engleski

Isogeometric based shape optimization of plate with hole under constant in-plane tension

Shape optimization usually implies some type of analysis as a background process for defining optimization objectives and/or constraints. In most of structural optimization approaches, the finite element method (FEM) has been employed for structural response analysis. This approach has one major drawback - geometric modeling and numerical analysis are based on different mathematical descriptions, i.e. geometry is defined using spline technology and FEM analysis based on Lagrangian and Hermitian polynomials only approximates given geometry. To overcome this design-analysis gap, T.J.Hughes and coworkers introduced the concept of isogeometric analysis (IGA). In IGA, spline basis used to describe geometry are used as a basis functions in numerical analysis as well, i.e there is no geometry approximation, meaning analysis is performed on exact geometry. This method is especially attractive when comes to shape optimization – the shape can be defined via relatively small number of control points which arise as a natural choice for optimization design variables, i.e. there is no need for additional parameterization between design variables and analysis model. In the present work, shape optimization of plate with hole under constant in-plane tension is carried-out. Shape of the hole is defined with 4 control points. The optimization is conducted for 4, 6 and 8 degrees of freedom i.e. with 4, 6 and 8 design variables - coordinates and weights of control points defining hole, respectively. The goal is to find an optimal hole shape which minimizes maximum stress, for a given amount of material (constant volume) using genetic algorithms. For the sake of comparison, optimization is also conducted using gradient method. When comparing to plate with circular hole, it is shown that maximum stress can be significantly reduced (several times) with different shape, i.e. when optimization is performed.

Isogeometric approah ; Shape optimization ; Genetic algorithms

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