Thermomechanical Response of Shells with Emphasis on a Conical Shell.

Abstract

Abstract : This research is concerned with the thermomechanical response of shells, with emphasis on a conical shell. Four topics of interest were identified and the results for each of these were written in the form of journal articles and submitted for publication. Topic 1 was concerned with developing a uniqueness theorem for thermoeleastic shells that admits generalized boundary conditions. Topic 2 was concerned with developing a nonlinear constrained theory of shells that includes tangential shear deformation. Topic 3 entailed proposing new values for certain constitutive coefficients for shells. Finally, we focused on Topic 4, which was concerned with heat conduction in rigid plates and shells, with emphasis on a conical shell. For each of these topics, we modeled the shell as a Cosserat surface. The conical shell was of particular interest because it has a converging geometry such that the shell near its tip is necessarily 'thick' even though the shell near its base may be 'thin'. To develop confidence in the Cosserat theory for both the thin-shell and thick-shell limits, we considered a number of problems for plates circular cylindrical shells, spherical shells, and a conical shell. It was shown that by appropriately modifying the constitutive equations, it is possible to include enough geometrical features of the shell to predict relatively accurate results even in the thick-shell limit.