Optimum and robust geometric design of mechanical parts

Some problems in constrained geometric optimization are considered. The goal has been to maximize or minimize a measure of device performance computed using CAE, with a CAD compatible representation and specified geometric constraints. This approach illustrates several issues in the integration of CAD and CAE systems. The freeform geometry of the device is represented by Bezier curves. Analysis tools such as a grid generator and the solver for device's performance are treated as a black box. The search pattern during the optimization process is suggested by the design of experiment methodology. The proposed framework is tested with four example problems: flow through a ninety degree bend in potential flow problem, a plane diffusers in laminar flow, an axisymmetric diffuser in laminar flow and a torque arm under static load. In all four problems the free form shape of the part is to be designed.; An optimum design is not an acceptable engineering solution unless it is also robust. For this reason, a method to identify robust designs of mechanical parts with free-form shapes is proposed. We attempt to quantify the robustness of a design by, first, introducing noise to the design using a design of experiments approach. With this approach a fixed number of samples are generated around the design. Then we evaluate the performance of all the samples. Next, four quantities are computed, which are the mean, standard deviation, probability of failure and Taguchi's signal-to-noise ratio (SNR). Finally, these four quantities are used to compare the robustness between different designs. The methodology is applied to the designs obtained from the four example optimization problems. The results show that an optimum design is not necessarily robust.; The previously mentioned portion of this work can be classified as a single objective design but, in practice, design problems usually involve multiple criteria. In the later part of the thesis we explore a multicriteria design problem. For this purpose the design of corrugated panel structures, a fixed form geometric design problem, is examined. The goal of this exercise is to find guidelines for robust-optimum design of these structures. For design optimization the objectives include maximizing natural frequency and minimizing maximum deflection for a given range of structural weight. The objectives of robust design are to maximize SNR with respect to natural frequency and maximum deflection. We consider all the objectives for optimality as well as robustness to formulate a multicriteria design problem. To solve this multicriteria design problem, a large data set of trial designs is generated over a range of structural weight. This data set not only allows us to perform an exhaustive search but also to fill the design space for robustness testing. A finite element model is created for each trial design to solve for natural frequency and maximum deflection. The finite element solver is, again, treated as a black box. SNR are computed by gathering the information from the neighborhood of each design. The data set is then screened and reduced to a smaller set of feasible designs. Finally a set of robust-optimum designs is identified and design rules are extracted from this design set.