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Topological shape optimization of power flow problems at high frequencies using level set approach
Cho, Seonho,Ha, Seung-Hyun,Park, Chan-Young Elsevier 2006 International journal of solids and structures Vol.43 No.1
<P><B>Abstract</B></P><P>Using a level set method we develop a topological shape optimization method applied to power flow problems in steady state. Necessary design gradients are computed using an efficient adjoint sensitivity analysis method. The boundaries are implicitly represented by the level set function obtainable from the “Hamilton–Jacobi type” equation with the “Up-wind scheme.” The implicit function is embedded into a fixed initial domain to obtain the finite element response and sensitivity. The developed method defines a Lagrangian function for the constrained optimization. It minimizes a generalized compliance, satisfying the constraint of allowable volume through the variations of implicit boundary. During the optimization, the boundary velocity to integrate the Hamilton–Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the established topology optimization method, the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations.</P>
Topological Shape Optimization Using Level Set and Meshfree Methods
Seonho Cho(조선호),Seung-hyun Ha(하승현) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.5
Using level set and meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Necessary design gradients are computed using an efficient adjoint design sensitivity analysis (DSA) method. The boundaries are represented by an implicit moving boundary (IMB) embedded in the level set function obtainable from the “Hamilton-Jacobi type” equation with the “Up-wind scheme.” Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity. Global nodal shape function derived on a basis of the reproducing kernel (RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian function for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.