3. Structure mechanics

This third chapter takes place in the physical context of structure mechanics. The most simple model is that of linear elasticity, but we shall deal with multiple other situations beyond.

Contents:

• 3.1. Linear elasticity
  • 3.1.1. Notations regarding vectors and tensors
  • 3.1.2. Kinematics
  • 3.1.3. Stresses
  • 3.1.4. Constitutive laws
  • 3.1.5. Boundary conditions
  • 3.1.6. Towards mathematical modeling: a typical boundary value problem
  • 3.1.7. Energy
• 3.2. Finite Elements for linear elasticity
  • 3.2.1. The variational setting for linear elasticity
  • 3.2.2. Resolution of a basic problem in linear elasticity
  • 3.2.3. A bimaterial situation
  • 3.2.4. Vibrations in an elastic structure
  • 3.2.5. The ersatz material method
  • 3.2.6. A 3d example
• 3.3. Hyperelasticity
  • 3.3.1. Solving a non linear elasticity problem by Newton’s method
  • 3.3.2. Energy minimization in hyperelasticity
• 3.4. Contact