Efficiency, manufacturability, and modeling challenges in structural design optimization

Abstract

This thesis presents new developments in structural design optimization on three topics: semi-analytical sensitivity analysis, design of composite structures fabricated via additive manufacturing, and topology optimization of structures under contact boundary conditions.

We first give a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady state, transient and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied.

In the second topic, we demonstrate a practical method for the optimization of fiber reinforced composite structures fabricated by additive manufacturing, that accommodate the manufacturability constraints of the direct ink writing process. To accomplish this, the toolpaths of each layer are defined by contours of a level-set function. With this representation, we can define the manufacturing constraints and the material model. We obtain optimal manufacturable toolpaths and maintain computational efficiency. We also propose to minimize manufacturing cost by solving a traveling salesman problem to obtain the linking sequence of these toolpaths.

Finally, we apply topology optimization to design systems with multiple deformable three-dimensional bodies in contact. We formulate and resolve the design simulation problem using large deformation continuum mechanics and the finite element method. The contact conditions are discretized via the mortar segment-to-segment approach which provides smooth force variations over the contact surfaces. Since the contact problem is computationally expensive to solve, we solve the optimization problem using efficient nonlinear programming algorithms which require the sensitivities of the cost and constraint functions. To this end, we formulate analytical adjoint sensitivity expressions to compute the gradients of general functionals. Additionally, we use a B-spline design parameterization to reduce the number of design variables compared to element-wise parameterizations and regularize the topology optimization problem.