Design and optimization of computationally expensive engineering systems

Engineering systems form the basis on which our day-to-day lives depend on. In many cases, designers are interested in identifying an optimal design of an engineering system. However, very often, the process of engineering design optimization is complex and involves time-expensive simulations or the need to satisfy not just one, but multiple objectives. This thesis aims to explore the area of efficient optimization algorithms applied to engineering system design. In particular, the engineering systems discussed here involve the use of rheologically complex materials. Engineers face many modeling challenges while trying to design systems with rheological materials, pertaining to mathematical modeling and optimization. However, the use of more flexible design methods in conjunction with rheologically complex materials enhances design freedom and diffuses design fixation. The first part of the thesis discusses the characteristics of such materials and introduces their usage in engineering design. A second kind of complex systems include the ones characterized by multiple objectives and time-expensive simulations. Design optimization is a cumbersome process in such a case. Using an approximation or a surrogate model of this kind of system helps to mitigate computational costs. The use of an adaptive surrogate modeling alogrithm (along with optimization) is demonstrated on such systems, that involve the use of complex fluids. The unifying theme of the thesis is the application of efficient optimization algorithms to computationally expensive material design problems. In this thesis, we introduce the use of direct optimal control to identify optimal material function targets. The thesis also details a novel adaptive surrogate modeling algorithm that was developed to solve multi-objective optimization problems. Both these ideas are demonstrated with the help of case studies and analytical examples