Simplified Analytical Methods of Elastic Plates

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