ABSTRACT

Mechanics plays a fundamental role in the optimality of engineering structures at various scales. Starting in the late nineteenth century, the field of structural optimization grew out of key observations on the criticality of load path and its implication on spatial deformation. Yet, as the field has evolved in pursuit of complex engineering challenges, its focus has shifted towards formulations of tractable optimization statements more than on mechanics guiding structural optimization. This award will support the development of a general topology optimization framework based on local stress constraints that will bring the fundamental principles of mechanics at the center of structural optimality. The theoretical and computational framework will be bridged with advanced additive manufacturing techniques for convergent outcomes. The work will empower the next generation of engineers to solve challenging structural optimization problems involving a large number of local constraints, and to connect topology optimization and additive manufacturing in an inexpensive and easy?to?use way for education at all levels. Guided by theoretical, computational, experimental, and manufacturing challenges, the award will provide educational opportunities to K?12 students through university programs and integration of research with the graduate curriculum, and support dissemination of the findings to the industry and the broader community through computer codes, outreach meetings, and workshops.

This research advances the theory needed to effectively couple mechanics and optimization of highly constrained problems, the computational framework needed to solve such problems, and the manufacturing approach to fabricate the resultant spatially varying multi?lattice parts. From a mathematical perspective, a tailored augmented Lagrangian approach will be employed to solve the stress?constrained mass minimization problem by incorporating local stresses. Specific contributions will include: (i) unifying local formulations of the stress?constrained topology optimization problems to handle a wide range of failure criteria with a single strength function and analytically deriving worst?case stress states from infinite load cases that can be used to define the stress constraints; (ii) reformulating the stress constrained problem to handle an arbitrary number of linear, nonlinear, and/or microstructural materials and deriving interfacial behavior that can be used to enforce stress constraints at material interfaces; and (iii) engineering and experimentally validating functionally?graded, single? and multi?lattice optimized parts using novel manufacturing techniques, such as gray?scale digital light processing (g-DLP) without expensive stereolithography (STL) files. The research will explore a multi?phase design space with on demand structural fidelity.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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