| 8. The biharmonic equation 8.1 The concept of a continuum 8.2 Displacements and strains in continua 8.2.1 Physical interpretations of the strain matrix 8.2.2 Physical interpretation of the rotation matrix 8.2.3 Indicial notation representations of strain and rotation 8.2.4 Transformation of the strain matrix 8.2.5 Principal strains and strain invariants 8.2.6 Compatibility of strains 8.3 Stresses in a continuum 8.3.1 The stress dyadic and the stress matrix 8.3.2 Tractions on an arbitrary plane 8.3.3 Equations of equilibrium 8.3.4 Symmetry of the stress matrix 8.3.5 Sign convention for stresses 8.3.6 Transformation of the stress matrix 8.3.7 Principal stresses and stress invariants 8.4 Constitutive equations for linear elastic solids 8.4.1 Generalized Hooke‘s Law 8.4.2 The strain energy density 8.4.3 Symmetry of the elasticity matrix 8.4.4 Isotopic elastic matrial 8.4.5 Thermodynaic constrants on the eletic constants 8.4.6 Boundary conditions 8.4.7 Time dervatives 8.5 Uniqueness theorem in the classical theory of elastictiy 8.6 Plane problems in classical elasticity 8.7 The Airy Stress function 8.8 Methods of solution of the biharmonic equation …… 9.Poisson's equation Bibliography Indes |
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