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Asymptotic Methods In The Buckling Theory Of Elastic Shells
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Book Synopsis Asymptotic Methods in the Buckling Theory of Elastic Shells by : P. E. Tovstik
Download or read book Asymptotic Methods in the Buckling Theory of Elastic Shells written by P. E. Tovstik and published by World Scientific. This book was released on 2001 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Equations of thin elastic shell theory. 1.1. Elements of surface theory. 1.2. Equilibrium equations and boundary conditions. 1.3. Errors of 2D shell theory of Kirchhoff-Love type. 1.4. Membrane stress state. 1.5. Technical shell theory equations. 1.6. Technical theory equations in the other cases. 1.7. Shallow shells. 1.8. Initial imperfections. 1.9. Cylindrical shells. 1.10. The potential energy of shell deformation. 1.11. Problems and exercises -- 2. Basic equations of shell buckling. 2.1. Types of elastic shell buckling. 2.2. The buckling equations. 2.3. The buckling equations for a membrane state. 2.4. buckling equations of the general stress state. 2.5. Problems and exercises -- 3. Simple buckling problems. 3.1. Buckling of a shallow convex shell. 3.2. Shallow shell buckling modes. 3.3. The non-uniqueness of buckling modes. 3.4. A circular cylindrical shell under axial compression. 3.5. A circular cylindrical shell under external pressure. 3.6. Estimates of critical load. 3.7. Problems and examples -- 4. Buckling modes localized near parallels. 4.1. Local shell buckling modes. 4.2. Construction algorithm of buckling modes. 4.3. Buckling modes of convex shells of revolution. 4.4. Buckling of shells of revolution without torsion. 4.5. Buckling of shells of revolution under torsion. 4.6. Problems and exercises -- 5. Non-homogeneous axial compression of cylindrical shells. 5.1. Buckling modes localized near generatrix. 5.2. Reconstruction of the asymptotic expansions. 5.3. Axial compression and bending of cylindrical shell. 5.4. The influence of internal pressure. 5.5. Buckling of a non-circular cylindrical shell. 5.6. Cylindrical shell with curvature of variable sign. 5.7. Problems and exercises -- 6. Buckling modes localized at a point. 6.1. Local buckling of convex shells. 6.2. Construction of the buckling mode. 6.3. Ellipsoid of revolution under combined load. 6.4. Cylindrical shell under axial compression. 6.5. Construction of the buckling modes. 6.6. Problems and exercises -- 7. Semi-momentless buckling modes. 7.1. Basic equations and boundary conditions. 7.2. Buckling modes for a conic shell. 7.3. Effect of initial membrane stress resultants. 7.4 Semi-momentless buckling modes of cylindrical shells. 7.5. Problems and exercises -- 8. Effect of boundary conditions on semi-momentless modes. 8.1. Construction algorithm for semi-momentless solutions. 8.2. Semi-momentless solutions. 8.3. Edge effect solutions. 8.4. Separation of boundary conditions. 8.5. The effect of boundary conditions on the critical load. 8.6. Boundary conditions and buckling of a cylindrical shell. 8.7. Conic shells under external pressure. 8.8. Problems and exercises -- 9. Torsion and bending of cylindrical and conic shells. 9.1. Torsion of cylindrical shells. 9.2. Cylindrical shell under combined loading. 9.3. A shell with non-constant parameters under torsion. 9.4. Bending of a cylindrical shell. 9.5. The torsion and bending of a conic shell. 9.6. Problems and exercises -- 10. Nearly cylindrical and conic shells. 10.1. Basic relations. 10.2. Boundary problem in the zeroth approximation. 10.3. Buckling of a nearly cylindrical shell. 10.4. Torsion of a nearly cylindrical shell. 10.5. Problems and exercises -- 11. Shells of revolution of negative Gaussian curvature. 11.1. Initial equations and their solutions. 11.2. Separation of the boundary conditions. 11.3. Boundary problem in the zeroth approximation. 11.4. Buckling modes without torsion. 11.5. The case of the neutral surface bending. 11.6. The buckling of a torus sector. 11.7. Shell with Gaussian curvature of variable sign. 11.8. Problems and exercises -- 12. Surface bending and shell buckling. 12.1. The transformation of potential energy. 12.2. Pure bending buckling mode of shells of revolution. 12.3. The buckling of a weakly supported shell of revolution. 12.4. Weakly supported cylindrical and conical shells. 12.5. Weakly supported shells of negative Gaussian curvature. 12.6. Problems and exercises -- 13. Buckling modes localized at an edge. 13.1. Rectangular plates under compression. 13.2. Cylindrical shells and panels under axial compression. 13.3. Cylindrical panel with a weakly supported edge. 13.4. Shallow shell with a weak edge support. 13.5. Modes of shells of revolution localized near an edge. 13.6. Buckling modes with turning points. 13.7. Modes localized near the weakest point on an edge. 13.8. Problems and exercises -- 14. Shells of revolution under general stress state. 14.1. The basic equations and edge effect solutions. 14.2. Buckling with pseudo-bending modes. 14.3. The cases of significant effect of pre-buckling strains. 14.4. The weakest parallel coinciding with an edge. 14.5. Problems and exercises.
Book Synopsis Asymptotic Theory Of Anisotropic Plates And Shells by : Lenser A Aghalovyan
Download or read book Asymptotic Theory Of Anisotropic Plates And Shells written by Lenser A Aghalovyan and published by World Scientific. This book was released on 2015-03-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A consistent theory for thin anisotropic layered structures is developed starting from asymptotic analysis of 3D equations in linear elasticity. The consideration is not restricted to the traditional boundary conditions along the faces of the structure expressed in terms of stresses, originating a new type of boundary value problems, which is not governed by the classical Kirchhoff-Love assumptions. More general boundary value problems, in particular related to elastic foundations are also studied.The general asymptotic approach is illustrated by a number of particular problems for elastic and thermoelastic beams and plates. For the latter, the validity of derived approximate theories is investigated by comparison with associated exact solution. The author also develops an asymptotic approach to dynamic analysis of layered media composed of thin layers motivated by modeling of engineering structures under seismic excitation.
Book Synopsis Asymptotic methods in mechanics of solids by : Svetlana M. Bauer
Download or read book Asymptotic methods in mechanics of solids written by Svetlana M. Bauer and published by Birkhäuser. This book was released on 2015-05-30 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Resolution Of The Twentieth Century Conundrum In Elastic Stability by : Isaac E Elishakoff
Download or read book Resolution Of The Twentieth Century Conundrum In Elastic Stability written by Isaac E Elishakoff and published by World Scientific. This book was released on 2014-05-29 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been stability theories developed for beams, plates and shells — the most significant elements in mechanical, aerospace, ocean and marine engineering. For beams and plates, the theoretical and experimental values of buckling loads are in close vicinity. However for thin shells, the experimental predictions do not conform with the theory, due to presence of small geometric imperfections that are deviations from the ideal shape.This fact has been referred to in the literature as ‘embarrassing’, ‘paradoxical’ and ‘perplexing’. Indeed, the popular adage, “In theory there is no difference between theory and practice. In practice there is”, very much applies to thin shells whose experimental buckling loads may constitute a small fraction of the theoretical prediction based on classical linear theory; because in practice, engineers use knockdown factors that are not theoretically substantiated.This book presents a uniform approach that tames this prima-donna-like and capricious behavior of structures that has been dubbed the ‘imperfection sensitivity’ — thus resolving the conundrum that has occupied the best minds of elastic stability throughout the twentieth century.
Book Synopsis Asymptotic Methods in Mechanics by : Rmi Vaillancourt
Download or read book Asymptotic Methods in Mechanics written by Rmi Vaillancourt and published by American Mathematical Soc.. This book was released on 1993-12-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
Book Synopsis Multiparameter Stability Theory with Mechanical Applications by : Alexander P. Seyranian
Download or read book Multiparameter Stability Theory with Mechanical Applications written by Alexander P. Seyranian and published by World Scientific. This book was released on 2003 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with fundamental problems, concepts, and methods ofmultiparameter stability theory with applications in mechanics. Itpresents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects ofnonconservative stability problems, analysis of singularities ofboundaries for the stability domains, stability analysis ofmultiparameter linear periodic systems, and optimization of structuresunder stability constraints
Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spatial Control of Vibration by : S. O. Reza Moheimani
Download or read book Spatial Control of Vibration written by S. O. Reza Moheimani and published by World Scientific. This book was released on 2003 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vibration is a natural phenomenon that occurs in a variety of engineering systems. In many circumstances, vibration greatly affects the nature of engineering design as it often dictates limiting factors in the performance of the system. The conventional treatment is to redesign the system or to use passive damping. The former could be a costly exercise, while the latter is only effective at higher frequencies. Active control techniques have emerged as viable technologies to fill this low-frequency gap. This book is concerned with the study of feedback controllers for vibration control of flexible structures, with a view to minimizing vibration over the entire body of the structure.The book introduces a variety of flexible structures such as beams, strings, and plates with specific boundary conditions, and explains in detail how a spatially distributed model of such systems can be obtained. It addresses the problems of model reduction and model correction for spatially distributed systems of high orders, and goes on to extend robust control techniques such as H-infinity and H2 control design methodologies to spatially distributed systems arising in active vibration control problems. It also addresses other important topics, such as actuator and sensor placement for flexible systems, and system identification for flexible structures with irregular boundary conditions. The text contains numerous examples, and experimental results obtained from laboratory-level apparatus, with details of how similar test beds may be built.
Book Synopsis Process Modelling and Simulation with Finite Element Methods by : William B. J. Zimmerman
Download or read book Process Modelling and Simulation with Finite Element Methods written by William B. J. Zimmerman and published by World Scientific. This book was released on 2004 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic description and case studies of chemical engineering modelling and simulation based on the MATLAB/FEMLAB tools, in support of selected topics in undergraduate and postgraduate programmes that require numerical solution of complex balance equations (ordinary differential equations, partial differential equations, nonlinear equations, integro-differential equations). These systems arise naturally in analysis of transport phenomena, process systems, chemical reactions and chemical thermodynamics, and particle rate processes. Templates are given for modelling both state-of-the-art research topics (e.g. microfluidic networks, film drying, multiphase flow, population balance equations) and case studies of commonplace design calculations -- mixed phase reactor design, heat transfer, flowsheet analysis of unit operations, flash distillations, etc. The great strength of this book is that it makes modelling and simulating in the MATLAB/FEMLAB environment approachable to both the novice and the expert modeller.
Book Synopsis Recent Approaches in the Theory of Plates and Plate-Like Structures by : Holm Altenbach
Download or read book Recent Approaches in the Theory of Plates and Plate-Like Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2022-01-01 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various approaches in establishment the basic equations of one- and two-dimensional structural elements. In addition, the boundaries of validity of the theories and the estimation of errors in approximate theories are given. Many contributions contain not only new theories, but also new applications, which makes the book interesting for researcher and graduate students.
Book Synopsis Shell Structures: Theory and Applications Volume 4 by : Wojciech Pietraszkiewicz
Download or read book Shell Structures: Theory and Applications Volume 4 written by Wojciech Pietraszkiewicz and published by CRC Press. This book was released on 2017-10-30 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shells are basic structural elements of modern technology and everyday life. Examples of shell structures in technology include automobile bodies, water and oil tanks, pipelines, silos, wind turbine towers, and nanotubes. Nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes or wings of insects. In the human body arteries, the eye shell, the diaphragm, the skin and the pericardium are all shells as well. Shell Structures: Theory and Applications, Volume 4 contains 132 contributions presented at the 11th Conference on Shell Structures: Theory and Applications (Gdansk, Poland, 11-13 October 2017). The papers reflect a wide spectrum of scientific and engineering problems from theoretical modelling through strength, stability and dynamic behaviour, numerical analyses, biomechanic applications up to engineering design of shell structures. Shell Structures: Theory and Applications, Volume 4 will be of interest to academics, researchers, designers and engineers dealing with modelling and analyses of shell structures. It may also provide supplementary reading to graduate students in Civil, Mechanical, Naval and Aerospace Engineering.
Book Synopsis Advances in Solid and Fracture Mechanics by : Holm Altenbach
Download or read book Advances in Solid and Fracture Mechanics written by Holm Altenbach and published by Springer Nature. This book was released on 2022-11-08 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of articles reporting the current challenges in solid and fracture mechanics. The book is devoted to the 90th birthday of academician Nikita F. Morozov—a well-known specialist in the field of solid and fracture mechanics.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Shell Structures: Theory and Applications by : Wojciech Pietraszkiewicz
Download or read book Shell Structures: Theory and Applications written by Wojciech Pietraszkiewicz and published by CRC Press. This book was released on 2013-09-18 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shells are basic structural elements of modern technology and everyday life. Examples are automobile bodies, water and oil tanks, pipelines, aircraft fuselages, nanotubes, graphene sheets or beer cans. Also nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes, the double helix of DNA or wings of insec
Book Synopsis Recent Developments in the Theory of Shells by : Holm Altenbach
Download or read book Recent Developments in the Theory of Shells written by Holm Altenbach and published by Springer Nature. This book was released on 2019-09-25 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book commemorates the 80th birthday of Prof. W. Pietraszkiewicz, a prominent specialist in the field of general shell theory. Reflecting Prof. Pietraszkiewicz’s focus, the respective papers address a range of current problems in the theory of shells. In addition, they present other structural mechanics problems involving dimension-reduced models. Lastly, several applications are discussed, including material models for such dimension-reduced structures.
Book Synopsis Asymptotical Mechanics of Thin-Walled Structures by : Igor V. Andrianov
Download or read book Asymptotical Mechanics of Thin-Walled Structures written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 their 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.
Book Synopsis Problems of Nonlinear Mechanics and Physics of Materials by : Igor V. Andrianov
Download or read book Problems of Nonlinear Mechanics and Physics of Materials written by Igor V. Andrianov and published by Springer. This book was released on 2018-07-31 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.
