Micropolar Theory of Shells and Plates

Preface
Preface to the Second Edition
	References
Introduction
	References
Contents
1 Main Equations and Relations of the Theory of Non-symmetric Elasticity
	1.1 Preliminary Remarks
	1.2 Equations of Motion
	1.3 Defining Equations or the Law of Small Elastic Deformations
	1.4 Compatibility Equations
	1.5 Orthogonal Curvilinear System of Coordinates
	1.6 Main Equations and Correlations in the Case of the Geometrically Nonlinear Problem
	References
2 Bending of Plates
	2.1 Remarks
	2.2 Initial Assumptions and Hypothesis
	2.3 Stresses, Internal Forces, and Momenta
	2.4 Averaged Equations of Motion and Boundary Conditions
	2.5 Another Example of a Bending Equation of a Pate at X pm = 0,Y pm = 0
	2.6 Theory of Bending of a Plate at α= 0
	2.7 Axisymmetric Bending of a Plate
	2.8 Few Remarks on the New Generalizing Elasticity Constant
	References
3 Some Trivial Problems of Plates
	3.1 Remarks
	3.2 Bending of a Plate Over a Cylindrical Surface
	3.3 A Sample Problem of Bending of a Hinged Rectangular Plate Under Normally Applied Sinusoidal Load
	3.4 Bending of a Hinged Rectangular Plate Under Arbitrary, Normally Applied Load
	3.5 Bending of a Semi-infinite Plate by a Load Distributed Along the Edge
	3.6 On the Problem of Axisymmetric Bending of a Circular Plate
	3.7 Yet Another Problem of the Statical Stability of a Plate
	3.8 Free Vibrations of a Plate: One-Dimensional Problem
	3.9 Free Vibrations of a Rectangular Plate Hinged Along the Entire Contour
	References
4 Membrane Theory of Plates
	4.1 Remarks
	4.2 Initial Statements and Hypothesis
	4.3 Stresses, Internal Forces, and Momenta
	4.4 Averaged Equations of Motion and Boundary Conditions
	4.5 Cylindrical Shell
	4.6 Some Problems of a Circular Cylindrical Shell
	4.7 Axisymmetrically Loaded Shells of Revolution
	4.8 Membrane Theory of Very Shallow Shells
	References
5 Theory of Very Shallow Shells
	5.1 Remarks
	5.2 Initial Statement and Hypothesis
	5.3 Stresses, Internal Forces and Momenta
	5.4 Averaged Equations of Motions and Boundary Conditions
	5.5 Circular Cylindrical Shell
	5.6 Axisymmetrically Loaded Shells of Revolution
	5.7 Axisymmetric Vibrations of a Circular Cylindrical Shell
	References
6 Other Aspects of the Theory of Plates and Shells
	6.1 Remarks
	6.2 Geometrically Nonlinear Theory of Rectangular Plates
	6.3 Rectangular Plate Hinged Along the Entire Contour. Nonlinear Problem
	6.4 Theory of Very Shallow Shells. Full Account of the Transverse Shifts
	6.5 Bending of a Plate Along a Cylindrical Surface
	References