Vectors and Tensors: Mathematical Preliminaries and Transformations

Related lectures (31)

Page 3 of 4

Covers linear and volume deformations, angular deformations, and rotation speed.

Covers strain-displacement relations, equilibrium equations, and energy functional in nonlinear beam theory with small strain and moderate rotation.

Delves into geometric nonlinearity in structural analysis, emphasizing the impact of large rotations on structural response.

Covers kinematics and deformation in continuum mechanics, focusing on displacement vectors and the deformation gradient tensor.

Covers kinematics, deformation mapping, rigid body translation, rotation, stretching, shearing, and the deformation gradient tensor.

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Explores the deformation of straight beams, calculating deflections and rotations under different load cases.

Covers the preservation of isometry by rotations and symmetries.

Explores the transformation of constraints and deformations in materials, focusing on stress analysis and tensor diagonalization.