Optimization of Arch and Shell Structures

Citation

Moronval, Marc Jules (1975) Optimization of Arch and Shell Structures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EMCP-7017. https://resolver.caltech.edu/CaltechTHESIS:09272010-093909310

Abstract

Structural optimization of structures with respect to their shape and thickness distribution is studied using a variational approach. The behavioral constraint is either the state of stress or the stiffness. The boundary value problems, derived using Optimal Control theory, are solved with the parallel shooting technique. For statically determinant arches subjected to a uniform pressure, the contribution of the shear force is included in the behavioral constraints to prevent the problems from being singular. For the case of membrane shells of revolution supporting a combined pressure and end traction loading case, solutions were obtained up to a critical value of the load coefficient. A physical interpretation of the singularity is obtained by including the possibility of discrete rings in the formulation. A set of optimality conditions for shells of revolution described by the bending theory, satisfying a stiffness constraint, is derived. The problem is found to be ill posed when the shear contribution is not included in the structural operator.

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