Some Basic Problems of The Mathematical Theory of Elasticity: Fundamentals Equations Plane Theory of Elasticity Torsion and Bending

Part - 1: Fundamental Equations of the Mechanics of an Elastic Body Analysis of Stress Analysis of Strain The Fundamental Law of the Theory of Elasticity; the Basic Equations Part - 2: General Formulae of the Plane Theory of Elasticity Basic Equations of the Plane Theory of Elasticity Stress Function. Complex Representation of the General Solution of the Equations of the Plane Theory of Elasticity Multi-Valued Displacements Thermal Stresses Transformation of the Basic Formulae for Conformal Mapping Part - 3: Solution of Several Problems of the Plane Theory of Elasticity By means of Power Series On Fourier series Solution for Regions, Bounded by a Circle The Circular Ring Part - 4: On Cauchy Integrals Fundamental Properties of Cauchy Integrals Boundary Values of Holomorphic Functions Part - 5: Application of Cauchy Integrals to the Solution of Boundary Problems of Plane Elasticity General Solution of the Fundamental Problems for Regions Bounded By One Contour Solution of the Fundamental Problems for Regions Mapped on to a Circle by Rational Functions. Extension to Approximate Solution for Regions of General Shape Solution of the Fundamental Problems for the half-Plane and for Semi-Infinite Regions Some General Methods of Solution of Boundary Value Problems. Generalizations. Part - 6: Solution of the boundary of the Plane Theory of Elasticity by Reduction to the Problem of Linear Relation Solution of the Fundamental Problems for the Half-Plane and for the Plane with Straight Cuts. Solution of Boundary Problems for Regions, Bounded by Circles, and for the Infinite Plane Cut Along Circular Arcs. Solution of the Boundary Problems for Regions, Mapped on to the Circle by Rational Functions Part - 7: Extension, Torsion and Bending of homogeneous and Compound Bars Torsion and Bending of Homogeneous Bars 9Problem of Saint-Venant) Torsion of Bars Consisting of different Materials Extension and Bending of Bars, Consisting of Different Materials with Uniform Poisson's Ratio Extension and Bending for Different Poisson's Ratios Appendix - 1: On the Concept of a Tensor Appendix - 2: On the Determination of functions from their Perfect Differentials in Multiply Connected Regions Appendix - 3: Determination of a Function of a Complex Variable from its Real Part. Indefinite Integrals of Holomorphic Functions.