Asymptotic Methods in the Buckling Theory of Elastic Shells PDF Download
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Author: P. E. Tovstik
Publisher: World Scientific
ISBN: 9789812794567
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: P. E. Tovstik
Publisher: World Scientific
ISBN: 9789812794567
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: Isaac E Elishakoff
Publisher: World Scientific
ISBN: 9814583553
Category : Technology & Engineering
Languages : en
Pages : 350
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Book Description
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.
Author: Igor V. Andrianov
Publisher: Springer Science & Business Media
ISBN: 354045246X
Category : Science
Languages : en
Pages : 527
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Book Description
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.
Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3030177475
Category : Technology & Engineering
Languages : en
Pages : 799
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Book Description
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.
Author: Wojciech Pietraszkiewicz
Publisher: CRC Press
ISBN: 1482229080
Category : Technology & Engineering
Languages : en
Pages : 600
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Book Description
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
Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3030871851
Category : Technology & Engineering
Languages : en
Pages : 326
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Book Description
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.
Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3031183932
Category : Technology & Engineering
Languages : en
Pages : 302
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Book Description
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.
Author: Gennadi I. Mikhasev
Publisher: CRC Press
ISBN: 1351630687
Category : Mathematics
Languages : en
Pages : 371
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Book Description
Localized Dynamics of Thin-Walled Shells focuses on localized vibrations and waves in thin-walled structures with variable geometrical and physical characteristics. It emphasizes novel asymptotic methods for solving boundary-value problems for dynamic equations in the shell theory, in the form of functions which are highly localized near both fixed and moving lines/points on the shell surface. Features First-of-its-kind work, synthesizing knowledge of the localization of vibrations and waves in thin-walled shells with a mathematical tool to study them Suitable for researchers working on the dynamics of thin shells and also as supplementary reading for undergraduates studying asymptotic methods Offers detailed analysis of wave processes in shells with varying geometric and physical parameters
Author: Holm Altenbach
Publisher: Springer
ISBN: 3319422774
Category : Science
Languages : en
Pages : 293
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Book Description
The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems:• comprehensive review of the most popular theories of plates and shells,• relations between three-dimensional theories and two-dimensional ones,• presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories),• modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc.,• applications in modeling of non-classical objects like, for example, nanostructures,• presentation of actual numerical tools based on the finite element approach.
Author: Francesco Tornabene
Publisher: Società Editrice Esculapio
ISBN: 8835328993
Category : Technology & Engineering
Languages : en
Pages : 1199
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Book Description
This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.
