Overview

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.

Full Product Details

Author:   Hideo Takabatake
Publisher:   Springer Verlag, Singapore
Imprint:   Springer Verlag, Singapore
Edition:   1st ed. 2019
Weight:   0.711kg
ISBN:  

9789811300851

ISBN 10:   9811300852
Pages:   344
Publication Date:   13 November 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Part  I  Static and Dynamic Analyses of Normal Plates 1   Static and Dynamic Analyses of Rectangular Normal Plates 1.1   Introduction  1.2   Equilibrium Equations of the Plate Element 1.3   Relationships Among Stress, Strain, and Displacements 1.4   Stress Resultants and Stress Couples Expressed in Term of w 1.5   Boundary Conditions of the Bending Theory 1.6   Analytical Method of Static Rectangular Plates Used the Galerkin Method 1.7   Selection of Shape Functions for Static Problems 1.8   Free Transverse Vibrations of Plates without Damping 1.9   Forced Vibrations of Rectangular Plates 1.10 Dynamic Response of Sinusoidal Dynamic Loads 1.11 Conclusions References 2   Static and Dynamic Analyses of Circular Normal Plates 2.1   Introduction 2.2   Governing Equations of Uniform Circular Plates 2.3   Governing Equations of Circular Plates Subjected to Rotationally Symmetric Loading 2.4   Conclusions References 3   Static and Dynamic Analyses of Rectangular Normal Plates with Edge Beams 3.1   Introduction 3.2   Governing Equations of a Normal Plate with Edge Beams 3.3   Static Analysis Used the Galerkin Method 3.4   Numerical Results for Static Solution 3.5   Free Transverse Vibrations of a Plate with Edge Beams 3.6   Numerical Results for Natural Frequencies 3.7   Forced Vibrations of a Plate with Edge Beams 3.8   Approximate Solutions for Forced Vibrations 3.9   Numerical Results for Dynamic Responses 3.10 Conclusions Appendix A3.1 Appendix A3.2 References Part II    Static and Dynamic Analyses of Various Plates 4   Static and Dynamic Analyses of Rectangular Plates with Voids 4.1   Introduction 4.2   Governing Equations of Plates with Voids 4.3   Static Analyses to Rectangular Plates with Voids 4.4   Numerical Results 4.5   Relationships between Theoretical and Experimental Results 4.6   Conclusions for the Static Problems 4.7   Free Transverse Vibrations of a Plate with Voids 4.8   Numerical Results for Natural Frequencies 4.9   Relationships between Theoretical Results and Experimental Results for Natural Frequencies 4.10 Forced Vibrations of Plates with Voids 4.11 Dynamic Analyses Based on the Linear Acceleration Method  4.12 Closed-form Approximate Solutions for Forced Vibrations 4.13 Numerical Results for Dynamical Responses; Discussions  4.14 Conclusions for Free and Forced Vibrations References 5   Static and Dynamic Analyses of Circular Plates with Voids 5.1   Introduction 5.2   Governing Equations of a Circular Plate with Voids 5.3   Static Analysis 5.4   Numerical Results for Static Problems 5.5   Free Transverse Vibrations of Plate with Voids 5.6   Numerical Results for Natural Frequencies 5.7   Forced Vibrations of Plates with Voids 5.8   Closed-form Approximate Solutions for Forced Vibrations  5.9   Numerical Results for Dynamic Responses: Discussions  5.10 Conclusions References 6   Static and Dynamic Analyses of Rectangular Cellular Plates 6.1   Introduction 6.2   Governing Equations of a Cellular Plate with Transverse Shear Deformations along with Frame Deformation 6.3   Transverse Shear Stiffness of Cellular Plates 6.4   Stress Resultants and Stress Couples of Platelets and Partition 6.5   Static Analysis 6.6   Numerical Results for Static Calculation 6.7   Free Transverse Vibrations of Cellular Plates 6.8   Numerical Results for Natural Frequencies  6.9   Forced Vibration of Cellular Plates 6.10 Approximate Solutions for Forced Vibrations 6.11 Numerical Results for Dynamic Responses  6.12 Conclusions  Appendix A6.1 Appendix A6.2 Appendix A6.3 References 7   Static and Dynamic Analyses of Circular Cellular Plates 7.1   Introduction 7.2   Governing Equations of a Circular Cellular Plate with Transverse Shear Deformations along with Frame Deformation 7.3   Transverse Shear Stiffness of Cellular Plates 7.4   Stress Resultants and Stress Couples of Platelets and Partition 7.5   Static Analysis 7.6   Numerical Results for Static Problem 7.7   Free Transverse Vibrations of Cellular Plates 7.8   Numerical Results for Natural Frequencies 7.9   Forced Vibration of Cellular Plates 7.10 Numerical Results for Dynamic Responses 7.11 Conclusions Appendix A7.1 Appendix A7.2 Appendix A7.3 Appendix A7.4 References 8   Static and Dynamic Analyses of Rectangular Plates with Stepped Thickness 8.1   Introduction 8.2   Governing Equations of Rectangular Plates with Stepped Thickness 8.3   Static Analysis 8.4   Numerical Results for Static Solution 8.5   Free Transverse Vibrations of Plate with Stepped Thickness 8.6   Numerical Results for Natural Frequencies 8.7   Forced Vibrations of Plate with Stepped Thickness 8.8   Approximate Solutions for Forced Vibrations 8.9   Numerical Results for Dynamic Responses 8.10 Conclusions Appendix A8.1 References Part  III   Static and Dynamic Analysis of Special Plates 9   Static and Dynamic Analyses of Rectangular Plates with Stepped Thickness Subjected to Moving Loads 9.1   Introduction 9.2   Governing Equations of Plate with Stepped Thickness Including the Effect of Moving Additional Mass 9.3   Forced Vibration of a Plate with Stepped Thickness 9.4   Approximate Solution Excluding the Effect of Additional Mass due to Moving Loads 9.5   Numerical Results 9.6   Conclusions  References 10 Static and Dynamic Analyses of Rectangular Floating Plates Subjected to Moving Loads 10.1 Introduction 10.2 Governing Equations of a Rectangular Plate on an Elastic Foundation 10.3 Free Transverse Vibrations 10.4 Forced Transverse Vibrations 10.5 Approximate Solutions for Forced Transverse Vibration 10.6 Numerical Results 10.7 Conclusions Appendix A10.1 References Part IV   Effects of Dead Loads on Elastic Plates 11 Effects of Dead Loads on Static and Dynamic Analyses of Rectangular Plates 11.1 Introduction 11.2 Governing Equations Including the Effect of Dead Loads for Plates 11.3 Formulation of Static Problem Including the Effect of Dead Loads 11.4 Numerical Results 11.5 Approximate Solution 11.6 Example 11.7 Transverse Free Vibration Based on the Galerkin Method 11.8 Closed-form Solution for Transverse Free Vibrations 11.9 Dynamic Analyses Based on the Galerkin Method 11.10 Dynamic Analyses Based on the Approximate Closed-form Solution 11.11 Numerical Results to Dynamic Live Loads 11.12 Method Reflected the Effect of Dead Loads in Dynamic Problems 11.13 Conclusions Appendix A11.1 References Part V   Effects of Dead Loads on Elastic Beams 12 Effects of Dead Loads on Static and Free Vibration Problems of Beams 12.1 Introduction  12.2 Advanced Governing Equations of Beams Including Effect of Dead Loads 12.3 Numerical Results Using Galerkin Method for Static Problems 12.4 Closed-form Solutions Including Effect of Dead Loads in Static Problems 12.5 Proposal How to Reflect the Effect of Dead Load on Static Beams 12.6 Free Transverse Vibrations of Uniform Beams 12.7 Numerical Results for Free Transverse Vibrations of Beams Using Galerkin Method 12.8 Closed-form Approximate Solutions for Natural Frequencies 12.9 Conclusions Appendix A12.1 References 13 Effects of Dead Loads on Dynamic Problems of Beams 13.1 Introduction 13.2 Dynamic Analyses of Beams Subject to Unmoving Dynamic Live Loads 13.3 Numerical Results for Beams Subject to Unmoving Dynamic Live Loads 13.4 Approximate Solutions for Simply Supported Beams Subject to Unmoving Dynamic Live Loads 13.5 How to Import the Effect of Dead Loads for Dynamic Beams Subject to Unmoving Dynamic Live Loads 13.6 Dynamic Analyses Using the Galerkin Method on Dynamic Beams Subject to Moving Live Loads 13.7 Various Moving Loads 13.8 Additional Mass due to Moving Loads 13.9 Approximate Solutions of Beams Subject to Moving Live Loads 13.10 Numerical Results for Beams Subject to Moving Live Loads 13.11 Conclusions References Part VI   Recent Topics of Plate Analysis 14 Refined Plate Theory in Bending Problem of Uniform Rectangular Plates 14.1 Introduction 14.2 Various Plate Theories 14.3 Analysis of Isotropic Plates Using Refined Plate Theory 14.4 The Governing Equation in RPT 14.5 Simplified RPT 14.6 Static Analysis Used Simplified RPT 14.7 Selection of Shape Functions for Static Problems 14.8 Free Transverse Vibrations of Plates without Damping 14.9 Forced Vibration of Plates in Simplified RPT 14.10 Advanced Transformation of Uncoupled Form in Simplified RPT 14.11 Advanced RPT 14.12 Conclusions References

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Author Information

Hideo Takabatake is a professor and a advisor of Institute of Disaster and Environmental Science at Kanazawa Institute of Technology, Japan. After completing the doctoral course at Kyoto University graduate school in 1973, he received a doctorate degree in engineering from Nagoya University in 1979.He has been a professor at Kanazawa Institute of Technology from 1978 until now. Concurrent post of director (2008-2017) and advisor (2017-2018) at Institute of Disaster and Environmental Science. He has authored several books on the many subjects of structural seismic design and structural mechanic. He presented a creative position in studies, such as static and dynamic problems of plates and beams, the clarification of thrown-out boulders for earthquake shaking, the relaxation method for earthquake pounding action between adjacent buildings, simple analytical method of skyscrapers, and a general analytical methodology for lateral buckling of partially stiffened beams.His researchstyle is characterized by a pioneering idea from a new viewpoint and a logical development of it and presenting it in a concise form against many problems in building engineering. The methods developed in this book are part of his pioneering idea. He served on the board of directors of the Architectural Institute of Japan (AIJ) and the chairman of several committees in the AIJ structural commission.

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