Simplified Analytical Methods of Elastic Plates

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

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 Stiffnes
About the Author:

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.