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Design optimization of structures subjected to transient dynamic loads under uncertainty
Thesis   Open access

Design optimization of structures subjected to transient dynamic loads under uncertainty

Ronald J. Vitola
Master of Science (M.S.), Drexel University
Jun 2020
DOI:
https://doi.org/10.17918/00000190
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Abstract

Structural optimization Uncertainty Structural Dynamics Topology
Structural design optimization is a useful computational tool to improve the performance of a structural system, develop non-intuitive solutions to a problem, and explore a design space. It has been predominantly developed for and applied to static scenarios. Although a wide variety of systems can be optimized under static conditions, situations where time-dependent and inertial effects need to be taken into consideration often necessitate the use of dynamic solution techniques. These situations include designing for impacts, controlling elastic wave propagation, and mitigating noise and vibration. For these cases, a dynamic response optimization method should be employed. Similarly, most designs are optimized under deterministic conditions. This can be problematic, because without considering the randomness and uncertainty often present in reality, the final solution will most likely be sub-optimal and could end in failure. To address these topics, this work develops a finite-element-based structural topology optimization framework capable of solving transient dynamic problems in the time domain under both deterministic and uncertain conditions. The components of the optimization framework are the primal analysis solved using a Newmark method, the sensitivity analysis performed using the adjoint variable method, the gradient-based optimization routine conducted with the method of moving asymptotes, and the uncertainty module which utilizes a non-intrusive polynomial chaos expansion approach to handle any sources of uncertainty in the material properties, load, boundary conditions, etc. In this density-based topology optimization approach, the solid isotropic material with penalization scheme and a design variable filter are used to prevent instability in the solution, to ensure mesh-independence, and to reduce the presence of intermediate volume fractions in the final design. Examples are solved to illustrate when dynamic response optimization is necessary, how its results compare to a statically optimized case, some of its notable characteristics, and the importance of considering uncertainty in optimization.

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