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A mixed finite element method is introduced in this thesis by two or three first-order C0 stress functions for plane or axisymmetric problems respectively, which satisfy the force equilibrium equations, along with a constraint to impose the moment equilibrium equations. The stresses so expressed are equivalent to those in terms of the higher order Airy or Love stress function. With compatibility condition satisfied in the same way as in a displacement finite element (FE) method, the remaining constitutive relation in elasticity, i.e. Hooke's law, is satisfied by minimizing a mixed functional, with variables of the displacement vector and two/three first-order stress functions. Some elementary problems in plane and axisymmetric elasticity are solved by this method. It is found that for an incompressible solid and a solid with a crack, the mixed model yields better results than the conventional FE method. The effects of Gaussian integration and Poisson's ratio on the solution are discussed in detail. Special attention is paid in bending a beam and a disc, where the importance of the constraint to enforce moment equilibrium is studied. For rigid-perfect-plasticity, the Levy-Mises flow rule and the corresponding yield condition are satisfied by another extremum principle. By substituting the plastic part of the elasto-plastic strain into the extremum for rigid plasticity, and the elastic part of the elasto-plastic strain into the extremum for elasticity, an extremum principle for elasto-plasticity is established straightaway. Applications of this method to some wellknown examples are discussed. In comparison with the conventional displacement method and/or analytical solution, this method offers very satisfactory results and good convergence of the solution. An interesting feature of this method is that the value of each functional indicates in some degree the solution error at a giving point or region. This may provide useful information for accuracy control or a remeshing procedure. A more sophisticated problem is solved by a so-called mixed fluid-FE model, which is the simulation of the flow of an adhesive between two aluminium sheets squeezed by a pair of electrodes in spot-process. The effects of various factors on the formation of the entrapment of the adhesive in the central area of faying surface are studied in detail. Very close results between displacement method and the mixed method are obtained in this study.

x, 97 leaves : ill., reprint / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1972

In addition to its usefulness in modeling and simulation processes, the modulus of elasticity is an index which is highly used in biomedical identifications and tissue characterizations. For many composite and viscoelastic materials an "accurate modulus" is an idealistic hypothesis and an "equivalent modulus" is normally of a high biomechanical significance. The composite shape of the trachea, which consists of the smooth muscles and cartilage rings, renders the fact that an equivalent modulus is in place for many applications. In this paper three in-vitro nondestructive testing techniques are presented to determine the Young modulus of elasticity of the trachea and the results are compared with the standard uniaxial state of stress method. These techniques are based on: (1) simulating the trachea as a pressurized vessel and deducing a special relationship between the pressure and the radial strain; (2) using two hydrophones and studying the variation in acoustic transmittance caused by the presence of the trachea in a water-bath; (3) considering the trachea as a thin cylindrical shell and determining the resonance vibration response. Elaborate discussion is presented to identify the "pros" and "cons" of each technique and final practical recommendations are made.

Thesis (Ph. D.)--Texas A&M University, 2005. / Vita. Abstract. Includes bibliographical references (p. 111-114).

Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaves 153-157). Also available on the World Wide Web.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references.

Thesis (Ph. D.)--University of Adelaide, Dept. of Applied Mathematics, 1992. / Includes bibliographical references (leaves 179-186).

Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1972.

Thesis (Ph.D.)--Université Laval, Québec, 2000. / Includes bibliographical references (leaves 187-205).