Continuum Mechanics

I am taking a class in continuum mechanics at the University of Alabama in Huntsville.

Here are some notes:

Derivation of the Epsilon-Delta Relationship:  epsilon_delta.pdf

Continuum Mechanics Formulas (Kronecker delta, permutation symbol, dot product, cross-product, etc.) :  cm_formulas.pdf

Del Operator Proofs (divergence, curl, cross-product, etc.): del_operator_proofs.pdf

Unit Vector Normal to an Inclined Plane: vector_normal_plane.pdf

Continuum Mechanics Formulas for Fluid Mechanics: cm_fluid_mechanics.pdf

Material Derivative:  material_derivative.pdf

Displacement Gradient and the Lagrangian Strain Tensor:  displacement_gradient.pdf

Laplace’s Equation:  Laplacian_equation.pdf

Calculations with Position Vectors: position_vectors.pdf

Derivation of the Cayley-Hamiliton Equation: Cayley_Hamilton.pdf

Conservation of Mass: conservation_mass.pdf

* * *

Homework_1.pdf

Homework_2.pdf

Homework_3.pdf

Homework_4a.pdf

Homework_5.pdf

Homework_6b.pdf

Homework_7.pdf

Homework_8.pdf

* * *

Matlab script:  continuum_mechanics_stress_strain.zip

Includes functions for calculating:

  • Principal stresses or strain in either 2D or 3D
  • Mohr’s circle and von Mises stress
  • Stress on an arbitrary plane defined by a unit normal vector
  • Thin-walled cylinder torsion with option for internal pressure
  • Deviatoric Stress Tensor
  • Octahedral Stress

* * *

References:

Continuum Mechanics – Solids

Constitutive Models Relations between Stress and Strain

NASA/TM–2011-217314, An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials 

* * *

See also: Linear Algebra

– Tom Irvine

One thought on “Continuum Mechanics

  1. Pingback: Kinetic & Strain Energy Formulas | Vibrationdata

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