LINEAR ELASTOSTATICS

6.161.8 LINEAR ELASTOSTATICS J.R.Barber Department of Mechanical Engineering, University of Michigan, USA Keywords Linear elasticity, Hooke’s law, stress functions, uniqueness, existence, variational methods, boundaryvalue problems, singularities, dislocations, asymptotic fields, anisotropic materials. Contents 1. Introduction 1.1. Notation for position, displacement and strain 1.2. Rigid-body displacement 1.3. Strain, rotation and dilatation 1.4. Compatibility of strain 2. Traction and stress 2.1. Equilibrium of stresses 3. Transformation of coordinates 4. Hooke’s law 4.1. Equilibrium equations in terms of displacements 5. Loading and boundary conditions 5.1. Saint-Venant’s principle 5.1.1. Weak boundary conditions 5.2. Body force 5.3. Thermal expansion, transformation strains and initial stress 6. Strain energy and variational methods 6.1. Potential energy of the external forces 6.2. Theorem of minimum total potential energy 6.2.1. Rayleigh-Ritz approximations and the finite element method 6.3. Castigliano’s second theorem 6.4. Betti’s reciprocal theorem 6.4.1. Applications of Betti’s theorem 6.5. Uniqueness and existence of solution 6.5.1. Singularities 7. Two-dimensional problems 7.1. Plane stress 7.2. Airy stress function 7.2.1. Airy function in polar coordinates 7.3. Complex variable formulation 7.3.1. Boundary tractions 7.3.2. Laurant series and conformal mapping 7.4. Antiplane problems 8. Solution of boundary-value problems 1

LINEAR ELASTOSTATICS

Documents

linear elasticity

hookeâ s law

stress functions

uniqueness

existence

variational methods

boundaryvalue problems

singularities