A dynamic optimization setting for problems in structural mechanics

This dissertation is focused on the utility of variational principles and the vast possibilities they offer as powerful tools for a suggestive use to solve optimization problems in structural mechanics. To this purpose, an introduction to the analytical approach to continuous dynamic optimization problems and the development of a dedicated computational method are addressed in the first part of the dissertation. For the sake of establishing a level of practical effectiveness and clarifying their vitality, a few concrete applications ranging from shape optimization problems for thin-walled axisymmetric pressure vessels and straight and curved beams to material optimization problems for functionally graded elastic bodies are addressed. The corresponding decision variables are the meridian shape, the cross sectional area distribution and the mechanical properties distributions along specific directions throughout the body, respectively. Potential performance criteria destined for optimization and possible structural constraints consist of reasonable combinations of lightweightness, storage capacity, compliance, resistance to buckling and load-bearing capacity. These problems are formulated in the second part of the dissertation, solved and thoroughly discussed and, when possible, compared to literature. In some cases, optimal solutions are derived analytically and are accompanied by prompt design charts, otherwise, in case of a cumbersome analytical tractability, they are obtained numerically by means of the computational method developed in the first part.

This dissertation is focused on the utility of variational principles and the vast possibilities they offer as powerful tools for a suggestive use to solve optimization problems in structural mechanics. To this purpose, an introduction to the analytical approach to continuous dynamic optimization problems and the development of a dedicated computational method are addressed in the first part of the dissertation. For the sake of establishing a level of practical effectiveness and clarifying their vitality, a few concrete applications ranging from shape optimization problems for thin-walled axisymmetric pressure vessels and straight and curved beams to material optimization problems for functionally graded elastic bodies are addressed. The corresponding decision variables are the meridian shape, the cross sectional area distribution and the mechanical properties distributions along specific directions throughout the body, respectively. Potential performance criteria destined for optimization and possible structural constraints consist of reasonable combinations of lightweightness, storage capacity, compliance, resistance to buckling and load-bearing capacity. These problems are formulated in the second part of the dissertation, solved and thoroughly discussed and, when possible, compared to literature. In some cases, optimal solutions are derived analytically and are accompanied by prompt design charts, otherwise, in case of a cumbersome analytical tractability, they are obtained numerically by means of the computational method developed in the first part.