Abstract
Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.
Highlights
Topology optimization (TO), which has been extensively studied over the last decades, is a process of determining optimal layout of materials inside a given design domain
Given that non-uniform rational B-spline (NURBS) basis functions associated with the interior control points vanish at the structural boundary when open-knot vectors are employed, the displacement boundary condition applied on the left and right sides of the beam is imposed by setting the displacement values at left and right boundary control points to zero
We solved maximum fundamental eigenfrequency TO problems with a level set model based on the isogeometric analysis (IGA) technique
Summary
Topology optimization (TO), which has been extensively studied over the last decades, is a process of determining optimal layout of materials inside a given design domain. TO has been applied to various structural optimization problems, such as minimum compliance [1,2] vibration [3,4], and thermal issues [5,6], after Bendsøe and Kikuchi These conventional TO methods, which are based on element-wise design variables, suffer from numerical instability problems, such as checkerboards and mesh dependency. Most LSMs rely on finite elements wherein boundaries are still represented by discretized mesh in the analysis field unless alternative techniques are utilized to map the geometry to the analysis model Most of these TOs are performed in a fixed domain of finite elements where FEM is used to solve optimization problems. We develop a new optimization method to formulate the TO problem for cases with maximum fundamental eigenfrequency by using LSM under the framework of IGA instead of conventional finite element analysis (FEA).
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