Topology Optimization with Isogeometric Concept - WCCM 2016

Topology Optimization with Isogeometric Concept Sang Jin LEE and Gyeong Im PARK ADOPT Research Group Department of Architectural Engineering, Gyeongsang National University Jinju, KOREA Topology optimization (TO) technique is proposed for plane structures. With the introduction of isogeometric concept, the NURBS basis function is used to represent both structural geometry and the field functions and the exact geometric models are consistently used in TO process. In addition, the NURBS basis functions are used to define the material distribution of structures. Since the node-wise design variables are used with the continuous material distribution function and the proposed TO technique is completely free from checker boarding phenomenon without additional constraints or a filtering technique. When we use the NURBS definition in the analysis, sometimes we may not be able to apply the point load at certain locations and so multi-patch isogeometric analysis is introduced in TO. The validity and applicability of the presented TO technique are demonstrated by using the benchmark tests for plane structures with some important features of isogeometric approach such as the refinement method and the order of basis function. The optimum topologies of the half ring structure are produced and the results are illustrated in the first Table below. The initial mesh begins with the size of 16x16. The hrefinement is performed twice and the 64x64 mesh is prepared for isogeometric analysis. From the numerical results, we found that almost identical optimum topologies and strain energy (SE) reduction are achieved with different order of basis function. The multi-patch isogeometric analysis is also tackled to model the point load at the center of beam end and the circle inside the beam. From the numerical results, multi-patch isogeometric analysis is successfully performed in TO process. Order Results

The order of basis function used in isogeometric analysis p=q=2

p=q=3

p=q=4

p=q=5

86.08%

86.15%

86.17%

86.22%

Optimum topologies

SE reduction

Cantilever beam Geometry Optimum (p=q=1)

Cantilever beam with a hole inside Geometry Optimum (p=q=2)

Keywords: Topology optimization, isogeometric concept, node-wise design variable, multipatch, checker-boarding