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|Title:||A convex optimization approach for moderately large deflection problems in circular membranes and circular paths|
|Doctoral Committee Chair(s):||Vaidya, Pravin M.|
|Department / Program:||Computer Science|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
|Rights Information:||Copyright 1996 Gaur, Rajeeva|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9702522|