{"product_id":"plate-and-shell-structures-9781118934548","title":"Plate and Shell Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePlate and Shell Structures: \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSelected Analytical and Finite Element Solutions\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMaria Radwañska, Anna Stankiewicz, Adam Wosatko, Jerzy Pamin\u003c\/p\u003e \u003cp\u003eCracow University of Technology, Poland\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\u003ci\u003eComprehensively covers the fundamental theory and analytical and numerical solutions for different types of plate and shell structures\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\u003ci\u003e\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePlate and Shell Structures: Selected Analytical and Finite Element Solutions\u003c\/i\u003e not only provides the theoretical formulation of fundamental problems of mechanics of plates and shells, but also several examples of analytical and numerical solutions for different types of shell structures. The book contains advanced aspects related to stability analysis and a brief description of modern finite element formulations for plates and shells, including the discussion of mixed\/hybrid models and locking phenomena.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eKey features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e52 example problems solved and il\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eNotation xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 1 Fundamentals: Theory and Modelling 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 General Information 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 Review of Theories Describing Elastic Plates and Shells 6\u003c\/p\u003e \u003cp\u003e1.3 Description of Geometry for 2D Formulation 9\u003c\/p\u003e \u003cp\u003e1.4 Definitions and Assumptions for 2D Formulation 16\u003c\/p\u003e \u003cp\u003e1.5 Classification of Shell Structures 21\u003c\/p\u003e \u003cp\u003eReferences 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Equations for Theory of Elasticity for 3D Problems 26\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReference 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Equations of Thin Shells According to the Three-Parameter Kirchhoff–Love Theory 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 General Equations for Thin Shells 31\u003c\/p\u003e \u003cp\u003e3.2 Specification of Lame Parameters and Principal Curvature Radii for Typical Surfaces 38\u003c\/p\u003e \u003cp\u003e3.3 Transition from General Shell Equations to Particular Cases of Plates and Shells 42\u003c\/p\u003e \u003cp\u003e3.4 Displacement Equations for Multi-Parameter Plate and Shell Theories 45\u003c\/p\u003e \u003cp\u003e3.5 Remarks 47\u003c\/p\u003e \u003cp\u003eReferences 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 General Information about Models and Computational Aspects 48\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Analytical Approach to Statics, Buckling and Free Vibrations 49\u003c\/p\u003e \u003cp\u003e4.2 Approximate Approach According to the Finite Difference Method 51\u003c\/p\u003e \u003cp\u003e4.3 Computational Analysis by Finite Element Method 54\u003c\/p\u003e \u003cp\u003e4.4 Computational Models – Summary 55\u003c\/p\u003e \u003cp\u003eReference 55\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Description of Finite Elements for Analysis of Plates and Shells 56\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 General Information on Finite Elements 56\u003c\/p\u003e \u003cp\u003e5.2 Description of Selected FEs 58\u003c\/p\u003e \u003cp\u003e5.3 Remarks on Displacement-based FE Formulation 69\u003c\/p\u003e \u003cp\u003eReferences 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 2 Plates 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Flat Rectangular Membranes 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 75\u003c\/p\u003e \u003cp\u003e6.2 Governing Equations 76\u003c\/p\u003e \u003cp\u003e6.3 Square Membrane under Unidirectional Tension 81\u003c\/p\u003e \u003cp\u003e6.4 Square Membrane under Uniform Shear 83\u003c\/p\u003e \u003cp\u003e6.5 Pure In-Plane Bending of a Square Membrane 85\u003c\/p\u003e \u003cp\u003e6.6 Cantilever Beam with a Load on the Free Side 88\u003c\/p\u003e \u003cp\u003e6.7 Rectangular Deep Beams 94\u003c\/p\u003e \u003cp\u003e6.8 Membrane with Variable Thicknesses or Material Parameters 97\u003c\/p\u003e \u003cp\u003eReferences 101\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Circular and Annular Membranes 102\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Equations of Membranes – Local and Global Formulation 102\u003c\/p\u003e \u003cp\u003e7.2 Equations for the Axisymmetric Membrane State 104\u003c\/p\u003e \u003cp\u003e7.3 Annular Membrane 105\u003c\/p\u003e \u003cp\u003eReferences 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Rectangular Plates under Bending 110\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 110\u003c\/p\u003e \u003cp\u003e8.2 Equations for the Classical Kirchhoff–Love Thin Plate Theory 110\u003c\/p\u003e \u003cp\u003e8.3 Derivation of Displacement Equation for a Thin Plate from the Principle of Minimum Potential Energy 117\u003c\/p\u003e \u003cp\u003e8.4 Equation for a Plate under Bending Resting on a Winkler Elastic Foundation 118\u003c\/p\u003e \u003cp\u003e8.5 Equations of Mindlin–Reissner Moderately Thick Plate Theory 119\u003c\/p\u003e \u003cp\u003e8.6 Analytical Solution of a Sinusoidally Loaded Rectangular Plate 122\u003c\/p\u003e \u003cp\u003e8.7 Analysis of Plates under Bending Using Expansions in Double or Single Trigonometric Series 127\u003c\/p\u003e \u003cp\u003e8.8 Simply Supported or Clamped Square Plate with Uniform Load 131\u003c\/p\u003e \u003cp\u003e8.9 Rectangular Plate with a Uniform Load and Various Boundary Conditions – Comparison of STSM and FEM Results 135\u003c\/p\u003e \u003cp\u003e8.10 Uniformly Loaded Rectangular Plate with Clamped and Free Boundary Lines – Comparison of STSM and FEM Results 139\u003c\/p\u003e \u003cp\u003e8.11 Approximate Solution to a Plate Bending Problem using FDM 143\u003c\/p\u003e \u003cp\u003e8.12 Approximate Solution to a Bending Plate Problem using the Ritz Method 151\u003c\/p\u003e \u003cp\u003e8.13 Plate with Variable Thickness 153\u003c\/p\u003e \u003cp\u003e8.14 Analysis of Thin and Moderately Thick Plates in Bending 155\u003c\/p\u003e \u003cp\u003eReferences 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Circular and Annular Plates under Bending 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 General State 160\u003c\/p\u003e \u003cp\u003e9.2 Axisymmetric State 162\u003c\/p\u003e \u003cp\u003e9.3 Analytical Solution using a Trigonometric Series Expansion 164\u003c\/p\u003e \u003cp\u003e9.4 Clamped Circular Plate with a Uniformly Distributed Load 166\u003c\/p\u003e \u003cp\u003e9.5 Simply Supported Circular Plate with a Concentrated Central Force 169\u003c\/p\u003e \u003cp\u003e9.6 Simply Supported Circular Plate with an Asymmetric Distributed Load 171\u003c\/p\u003e \u003cp\u003e9.7 Uniformly Loaded Annular Plate with Static and Kinematic Boundary Conditions 174\u003c\/p\u003e \u003cp\u003eReferences 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 3 Shells 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Shells in the Membrane State 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 181\u003c\/p\u003e \u003cp\u003e10.2 General Membrane State in Shells of Revolution 182\u003c\/p\u003e \u003cp\u003e10.3 Axisymmetric Membrane State 183\u003c\/p\u003e \u003cp\u003e10.4 Hemispherical Shell 186\u003c\/p\u003e \u003cp\u003e10.5 Open Conical Shell under Self Weight 193\u003c\/p\u003e \u003cp\u003e10.6 Cylindrical Shell 195\u003c\/p\u003e \u003cp\u003e10.7 Hemispherical Shell with an Asymmetric Wind Action 199\u003c\/p\u003e \u003cp\u003eReferences 204\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Shells in the Membrane-Bending State 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Cylindrical Shells 205\u003c\/p\u003e \u003cp\u003e11.2 Spherical Shells 221\u003c\/p\u003e \u003cp\u003e11.3 Cylindrical and Spherical Shells Loaded by a Uniformly Distributed Boundary Moment and Horizontal Force 229\u003c\/p\u003e \u003cp\u003e11.4 Cylindrical Shell with a Spherical Cap – Analytical and Numerical Solution 232\u003c\/p\u003e \u003cp\u003e11.5 General Case of Deformation of Cylindrical Shells 237\u003c\/p\u003e \u003cp\u003e11.6 Cylindrical Shell with a Semicircular Cross Section under Self Weight – Analytical Solution of Membrane State 238\u003c\/p\u003e \u003cp\u003e11.7 Cylindrical Scordelis-Lo Roof in the Membrane-Bending State – Analytical and Numerical Solution 242\u003c\/p\u003e \u003cp\u003e11.8 Single-Span Clamped Horizontal Cylindrical Shell under Self Weight 246\u003c\/p\u003e \u003cp\u003eReferences 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Shallow Shells 256\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Equations for Shallow Shells 256\u003c\/p\u003e \u003cp\u003e12.2 Pucher’s Equations for Shallow Shells in the Membrane State 260\u003c\/p\u003e \u003cp\u003e12.3 Hyperbolic Paraboloid with Rectangular Projection 262\u003c\/p\u003e \u003cp\u003e12.4 Remarks on Engineering Applications 266\u003c\/p\u003e \u003cp\u003eReferences 267\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Thermal Loading of Selected Membranes, Plates and Shells 268\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 268\u003c\/p\u003e \u003cp\u003e13.2 Uniform Temperature Change along the Thickness 270\u003c\/p\u003e \u003cp\u003e13.3 Linear Temperature Change along the Thickness – Analytical Solutions 275\u003c\/p\u003e \u003cp\u003eReferences 286\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 4 Stability and Free Vibrations 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Stability of Plates and Shells 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Overview of Plate and Shell Stability Problems 289\u003c\/p\u003e \u003cp\u003e14.2 Basis of Linear Buckling Theory, Assumptions and Computational Models 291\u003c\/p\u003e \u003cp\u003e14.3 Description of Physical Phenomena and Nonlinear Simulations in Stability Analysis 298\u003c\/p\u003e \u003cp\u003e14.4 Analytical and Numerical Buckling Analysis for Selected Plates and Shells 301\u003c\/p\u003e \u003cp\u003e14.5 Snap-Through and Snap-Back Phenomena Observed for Elastic Shallow Cylindrical Shells in Geometrically Nonlinear Analysis 319\u003c\/p\u003e \u003cp\u003eReferences 321\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Free Vibrations of Plates and Shells 323\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 323\u003c\/p\u003e \u003cp\u003e15.2 Natural Transverse Vibrations of a Thin Rectangular Plate 325\u003c\/p\u003e \u003cp\u003e15.3 Parametric Analysis of Free Vibrations of Rectangular Plates 328\u003c\/p\u003e \u003cp\u003e15.4 Natural Vibrations of Cylindrical Shells 333\u003c\/p\u003e \u003cp\u003e15.5 Remarks 337\u003c\/p\u003e \u003cp\u003eReferences 338\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 5 Aspects of FE Analysis 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Modelling Process 341\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Advantages of Numerical Simulations 341\u003c\/p\u003e \u003cp\u003e16.2 Complexity of Shell Structures Affecting FEM 342\u003c\/p\u003e \u003cp\u003e16.3 Particular Requirements for FEs in Plate and Shell Discretization 343\u003c\/p\u003e \u003cp\u003eReferences 346\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Quality of FEs and Accuracy of Solutions in Linear Analysis 347\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Order of Approximation Function versus Order of Numerical Integration Quadrature 347\u003c\/p\u003e \u003cp\u003e17.2 Assessment of Element Quality via Spectral Analysis 347\u003c\/p\u003e \u003cp\u003e17.3 Numerical Effects of Shear Locking and Membrane Locking 350\u003c\/p\u003e \u003cp\u003e17.4 Examination of Element Quality – One-Element and Patch Tests 354\u003c\/p\u003e \u003cp\u003e17.5 Benchmarks for Membranes and Plates 357\u003c\/p\u003e \u003cp\u003e17.6 Benchmarks for Shells 359\u003c\/p\u003e \u003cp\u003e17.7 Comparison of Analytical and Numerical Solutions, Application of Various FE Formulations 361\u003c\/p\u003e \u003cp\u003eReferences 362\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Advanced FE Formulations 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 365\u003c\/p\u003e \u003cp\u003e18.2 Link between Variational Formulations and FE Models 366\u003c\/p\u003e \u003cp\u003e18.3 Advanced FEs 373\u003c\/p\u003e \u003cp\u003eReferences 383\u003c\/p\u003e \u003cp\u003eA List of Boxes with Equations 387\u003c\/p\u003e \u003cp\u003eB List of Boxes with Data and Results for Examples 389\u003c\/p\u003e \u003cp\u003eIndex 391\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528841961815,"sku":"9781118934548","price":101.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118934548.jpg?v=1731873234","url":"https:\/\/bookcurl.com\/products\/plate-and-shell-structures-9781118934548","provider":"Book Curl","version":"1.0","type":"link"}