Overview about Solution Representations for Elasticity Problems and Some Selected Particular Solutions

Solution representations for elasticity problems are presented in this overview article. The types of problems covered are (i) plane strain/stress for isotropic and anisotropic materials, (ii) plate bending for isotropic and anisotropic thin plates, (iii) three-dimensional plate analysis, and (iv) three-dimensional elasticity problems. The solution contributions are decomposed into homogeneous and particular solutions. All homogeneous solution representations involve arbitrary complex valued functions. Choosing different types of complex functions, it becomes possible to construct easily infinite sets of functions satisfying the governing differential equations. The solution representations are very useful for (i) solving problems analytically, (ii) analyzing a local solution behavior (as, for example, near comers, cracks, or holes), and (iii) for application in numerical methods.