Poisson Theory of Elastic Plates

Foreword
Preface
Introduction
	Brief Historical Background
	Suggested Readings for Historical Background
Contents
About the Editors
1 Poisson Theory of Isotropic Plates in Bending
	1.1 Brief Introduction
	1.2 Kirchhoff Theory
		1.2.1 Classical Sixth-Order Theories
		1.2.2 Poisson Theory
		1.2.3 First-Order Shear Deformation Theory (FSDT)
		1.2.4 Reissner’s Theory
		1.2.5 Associated Torsion Problem
	1.3 Bending of Square Plates
		1.3.1 Bending Problem of Homogeneous Isotropic Plate
		1.3.2 Resolution of Poisson–Kirchhoff Boundary Conditions Paradox
		1.3.3 Higher-Order Poisson Theories
		1.3.4 Neutral Plane Deflection
		1.3.5 Exact Solution with w(x, y, z) as Domain Variable
		1.3.6 Exact Solution with w0(x, y) as Face Variable
		1.3.7 Some Remarks on Solution of Kirchhoff’s Primary Bending Problem
	1.4 New Primary Bending Problems
		1.4.1 Neutral Plane Deflection
	1.5 Conclusions
	Appendices
		Appendix 1.1—Derivation of Eq. (1.88)
		Appendix 1.2—Derivation of Eq. (1.90) from Eq. (1.88)
		Appendix 1.3—Derivation Eq. (1.91) from Eq. (1.90)
	References
2 Extension Problems: Higher-Order Approximations
	2.1 Analysis of Extension Problems
	2.2 Some Observations on the Classical Theories
		2.2.1 Airy’s In-plane Stress Function Φ(x, y)
		2.2.2 Analysis in Terms of Displacements
		2.2.3 Related Bending Problem
	2.3 Bi-harmonic Function in Extension Problems
		2.3.1 Sequence of Uncoupled 2-D Problems
	2.4 Initial Solutions of Primary Extension Problems
		2.4.1 Unusual Problem: Need for Poisson Theory
	2.5 Poisson Theory of Extension Problem
		2.5.1 Thick Plate Analysis
	2.6 Conclusions
	Appendix
	References
3 Homogeneous Anisotropic Plates
	3.1 Introduction
	3.2 Homogeneous Anisotropic Plates
		3.2.1 Stress–Strain and Strain–Displacement Relations
		3.2.2 Equilibrium Equations in Terms of In-plane Strains
		3.2.3 Displacements [u, v, w]
	3.3 Analysis of Primary Bending Problems
		3.3.1 Application of Poisson Theory
		3.3.2 Iterative Procedure
		3.3.3 Summary of Results from the First Stage of Iterative Procedure
	3.4 Associated Torsion Problems
	3.5 Extension Problems
		3.5.1 Preliminary Analysis
		3.5.2 Higher-Order Corrections
	3.6 Conclusions
	References
4 Laminated Plates with Anisotropic Plies Part I: Single-Layer Theories
	4.1 Introduction
	4.2 Geometry and Ply-Wise Constitutive Laws of Anisotropic Material
		4.2.1 Equilibrium Equations
		4.2.2 Equilibrium Equations in Terms of Strains
	4.3 Modified Homogeneous Plate Theories (MHPT) of Symmetric Laminates
		4.3.1 Analysis of Primary Bending Problem
		4.3.2 Analysis of Primary Extension Problem
	4.4 Un-symmetrical Laminates: Alternate Form (ACLPT) of CLPT
		4.4.1 Bending Problem
		4.4.2 Extension Problem
		4.4.3 Contrast Between CLPT and ACLPT
	4.5 Conclusions
	References
5 Laminated Plates with Anisotropic Plies Part II: Layerwise Theories
	5.1 Introduction
	5.2 Preliminaries in the Analysis of Symmetric Laminates
		5.2.1 fk(z) Functions
		5.2.2 Displacements [u, v, w]
		5.2.3 Edge Conditions in Each Ply
	5.3 Analysis of Primary Bending Problems
		5.3.1 Corrective In-plane Displacements in the Face Ply
		5.3.2 Continuity of Displacements and Transverse Stresses Across Interfaces
		5.3.3 Vertical Deflection w(x, y, z)
	5.4 Higher-Order Corrections in the Ply from the Iterative Procedure
		5.4.1 Correction to Vertical Displacement
		5.4.2 Corrective Displacements in the Face Ply
	5.5 Associated Torsion Problems
	5.6 Extension Problems
		5.6.1 Preliminary Analysis of the Ply
		5.6.2 Higher-Order Corrections in the Ply
	5.7 Un-symmetrical Laminates
		5.7.1 Bending Problem
		5.7.2 Associated Extension Problem in Bending
		5.7.3 Extension Problem
		5.7.4 Associated Bending Problem in Extension
	5.8 Conclusions
	References
6 Poisson Theory of Plates with Fourier Sinusoidal Series
	6.1 Introduction
	6.2 Initial Sets of Solutions with fn(z) Functions
	6.3 Use of Fourier Sinusoidal Series [4]
		6.3.1 Analysis of Flexure (Bending) Problem
		6.3.2 Note on the Determination of Vertical Displacement in Bending Problems
		6.3.3 Associated Torsion Problem
		6.3.4 Analysis of Extension Problem
	6.4 Symmetrical Laminated Plates
	6.5 Un-symmetrical Laminated Plates
		6.5.1 Bending Problem
		6.5.2 Extension Problem
	6.6 Conclusions
	References
Data from Research Gate
Epilogue