@phdthesis{bibcite_3101,
  author = {Emily Alcazar},
  title = {Topology optimization: From spatially varying loads to elastoplasticity},
  abstract = {<p>The pursuit of highly efficient structures with enhanced design performance remains central to the development of innovative and advanced engineering systems. Topology optimization, a computation design method, is a practical approach in designing structures to enhance a specified objective function while adhering to certain design and physical constraints, informing the optimal placement of the material and ultimately resulting in highperformance structures. Despite the breadth and significant advancements of the topology optimization field, there still remains areas to be further developed such as robust design optimization and the incorporation of more realistic material modeling in the optimizationframework. Thus the aim of this research is to contribute in these areas through novel theoretical frameworks, numerical implementations to support these frameworks, and lastly by providing open-source educational software to stimulate further development in the field. The contributions of this thesis are two-fold. Towards the first part, a topology optimization framework is presented in the discrete (truss) setting to design structures for the worst-case loading scenario, handling single or distributed spatially varying loads. The deterministic min-max optimization statement was proven to encompass a maximum eigenvalue problem, with implications of ill-posed gradients, which were treated by a smooth maximum regularization function. The results obtained by the presented framework demonstrated robust designs with high performance in all possible loading directions. In the second part of the thesis, we focus in the area of continuum (density-based) topology optimization frameworks considering nonlinear dissipative physics. We present an original attempt at an open-source, modular topology optimization software considering von-Mises elastoplasticity in conjunction with a thorough explanation on the pathdependent algorithm for the sensitivity analysis. Additionally a comprehensive framework is presented to incorporate a Smooth Hyperbolic Drucker-Prager constitutive model into the topology optimization framework to treat the gradient-discontinuity at the apex of the original Drucker-Prager yield surface. The relevance of such frameworks is highlighted in the numerical results which demonstrate unique insights on realistic engineering designs.</p>},
  year = {2025},
  journal = {Civil and Environmental Engineering Department, Princeton University},
  publisher = {Princeton University},
  url = {http://arks.princeton.edu/ark:/88435/dsp01w9505390n},
}