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This review covers essential topics for the mid-term exam, including vector and index notation, matrix-tensor theory, and coordinate transformations. Key areas include principal value problems, vector calculus, and the applications of strain-displacement and rotation-displacement relations. The review also encompasses strain compatibility equations, traction vector, stress tensor definitions, equilibrium equations, and forms of Hooke’s law. Additionally, it addresses boundary-value problem formulations, displacement and stress formulation techniques involving Navier’s equations, Beltrami-Michell compatibility, and foundational aspects of strain energy.
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Review for Mid-Term Exam Basic knowledge of vector & index notation, matrix-tensor theory, coordinate transformation, principal value problems, vector calculus Use of strain-displacement & rotation-displacement relations; determine strains/rotations given the displacements, integrate strains to find displacements Use of strain compatibility equations Traction vector & stress tensor definitions and relations Use of equilibrium equations Use of general and isotropic forms of Hooke’s law; both stress in terms of strain, and strain in terms of stress General elasticity boundary-value problem formulation Boundary condition specifications Displacement formulation – Navier’s equations Stress formulation – Beltrami-Michell compatibility + equilibrium equations Strain energy – basic forms
