Presenting the mathematical theory of period problems in plane elasticity by methods of complex variables. The most general formulations of such problems are proposed under the assumption that the stresses are periodic and the displacements are quasi-periodic. The general expression of complex displacements are illustrated. Periodic welding problems are studied by reducing them to periodic Riemann boundary value problems. Various periodic problems of the elastic half-plane (fundamental problems, contact problems) are treated and solved by reduction to Riemann-Hilbert boundary value problems with discontinuous coefficient. Periodic crack problems are investigated which are transferred to singular integral equations whose unique solvability is guaranteed.
Table of Contents
1. Periodic Boundary Value Problems for Analytic Functions 2. Periodic Problems for Isotropic Material in Plane Elastic Problems 3. Periodic Problems for Anistropic Medium 4. Problems with Periodic Moving Loads on Isotropic Elastic Half-Plane 5. Periodic Crack Problems in Plane Elasticity 6. Doubly-Periodic Problems in Plane Elasticity