Simplified Analytical Methods of Elastic Plates

en Limba Engleză Hardback – 12 noi 2018

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.

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Specificații

ISBN-13: 9789811300851
ISBN-10: 9811300852
Pagini: 280
Ilustrații: XVII, 344 p. 136 illus.
Dimensiuni: 155 x 235 x 23 mm
Greutate: 0.69 kg
Ediția:1st ed. 2019
Editura: Springer Nature Singapore
Colecția Springer
Locul publicării:Singapore, Singapore

Cuprins

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

Notă biografică

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 research style 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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Caracteristici

Enables readers to easily formulate unique and expandable theories on various plates with variable stiffness and mass by employing the extended Dirac function
Demonstrates step by step how to obtain closed-form solutions from the governing equation
Offers simple solutions to a wide range of plate problems in practical civil engineering

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