The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for writing these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universities. The approach is distinctly different to that which would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling of Problems in Engineering". An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equations, kinematic constraints, constitutive responses, thermodynamic restrictions, etc.
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 equationBibliographyIndes
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