure interaction, flow through porous media, biomechanics, fracture, fatigue, bond, creep, shrinkage). Other contributions report on (iii) recent advances in computational modelling and testing (numerical simulations, finite-element modeling, experimental testing), and (iv) developments and innovations in structural engineering (planning, analysis, design, construction, assembly, maintenance, repair and retrofitting of structures). Insights and Innovations in Structural Engineering, Mechanics and Computation is particularly of interest to civil, structural, mechanical, marine and aerospace engineers. Researchers, developers, practitioners and academics in these disciplines will find the content useful. Short versions of the papers, intended to be concise but self-contained summaries of the full papers, are collected in the book, while the full versions of the papers are on the accompanying CD.

Modeling Of Creep For Structural Analysis

Author : Konstantin Naumenko
ISBN : 9783540708391
Genre : Technology & Engineering
File Size : 24. 96 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.

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