Simplified analytical methods of elastic plates
By: Takabatake, Hideo
Material type:
BookPublisher: Singapore : Springer, c2019.Description: xvii, 344 p. : ill. ; 25 cm.ISBN: 9789811300851Subject(s): Elastic plates and shells | Solid Mechanics | Building Construction and Design | Mechanics, AppliedDDC classification: 624.1776 TA SI Online resources: Location Map | Item type | Home library | Call number | Status | Notes | Date due | Barcode | Item holds |
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| REGULAR | University of Wollongong in Dubai Main Collection | 624.1776 TA SI (Browse shelf) | Available | June2019 | T0062517 |
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| 624.151 KE GE Geology for engineers and environmental scientists | 624.151 RI SK Risk and reliability in geotechnical engineering | 624.151 YI PR Practice of optimisation theory in geotechnical engineering | 624.1776 TA SI Simplified analytical methods of elastic plates | 624 BI MO Movable bridge design | 624 BR GE Geotechnical engineering : | 624 CI VI The civil engineering handbook |
Part I Static and Dynamic Analyses of Normal Plates1 Static and Dynamic Analyses of Rectangular Normal Plates1.1 Introduction 1.2 Equilibrium Equations of the Plate Element1.3 Relationships Among Stress, Strain, and Displacements1.4 Stress Resultants and Stress Couples Expressed in Term of w1.5 Boundary Conditions of the Bending Theory1.6 Analytical Method of Static Rectangular Plates Used the Galerkin Method1.7 Selection of Shape Functions for Static Problems1.8 Free Transverse Vibrations of Plates without Damping1.9 Forced Vibrations of Rectangular Plates1.10 Dynamic Response of Sinusoidal Dynamic Loads1.11 ConclusionsReferences2 Static and Dynamic Analyses of Circular Normal Plates2.1 Introduction2.2 Governing Equations of Uniform Circular Plates2.3 Governing Equations of Circular Plates Subjected to Rotationally Symmetric Loading2.4 ConclusionsReferences3 Static and Dynamic Analyses of Rectangular Normal Plates with Edge Beams3.1 Introduction3.2 Governing Equations of a Normal Plate with Edge Beams3.3 Static Analysis Used the Galerkin Method3.4 Numerical Results for Static Solution3.5 Free Transverse Vibrations of a Plate with Edge Beams3.6 Numerical Results for Natural Frequencies3.7 Forced Vibrations of a Plate with Edge Beams3.8 Approximate Solutions for Forced Vibrations3.9 Numerical Results for Dynamic Responses3.10 ConclusionsAppendix A3.1Appendix A3.2ReferencesPart II Static and Dynamic Analyses of Various Plates 4 Static and Dynamic Analyses of Rectangular Plates with Voids4.1 Introduction4.2 Governing Equations of Plates with Voids4.3 Static Analyses to Rectangular Plates with Voids4.4 Numerical Results4.5 Relationships between Theoretical and Experimental Results4.6 Conclusions for the Static Problems4.7 Free Transverse Vibrations of a Plate with Voids4.8 Numerical Results for Natural Frequencies4.9 Relationships between Theoretical Results and Experimental Results for Natural Frequencies4.10 Forced Vibrations of Plates with Voids4.11 Dynamic Analyses Based on the Linear Acceleration Method 4.12 Closed-form Approximate Solutions for Forced Vibrations4.13 Numerical Results for Dynamical Responses; Discussions 4.14 Conclusions for Free and Forced VibrationsReferences5 Static and Dynamic Analyses of Circular Plates with Voids5.1 Introduction5.2 Governing Equations of a Circular Plate with Voids5.3 Static Analysis5.4 Numerical Results for Static Problems5.5 Free Transverse Vibrations of Plate with Voids5.6 Numerical Results for Natural Frequencies5.7 Forced Vibrations of Plates with Voids5.8 Closed-form Approximate Solutions for Forced Vibrations 5.9 Numerical Results for Dynamic Responses: Discussions 5.10 ConclusionsReferences6 Static and Dynamic Analyses of Rectangular Cellular Plates6.1 Introduction6.2 Governing Equations of a Cellular Plate with Transverse Shear Deformations along with Frame Deformation6.3 Transverse Shear Stiffness of Cellular Plates6.4 Stress Resultants and Stress Couples of Platelets and Partition6.5 Static Analysis6.6 Numerical Results for Static Calculation6.7 Free Transverse Vibrations of Cellular Plates6.8 Numerical Results for Natural Frequencies 6.9 Forced Vibration of Cellular Plates6.10 Approximate Solutions for Forced Vibrations6.11 Numerical Results for Dynamic Responses 6.12 Conclusions Appendix A6.1Appendix A6.2Appendix A6.3References7 Static and Dynamic Analyses of Circular Cellular Plates7.1 Introduction7.2 Governing Equations of a Circular Cellular Plate with Transverse Shear Deformations along with Frame Deformation7.3 Transverse Shear Stiffness of Cellular Plates7.4 Stress Resultants and Stress Couples of Platelets and Partition7.5 Static Analysis7.6 Numerical Results for Static Problem7.7 Free Transverse Vibrations of Cellular Plates7.8 Numerical Results for Natural Frequencies7.9 Forced Vibration of Cellular Plates7.10 Numerical Results for Dynamic Responses7.11 ConclusionsAppendix A7.1Appendix A7.2Appendix A7.3Appendix A7.4References8 Static and Dynamic Analyses of Rectangular Plates with Stepped Thickness8.1 Introduction8.2 Governing Equations of Rectangular Plates with Stepped Thickness8.3 Static Analysis8.4 Numerical Results for Static Solution8.5 Free Transverse Vibrations of Plate with Stepped Thickness8.6 Numerical Results for Natural Frequencies8.7 Forced Vibrations of Plate with Stepped Thickness8.8 Approximate Solutions for Forced Vibrations8.9 Numerical Results for Dynamic Responses8.10 ConclusionsAppendix A8.1ReferencesPart III Static and Dynamic Analysis of Special Plates9 Static and Dynamic Analyses of Rectangular Plates with Stepped Thickness Subjected to Moving Loads9.1 Introduction9.2 Governing Equations of Plate with Stepped Thickness Including the Effect of Moving Additional Mass9.3 Forced Vibration of a Plate with Stepped Thickness9.4 Approximate Solution Excluding the Effect of Additional Mass due to Moving Loads9.5 Numerical Results9.6 Conclusions References10 Static and Dynamic Analyses of Rectangular Floating Plates Subjected to Moving Loads10.1 Introduction10.2 Governing Equations of a Rectangular Plate on an Elastic Foundation10.3 Free Transverse Vibrations10.4 Forced Transverse Vibrations10.5 Approximate Solutions for Forced Transverse Vibration10.6 Numerical Results10.7 ConclusionsAppendix A10.1References Part IV Effects of Dead Loads on Elastic Plates 11 Effects of Dead Loads on Static and Dynamic Analyses of Rectangular Plates11.1 Introduction11.2 Governing Equations Including the Effect of Dead Loads for Plates11.3 Formulation of Static Problem Including the Effect of Dead Loads11.4 Numerical Results11.5 Approximate Solution11.6 Example11.7 Transverse Free Vibration Based on the Galerkin Method11.8 Closed-form Solution for Transverse Free Vibrations11.9 Dynamic Analyses Based on the Galerkin Method11.10 Dynamic Analyses Based on the Approximate Closed-form Solution11.11 Numerical Results to Dynamic Live Loads11.12 Method Reflected the Effect of Dead Loads in Dynamic Problems 11.13 ConclusionsAppendix A11.1ReferencesPart V Effects of Dead Loads on Elastic Beams12 Effects of Dead Loads on Static and Free Vibration Problems of Beams12.1 Introduction 12.2 Advanced Governing Equations of Beams Including Effect of Dead Loads12.3 Numerical Results Using Galerkin Method for Static Problems12.4 Closed-form Solutions Including Effect of Dead Loads in Static Problems12.5 Proposal How to Reflect the Effect of Dead Load on Static Beams12.6 Free Transverse Vibrations of Uniform Beams12.7 Numerical Results for Free Transverse Vibrations of Beams Using Galerkin Method12.8 Closed-form Approximate Solutions for Natural Frequencies12.9 ConclusionsAppendix A12.1References13 Effects of Dead Loads on Dynamic Problems of Beams13.1 Introduction13.2 Dynamic Analyses of Beams Subject to Unmoving Dynamic Live Loads13.3 Numerical Results for Beams Subject to Unmoving Dynamic Live Loads13.4 Approximate Solutions for Simply Supported Beams Subject to Unmoving Dynamic Live Loads13.5 How to Import the Effect of Dead Loads for Dynamic Beams Subject to Unmoving Dynamic Live Loads13.6 Dynamic Analyses Using the Galerkin Method on Dynamic Beams Subject to Moving Live Loads13.7 Various Moving Loads13.8 Additional Mass due to Moving Loads13.9 Approximate Solutions of Beams Subject to Moving Live Loads13.10 Numerical Results for Beams Subject to Moving Live Loads13.11 ConclusionsReferencesPart VI Recent Topics of Plate Analysis14 Refined Plate Theory in Bending Problem of Uniform Rectangular Plates14.1 Introduction14.2 Various Plate Theories14.3 Analysis of Isotropic Plates Using Refined Plate Theory14.4 The Governing Equation in RPT14.5 Simplified RPT14.6 Static Analysis Used Simplified RPT14.7 Selection of Shape Functions for Static Problems14.8 Free Transverse Vibrations of Plates without Damping14.9 Forced Vibration of Plates in Simplified RPT14.10 Advanced Transformation of Uncoupled Form in Simplified RPT14.11 Advanced RPT14.12 ConclusionsReferences.
This book presents simplified analytical methodologies for static and dynamic problems concerning various elastic thin plates in the bending state and the potential effects of dead loads on static and dynamic behaviors. The plates considered vary in terms of the plane (e.g. rectangular or circular plane), stiffness of bending, transverse shear and mass. The representative examples include void slabs, plates stiffened with beams, stepped thickness plates, cellular plates and floating plates, in addition to normal plates. The closed-form approximate solutions are presented in connection with a groundbreaking methodology that can easily accommodate discontinuous variations in stiffness and mass with continuous function as for a distribution. The closed-form solutions can be used to determine the size of structural members in the preliminary design stages, and to predict potential problems with building slabs intended for human beings’ practical use.