Lurie A.I. Theory of Elasticity

Springer-Verlag, Berlin, Heidelberg, 2005. — 1036 p. — (Foundations of Engineering Mechanics) — ISBN: 9783540245568The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods for stating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelasticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics.Basic concepts of continuum mechanics
Stress tensor
Deformation of a continuum
Governing equations of the linear theory of elasticity
The constitutive law in the linear theory of elasticity
Governing relationships in the linear theory of elasticity
Special problems of the linear theory of elasticity
Three-dimensional problems in the theory of elasticity
Saint- Venant's problem
The plane problem of the theory of elasticity
Basic relationships in the nonlinear theory of elasticity
Constitutive laws for nonlinear elastic bodies
Problems and methods of the nonlinear theory of elasticity
Appendices
Basics tensor algebra
Main operations of tensor analysis
Orthogonal curvilinear coordinates
Tensor algebra in curvilinear basis
Operations of tensor analysis in curvilinear coordinates
Some information on spherical and ellipsoidal function