Search results for "Shape optimization"
showing 10 items of 44 documents
Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation
2009
Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi-Uda array using the presented AD technique, traditional response level finite difference sens…
Sizing and shape optimization material use in 10 bar trusses
2021
Truss optimization has the goal of achieving savings in costs and material while maintaining structural characteristics. In this research a 10 bar truss was structurally optimized in Rhino 6 using genetic algorithm optimization method. Results from previous research where sizing optimization was limited to using only three different cross-sections were compared to a sizing and shape optimization model which uses only those three cross-sections. Significant savings in mass have been found when using this approach. An analysis was conducted of the necessary bill of materials for these solutions. This research indicates practical effects which optimization can achieve in truss design.
Trial Methods for Nonlinear Bernoulli Problem
1997
In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.
On Fixed Point (Trial) Methods for Free Boundary Problems
1992
In this note we consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.
A boundary controllability approach in optimal shape design problems
2005
We indicate a formulation of optimal shape design problems as boundary control problems, based on some approximate controllability-type results. Numerical examples and a comparison with the standard method are included.
Signorini problem with Coulomb's law of friction. Shape optimization in contact problems
1992
Sur les problèmes d'optimisation structurelle
2000
We discuss existence theorems for shape optimization and material distribution problems. The conditions that we impose on the unknown sets are continuity of the boundary, respectively a certain measurability hypothesis. peerReviewed
Optimal Shape Design in Contact Problems
1989
From the mathematical point of view, optimal shape design (or optimum design, optimization of the domain, structural optimization) is a branch of the calculus of variations and especially of optimal control where study is devoted to the problem of finding the optimal shape for an object. In an optimal shape design process the objective is to optimize certain criteria involving the solution of a partial differential equation with respect to its domain of definition, [2, 3, 5].
Optimization of the domain in elliptic variational inequalities
1988
This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.