Parametric Optimization for Structural Design Problems

Abstract

Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

Topology and Parametric Optimization-Based Design Processes for Lightweight Structures

“…In addition, mesh control was used around the hole area. A structural ASTM (American Society for Testing and Materials) A36 steel was assigned to the 3D-model with the following properties: E = 200,000 MPa, ν = 0.3, ρ = 7.85 g/cm 3 , yield strength of 250 MPa, and ultimate strength of 460 MPa. The initial mass of the Hollow Plate was 1103.5 g. The design parameters (factors) and their allowable value range that were used in the size/shape parametric optimizations are presented in Table 2.…”

“…On the one hand, PO allows a selective optimization of the model based on the given parameters and their value range. It can easily guide to global shape and size optimum solutions for linear and convex problems, but it cannot optimize the topology of the structure [3]. Furthermore, both the Design of Experiments (DOE) and Sensitivity Analysis (SA) were developed simultaneously with the PO to support the implementation and the choice of the most crucial parameters in optimization, respectively [4].…”