Study of the dynamic response of minimum weight structures.

摘要

Topology optimization is a tool used during the early stages of design to identify configurations that might not be intuitive. In this thesis, topologies that have been optimized for static loading are evaluated for their performance under dynamic loading conditions. The response of these structures to dynamic loads is not understood and has yet to be investigated. This study seeks to compare the dynamic response of structures that have been optimized for static stiffness to more traditional weight minimizing structures consisting of periodic geometric patterns. A domain is optimized for a loading case using an available static optimization scheme. The domain and case were chosen specifically so that it can be tested dynamically in the laboratory, using an instrumented drop weight impact test machine. The drop test experiment is simulated using a Finite Element Analysis (FEA). The experimental data for a particular topology with a low volume fraction is used to validate the FEA model. Similar topologies with higher volume fraction are then evaluated by FEA simulations.;Understanding the dynamic response of statically optimized structures will provide insight into the development of an algorithm that could optimize a structure subjected to dynamic loading conditions. Such an algorithm would be very useful in the design of lightweight bulkheads for underwater vehicles, torpedoes, cruise missiles and other aerospace applications. In such applications, structural weight savings are critical and static loads are well defined. However, these structures are also subjected to dynamic loads which must be characterized and taken into account during the design phase.;As expected, the optimized topologies exhibit very high stiffness when subjected to either static or dynamic loading. At low energy levels where no critical damage is observed, optimized topologies perform better with a much high stiffness before and after impact and deflected less during the impact. The optimized topologies perform better than the traditional topologies until the kinetic energy increases enough to compromise the structure in the form of tensile failures, as observed in the lower volume fraction topologies. At critical high impact conditions, however, high stiffness can prove to be a hindrance. Statically optimized structures are uniformly stressed at all material points. Under high impact conditions, the structure is quickly loaded to a failure state, typically tensile failure in regions subjected to stress concentrations or compressive failure of slender compressive members. Such failures dramatically reduce the stiffness of the structure since the optimized structure requires all members to remain intact to effectively transmit the loads. As a result, due to their high stiffness and loss of structural integrity after initial failure, the statically optimized structures do not allow sufficient time prior to failure to decelerate the dropped mass. By comparison, the more traditional lightweight structures have lower stiffness and decelerate the mass over a longer distance and time. These structures also experienced localized failures, most often due to buckling, but were able to carry loads effectively after failures because the structure had multiple load paths. Topologies optimized for stiffness do not perform well under high impact conditions because some compliance is required to effectively absorb high impact energy.;One of the objectives of this study is to provide insights that can be used to develop new algorithms for the optimization of structures for resisting dynamic loads. The results of this study reveal that the optimization schemes for a structure's dynamic response will need to identify design parameters that provide an optimal combination of initial stiffness, initial failure, and post-failure energy absorption.