PHYSICAL COMPONENTS OF TENSORS (Paperback)

Finite-Dimensional Vector Spaces Vector spaces and subspaces Basis of a vector space Inner products, norms, and metrics Contravariant and covariant components Coordinate systems Change of coordinate systems Exercises Vector and Tensor Algebras Vector Algebra Tensor Algebra Exercises Tensor Calculus Tensor fields Integral theorems for scalar and vector fields Exercises Physical and Anholonomic Components of Tensors Physical and anholonomic components of vectors Physical and anholomic components of tensors Coordinate transformations of physical components of tensors Examples of transformation of coordinates for physical components Anholonomic connections Strain tensor Dimensional analysis for tensors Exercises Deformation of Continuous Media Stress tensor and equations of motion Strain-displacement relations for elastic bodies Characterization of thin shells Strain-displacement relations for shells Kinematic relations for shells Equations of motion for shells Constitutive equations for thermoelastic shells Bibliography Index