TY - JOUR
T1 - Overview about Solution Representations for Elasticity Problems and Some Selected Particular Solutions
AU - Piltner, Reinhard
PY - 2001/4/1
Y1 - 2001/4/1
N2 - 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.
AB - 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.
KW - Complex Fimction Representations
KW - Elasticity Problems
KW - Elasticity Solutions
UR - https://doi.org/10.1177/108128650100600205
U2 - 10.1177/108128650100600205
DO - 10.1177/108128650100600205
M3 - Article
SN - 1081-2865
VL - 6
JO - Mathematics and Mechanics of Solids
JF - Mathematics and Mechanics of Solids
ER -