A convex optimization approach for moderately large deflection problems in circular membranes and circular paths
Gaur, Rajeeva
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https://hdl.handle.net/2142/20434
Description
Title
A convex optimization approach for moderately large deflection problems in circular membranes and circular paths
Author(s)
Gaur, Rajeeva
Issue Date
1996
Doctoral Committee Chair(s)
Vaidya, Pravin M.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Engineering, Civil
Engineering, Mechanical
Language
eng
Abstract
Circular membranes and circular plates are used in several types of equipments. For the better design of these equipments an accurate computation of the stresses and the displacements in circular membranes and circular plates are very important. Since larger loads on membranes (plates) leads to stresses as nonlinear functions of displacements, little is known about the existence and the uniqueness of the solution even for the case where a circular membrane (plate) is subjected to axisymmetric transverse loads and axisymmetric boundary conditions.
Membranes are a limiting case of the plates where the bending stiffness of the plate goes to zero. In this thesis, a variational formulation is obtained for the problem of moderately large deflections in circular membranes subjected to axisymmetric transverse loads and axisymmetric boundary conditions. For this variational formulation, unique stresses and displacements are shown to exist under quite general loading conditions. And, the variational formulation is cast as a constrained convex optimization problem. Furthermore, an algorithm for computing the stresses and a procedure for obtaining the displacements from the stresses is given.
Unique stresses and displacements are also shown to exist for the problem of moderately large deflections in circular plates subjected to axisymmetric transverse loads and axisymmetric boundary conditions. And, an algorithm for computing the stresses and the corresponding displacements from the stresses is given.
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