krainaksiazek nonlinear analysis of rectangular laminated plates 20124143
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Mechanics of Laminated Composite Plates and Shells Taylor & Francis Inc
Książki / Literatura obcojęzyczna
Offers coverage of the theories, analytical solutions, and linear and nonlinear finite element models of plate and shell laminated composite structures. This work includes a chapter dedicated to the theory and analysis of laminated shells. It contains discussions addressing smart structures and functionally graded materials.
Geometrically non-linear analysis of layered composite plates and shells Politechnika Gdańska
This monograph includes the results of investigations carried out by the author since 1992. The whole period was divided into several research intervals of a different intensity. It all started during the author participation in the DFG-Research Project "Theory and Nonlinear FEM-Analysis of Elastic and Elasto-Plastic Anisotropic Structures Including Material Damage" performed under a supervision of Prof. Dieter Weichert and Dr-Ing. Rüdiger Schmidt at the University of Wuppertal, Germany in the period of 1991-1993r). Concurrently to, and to some extend separately from the main subject of the DFG project a scientific cooperation with Dr-Ing. Rüdiger Schmidt was initiated that was devoted to the FEM implementation of the Moderate Rotation Theory of anisotropic shells proposed by Schmidt and Reddy . First versions of computer programs for the geometrically nonlinear analysis of layered shells were prepared by the author already in Wuppertal. The results of this period of research were presented in two conference reports (Bödefeld et al. , Kreja and Schmidt ) and one journal paper (Kreja et al. ). After his return to the Gdansk University of Technology in 1993 the author continued the research searching for possible improvements in the accuracy of the results by including additional terms in strain-displacement relations, improving procedures of the rotation update (Kreja and Schmidt ) and exploring assumed natural strain approach (Kreja and Schmidt ). After several months of break related to the intensive involvement in other research projects the author returned to the investigations on large deformations of anisotropic shells resulted in a computer implementation of the large rotation theory of anisotropic shells proposed by Librescu . The results of that research activity were presented at several international conferences (Ferro et al. , Kreja , Kreja and Schmidt [266, 267]) and in one journal paper Kreja and Schmidt . The present report starts with an extensive literature survey on the main concepts of theoretical models for multi-layered plates and shells. Then a systematic construction of a computational model is presented for a large rotation analysis of elastic laminated shells including a Finite Element Method implementation of the proposed algorithm. An essential part of the present report is devoted to the examination on the relevance of various approximation decisions in the large deformation analysis of plate and shell problems. A number of sample problems of non-linear, large rotation response of composite laminated structures are discussed. The report ends with a short summary of main conclusions and some recommendations for the potential areas of future research. The supplemented list of references contains 512 items cited in the text. Spis treści: PREFACE LIST OF SYMBOL AND ABBREVIATIONS 1. INTRODUCTION 1.1. Plates and shells - from Nature to space industry 1.2. Laminated composites and sandwich panels 1.3. Scope and objectives of this report 2. LITERATURE REVIEW AND MODELING CONSIDERATIONS 2.1. Development of theoretical models for plates and shells 2.2. Geometrically non-linear analysis of plates and shells 2.3. Theoretical models for layered thin-walled structures 2.4. Numerical implementation of plate and shell theories 2.5. Modeling considerations resulted from the presented review 3. INCREMENTAL FORMULATION OF NONLINEAR SHELL ANALYSIS 3.1. Incremental formulation 3.2. Shell geometry 3.3. Shell deformation 3.4. Strain-displacement relations 3.5. Virtual work principle 3.6. Constitutive relations 4. FINITE ELEMENT METHOD IMPLEMENTATION 4.1. Finite element discretization of the problem 4.2. Incremental equilibrium equations of FE model 4.3. Solving of incremental equilibrium equations 4.4. Finite elements used in this study 4.5. Computer implementation of the proposed FEA algorithm 4.6. Assessment of selected elements in linear analysis 5. LARGE DEFORMATION ANALYSIS EXAMPLES 5.1. Instability of clamped-hinged circular arches 5.2. Clamped laminated shallow arch under point load 5.3. Hinged laminated cylindrical panels under point load 5.4. Glass-epoxy cylinder under internal pressure 5.5. Asymmetric cross-ply simply supported plate strip 5.6. Clamped laminated cylindrical panels under point load 5.7. Stretching of an open cylinder 5.8. Pinched hemispherical shell with 18° hole 5.9. Axial compression of composite cylindrical panel 5.10. Buckling of composite cylindrical panels with square cut-outs 6. CONCLUSIONS AND FUTURE PERSPECTIVES 6.1. Concluding Remarks 6.2. Original Contribution 6.3. Recommendations and Future Perspectives ACKNOWLEDGEMENTS DEDICATION REFERENCES SUMMARY IN ENGLISH SUMMARY IN POLISH
Analysis of Plates Alpha Science International Ltd.
This book deals with the classical plate theory most commonly used for the analysis of thin metallic plate structures. The basic assumptions of the plate theory are not straightaway taken for granted but are deduced as logical inferences from a three-dimensional elasticity solution for a thin rectangular slab. In addition the elasticity results are used to verify the accuracy of the plate theory. Statics dynamics as well as stability of plates are dealt with. Besides a lucid explanation of the theory exact and approximate solution methodologies are discussed. The approach adopted throughout--with emphasis on close correspondence with the three-dimensional theory of elasticity and on the implications of each assumption of the plate theory--enables the reader to easily progress on to the study of state-of-the-art topics such as geometric and material nonlinearities refined plate theories accounting for warping and stretching of the normal and laminated construction and material orthotropy typical of fibre-reinforced composites.
Theory of Thermal Stresses Dover Publications
Książki / Literatura obcojęzyczna
Note on Bibliographical References Part 1 BASIC THEORY Chapter 1. Mechanical and Thermodynamical Foundations 1.1 Introduction 1.2 Notation 1.3 Deformation; Small-Strain Tensor 1.4 Equations of Motion 1.5 Thermodynamics; Basic Definitions 1.6 Thermodynamics of Uniform Systems 1.7 Transition to Nonuniform Systems 1.8 Conservation of Energy in Nonuniform Systems 1.9 Preliminaries to the Second Law of Thermodynamics for Continua 1.10 Carathéodory's Statement of the Second Law of Thermodynamics and Its Consequences 1.11 Irreversible Theromodynamics; Entropy Production 1.12 Stress-Strain Relations and Energy Equation 1.13 Stress-Strain Relations and Energy Equation for an Isotropic Elastic Solid 1.14 Summary of Linear Coupled Thermoelastic Theory; Uniqueness Theorem Chapter 2. Uncoupled Quasi-Static Thermoelastic Theory 2.1 Introduction 2.2 General Remarks on the Effects of Coupling and Inertia 2.3 Solution of a Coupled Thermoelastic Problem 2.4 Discussion of Article 2.5 Effect of Inertia 2.6 Uncoupled Quasi-Static Foundation 2.7 "Uniqueness Theorems for the Uncoupled, Quasi-Static Thermoelastic Theory" Appendix Thermoelastic Damping Chapter 3. Alternate Formulations of Thermoelastic Problems 3.1 Introduction 3.2 Displacement Formulation 3.3 Body-Force Analogy 3.4 Reduction of the Thermoelastic Problem to One at Constant Temperature with No Body Forces; Goodier's Method 3.5 Use of Boussinesq-Papkovich Functions 3.6 Stress-Formulation 3.7 Necessity of Compatibility Equations 3.8 Stress-Formulation for Multiply Connected Bodies 3.9 Temperature Distributions Which Result in Zero Stress 3.10 Dislocations Chapter 4. Two-Dimensional Thermoelastic Formulations 4.1 Introduction 4.2 Plane-Strain Thermoelastic Problems 4.3 Boundary Conditions on the End Faces for the Case of Plane Strain 4.4 Stress Formulation of the Plane-Strain Problems 4.5 Stress Formulation in Terms of a Stress Function 4.6 Plane-Stress Thermoelastic Problems 4.7 Discussion of the Plane-Stress Solutions 4.8 Plane Stress as a Limiting Case of a Three-Dimensional State of Stress for Thin Slices 4.9 Steady-State Temperature Distributions 4.10 Dislocation Analogy Part 2 HEAT CONDUCTION Chapter 5. The Formulation of Heat Transfer Problems 5.1 Introduction 5.2 Modes of Heat Transfer 5.3 The Fourier Heat Conduction Equation 5.4 Initial and Boundary Conditions 5.5 Dimensionless Parameters 5.6 Discussion of the Boundary Conditions 5.7 Uniqueness Theorem 5.8 One-Dimensional Formulations for Thin Sections Chapter 6. Some Basic Problems in Heat Conduction 6.1 Introduction 6.2 Sources and Sinks in an Infinite Solid 6.3 A More General Solution of Eq. 6.2.3b 6.4 The Semi-Infinite Solid under Time-Dependent Boundary Conditions 6.5 Solutions Obtained by Superposition and Imaging of Sources Conditions 6.6 Alternative Forms of Series Solutions; Poisson's Formula 6.7 Temperatures Due to Sources Regarded as Fundamental Solutions (Green's Functions) 6.8 Saint-Venant's Principle in Heat Conduction Problems 6.9 Upper and Lower Bounds on the Temperature 6.10 Over-All Heat Balance; the Melting Slab Chapter 7. Methods of Solution of Heat Conduction Problems 7.1 Introduction 7.2 Separation of Variables (Method of Characteristic Functions) 7.3 Laplace Transforms 7.4 Conformal Mapping 7.5 Numerical Methods 7.6 Electrical Analogy 7.7 Approximate Analytical Procedures 7.8 Some Techniques for Extending Previous Solutions Part 3 THERMAL STRESS ANALYSIS FOR ELASTIC SYSTEMS Chapter 8. Summary of the Formulation of Thermoelastic Problems 8.1 Introduction 8.2 Thermoelastic Stress-Strain Relations 8.3 Equations of Equilibrium 8.4 Strain-Displacement Relations 8.5 Boundary Conditions 8.6 Mathematical Formulation of the Problem of Thermoelasticity 8.7 Principle Stresses and Strains 8.8 Separation of Stresses Due to Temperature and to External Loads 8.9 Alternative Formulations of the Problem of Thermoelasticity 8.10 Two-Dimensional Formulations 8.11 Energy Methods 8.12 Methods of Solution of Thermoelastic Problems Chapter 9. Some Basic Problems in Thermoelasticity 9.1 Introduction 9.2 Three-Dimensional Problems in Which the Stresses Are Zero 9.3 Three-Dimensional Problems in Which the Displacements Are Zero 9.4 Two-Dimensional Problems in which the Stresses in the Plane Are Zero 9.5 Free Plate with Temperature Variation through the Thickness Only 9.6 Rectangular Beam with Temperature Variation through the Depth Only 9.7 Discussion of Articles 9.5 and 9.6 9.8 Example for Articles 9.5 and 9.6 9.9 Slowly Heated Beam or Plate 9.10 Circular Disc or Cylinder with Radial Temperature Variation 9.11 Circular Disc or Cylinder with Plane-Harmonic Temperature Distribution 9.12 Additional References on Thermal Stresses in Cylinders 9.13 Circular Rectangular Beam with Radial Temperature Variation 9.14 Solid or Hollow Sphere under Radial Temperature Variation 9.15 Over-All Thermoelastic Deformation Chapter 10. Thermal Stresses in Beams 10.1 Introduction 10.2 Elementary Formulas for Normal Thermal Stresses in Free Beams 10.3 Thermal Deflections of Beams 10.4 Beam End-Conditions; Statically Indeterminate Beams 10.5 Thermal Shear Stresses in Thin-Walled Beams 10.6 Exact Two-Dimensional Thermoelastic Solution for Rectangular Beams under Arbitrary Temperature Distributions 10.7 Discussion of Article 10.6; Relation to Strength-of-Materials Theory 10.8 Exact Theory for Free Beams of Arbitrary Simply-Connected Cross Section with Linear Spanwise Temperature Distributions 10.9 Discussion of Article 10.8; Relation to Strength-of-Materials Theory 10.10 Use of Dummy Loads for the Calculation of Beam Deflections 10.11 Thermally Induced Vibrations of Beams Appendix The End-Problem in Beams; Saint-Venant's Principle "Chapter 11. Thermal Stresses in Curved Beams, Rings, Trusses, Frames, and Built-up Structures" 11.1 Introduction 11.2 Strength-of-Materials Theory for Thermal Stresses in Curved Beams 11.3 Discussion of Article 11.2; Relation to Exact and to Straight-Beam Analyses 11.4 Thermal Stresses in Rings 11.5 Thermal Stresses in Statically Determinate Trusses 11.6 Thermal Stresses in Statically Indeterminate Trusses 11.7 Thermal Stresses in Rigid Frames 11.8 Use of Influence Coefficients 11.9 References on the Analysis of Reinforced Sheet Structures Chapter 12. Thermal Stresses in Plates 12.1 Introduction 12.2 Basic Plate Equations 12.3 Plate Boundary Conditions 12.4 Solutions of Thermoelastic Plate Problems 12.5 Plates with Temperature Distributions Varying Through the Thickness Only 12.6 Relation of Thin-Plate Theory to Exact Thermoelastic Solutions 12.7 Thermally Induced Vibrations of Plates Chapter 13. Thermoelastic Stability and Related Problems 13.1 Introduction 13.2 Heated Beam-Columns with Ends Axially Unrestrained 13.3 Heated Beam-Columns with Ends Axially Restrained 13.4 Heated Beams under Axial Loads: General Theory 13.5 Discussion of Article 13.6 Bending and Buckling of Bimetallic Beams 13.7 Thermal Buckling of Plates 13.8 Buckling of Plates Subjected to Heat and No Transverse Loads with Edges Unrestrained in the Plane 13.9 Buckling of Plates Subjected to Heat and Loads in the Plane; Edges Unrestrained in the Plane 13.10 Plates with Their Edges Restrained in the Plane 13.11 Large Deflections and Post-Buckling Behavior of Plates Part 4 THERMAL STRESS ANALYSIS FOR INELASTIC SYSTEMS Chapter 14. The Formulation of Inelastic Thermal Stress Problems 14.1 Introduction 14.2 Stress Relaxation and Creep 14.3 Plastic Flow and Work-Hardening 14.4 Idealized Theories and Materials 14.5 Viscoelastic Stress-Strain Relations 14.6 Idealized Plasticity Theory: Work-Hardening Solid 14.7 Idealized Plasticity Theory: Perfectly Plastic Solid 14.8 Uniqueness Theorem for Perfectly Plastic Solid 14.9 The Mises Yield Condition 14.10 The Tresca Yield Condition 14.11 Combined Viscoelastic and Plastic Effects Chapter 15. Viscoelastic Stress Analysis 15.1 Introduction 15.2 Viscoelastic-Elastic Analogy 15.3 Discussion of the Viscoelastic-Elastic Analogy 15.4 Example for the Viscoelastic-Elastic Analogy 15.5 Linear Viscoelastic Strength-of-Materials Theory 15.6 Initial Conditions for a Linear Viscoelastic Solid 15.7 Nonlinear Viscoelastic Analyses 15.8 Nonlinear Viscoelastic Strength-of-Materials Theory; Creep Rupture in Tension 15.9 Creep Buckling 15.10 Further Investigations of Creep Buckling Chapter 16. Plastic Stress Analysis 16.1 Introduction 16.2 Elastoplastic Free Plate Analysis 16.3 Two Examples of Elastoplastic Plate Analysis 16.4 "Free Plate Analysis, Including a Temperature-Dependent Yield Condition and Viscoelastic Effects" 16.5 Elastoplastic Cylinder Analysis-Tresca Condition 16.6 Elastoplastic Cylinder Analysis-Mises Condition AUTHOR INDEX SUBJECT INDEX
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t1=0.051, t2=0, t3=0, t4=0.026, t=0.051