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The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of the finite element method. For this purpose, the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. The coordinates of control points which are also used for constructing the density function, are considered as design variables of the optimization problem. In order to change the design variables towards optimum, the Method of Moving Asymptotes (MMA) is used. To alleviate the formation of layouts with porous media, the density function is penalized during the optimization process. A few examples are presented to demonstrate the performance of the method.

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The Isogeometric Analysis (IA) is utilized for structural topology optimization  considering minimization of weight and local stress constraints. For this purpose, material density of the structure  is  assumed  as  a  continuous  function  throughout  the  design  domain  and approximated using the Non-Uniform Rational B-Spline (NURBS) basis functions. Control points of the density surface are considered as design variables of the optimization problem that can change the topology during the optimization process. For initial design, weight and stresses of the structure are obtained based on full material density over the design domain. The  Method  of  Moving  Asymptotes  (MMA)  is  employed  for  optimization  algorithm. Derivatives of the objective function and constraints with respect to the design variables are determined  through  a  direct  sensitivity  analysis.  In  order  to  avoid  singularity  a  relaxation technique  is  used  for  calculating  stress  constraints.  A  few  examples  are  presented  to demonstrate the performance of the method. It is shown that using the IA method and an appropriate stress relaxation technique can lead to reasonable optimum layouts.

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Keeping the eigenfrequencies of a structure away from the external excitation frequencies is one of the main goals in the design of vibrating structures in order to avoid risk of resonance. This paper is devoted to the topological design of freely vibrating continuum structures with the aim of maximizing the fundamental eigenfrequency. Since in the process of topology optimization some areas of domain can potentially be removed, it is quite possible to encounter the problem of localized modes. Hence, the modified Solid Isotropic Material with Penalization (SIMP) model is here used to avoid artificial modes in low density areas. As during the optimization process, the first natural frequency increases, it may become close to the second natural frequency. Due to lack of the usual differentiability of the multiple eigenfrequencies, their sensitivity are calculated by the mathematical perturbation analysis. The optimization problem is formulated by a variable bound formulation and it is solved by the Method of Moving Asymptotes (MMA). Two dimensional plane elasticity problems with different sets of boundary conditions and attachment of a concentrated nonstructural mass are considered. Numerical results show the validity and supremacy of this approach.