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Full-Text Articles in Physical Sciences and Mathematics
Boundary Value Problems In Rectilinearly Anisotropic Thermoelastic Solids, Gilbert Kerr
Boundary Value Problems In Rectilinearly Anisotropic Thermoelastic Solids, Gilbert Kerr
Mathematics & Statistics Theses & Dissertations
The boundary value problems which are considered are the type that arise due to the presence of a Griffith crack (or cracks) in an anisotropic thermoelastic solid. The thermoelastic field, in such materials, when the infinitesimal theory is employed, is governed by a set of elliptic partial differential equations. The general solution of these equations is expressed in terms of arbitrary analytic functions whose real parts, in turn, are expressed in terms of Fourier type integrals or Fourier series. Integral transform techniques are then used to determine the stress intensity factors (and other pertinent information) for various crack geometries. In …
Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson
Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson
Mathematics & Statistics Theses & Dissertations
In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …