Plane Theory of Elasticity in Rectangular Cartesian Coordinates

This chapter contains sections titled: Plane Strain Problem Set 5‐1 Generalized Plane Stress Problem Set 5‐2 Compatibility Equation in Terms of Stress Components Problem Set 5‐3 Airy Stress Function Problem Set 5‐4 Airy Stress Function in Terms of Harmonic Functions Displacement Components for Plane Elasticity Problem Set 5‐6 Polynomial Solutions of Two‐Dimensional Problems in Rectangular Cartesian Coordinates Problem Set 5‐7 Plane Elasticity in Terms of Displacement Components Problem Set 5‐8 Plane Elasticity Relative to Oblique Coordinate Axes Plane Elasticity with Couple Stresses 5A‐1 Introduction 5A‐2 Equations of Equilibrium 5A‐3 Deformation in Couple Stress Theory 5A‐4 Equations of Compatibility 5A‐5 Stress Functions for Plane Problems with Couple Stresses Plane Theory of Elasticity in Terms of Complex Variables 5B‐1 Airy Stress Function in Terms of Analytic Functions Ψ(z) and χ(z) 5B‐2 Displacement Components in Terms of Analytic Functions Ψ(z) and χ(z) 5B‐3 Stress Components in Terms of Ψ(z) and χ(z) 5B‐4 Expressions for Resultant Force and Resultant Moment 5B‐5 Mathematical Form of Functions Ψ(z) and χ(z) 5B‐6 Plane Elasticity Boundary Value Problems in Complex Form 5B‐7 Note on Conformal Transformation Problem Set 5B‐7 5B‐8 Plane Elasticity Formulas in Terms of Curvilinear Coordinates 5B‐9 Complex Variable Solution for Plane Region Bounded by Circle in the z Plane Problem Set 5B References Bibliography