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Applied Mathematics Seminar 291 (9/15/17)

September 15, 2017 - 10:00pm

Boyan Lazarov, Ph.D., Lawrence Livermore National Laboratory


Topology optimization has gained the status of being the preferred optimization tool in the mechanical, automotive, and aerospace industries. It has undergone tremendous development since its introduction in 1988, and nowadays it has spread to many other disciplines such as acoustics, optics, and material design. The basic idea is to distribute material in a predefined domain by minimizing a selected objective function and fulfilling a set of constraints. The procedure consists of repeated system analyses, gradient evaluation steps by adjoint sensitivity analysis, and design updates based on mathematical programming methods. The existence of a solution is ensured by regularization techniques which result in intermediate density material regions. Manufacturing of the final optimized design requires post processing. However, any amendments can nullify the effect of the optimization. Therefore, the aim of this talk is to present recent developments in obtaining black and white manufacturable designs with clearly defined length scale. The focus is on the mathematical modeling of the material density, its link to micro- and nano- scale production techniques, and on the introduction of uncertainties in the optimization. The unified model results in manufacturable black and white designs with performance which is robust with respect to variations in the production process. 


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Arnold Kim