Special Issue "Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization"

Submission Deadline: 15 March 2020 (closed)
Guest Editors
Prof. Yingjun Wang, South China University of Technology, China.
Dr. Zhenpei Wang, Singapore Agency for Science, Technology and Research (A*STAR), Singapore
Prof. Xiaowei Deng, the University of Hong Kong, Hong Kong SAR
Prof. David J. Benson, University of California San Diego, USA
Prof. Damiano Pasini, McGill University, Canada
Prof. Shuting Wang, Huazhong University of Science and Technology, China


Isogeometric analysis (IGA), which directly uses CAD models for analysis, is one of the most active research topics in both computational mechanics and computer-aided geometric design. The rapidly growing interests in IGA has led to profound developments of relevant theories and applications, among which is structural design optimization. The advantages of using IGA in structural optimization lies mainly in three aspects: (i) the integration between CAD and FE models averts the manual transition efforts; (ii) the high-order continuity of basis function enhances sensitivity analysis; and (iii) the ease of mesh refinements enriches the design flexibilities by controlling design variables. 

However, there are barriers limiting the development of IGA and IGA-based design optimization. First, as many CAD parameterization methods are not analysis-suitable, it is essential to develop general and powerful parameterization methods that are not only capable of describing complex geometries, but also analysis-suitable. Meanwhile, structural design optimization based on such parameterization methods needs to be investigated to make the best use of the developments. Secondly, as CAD modeling tools are intensively involved in IGA, the numerical implementations of IGA-based studies can be less accessible for researchers with a background of mechanics. Hence, works with detailed numerical implementations, preferably with software codes for benchmark problems, should be highly valued. Last but not least, as most of the studies have been demonstrated to solve simple benchmark problems, studies for potential engineering applications or complex geometries should be encouraged. 

With the rapid growth of researches in IGA, we initiate this special issue to highlight the recent developments, challenges and opportunities of IGA and IGA-based structural design optimization, with particular focus on theory developments, numerical implementations and potential applications. 

Topics of interest include but are not restricted to: 
1. Isogeometric analysis and analysis-suitable parameterization methods
2. Isogeometric shape optimization
3. Isogeometric topology optimization
4. Multiscale isogeometric structural optimization
5. Automatic model generation for isogeometric analysis
6. Isogeometric analysis for complex problems
7. High-efficient isogeometric analysis/isogeometric structural optimization
8. Engineering applications using isogeometric analysis/isogeometric structural optimization
9. Numerical implementations and software codes

Isogeometric Analysis; Shape Optimization; Topology Optimization; Numerical method; Optimization Algorithm

Published Papers

  • Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam
  • Abstract Geometric fitting based on discrete points to establish curve structures is an important problem in numerical modeling. The purpose of this paper is to investigate the geometric fitting method for curved beam structure from points, and to get high-quality parametric model for isogeometric analysis. A Timoshenko beam element is established for an initially curved spacial beam with arbitrary curvature. The approximation and interpolation methods to get parametric models of curves from given points are examined, and three strategies of parameterization, meaning the equally spaced method, the chord length method and the centripetal method are considered. The influences of the different… More
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  • IGA Based Bi-Layer Fiber Angle Optimization Method for Variable Stiffness Composites
  • Abstract This paper presents a topology optimization method for variable stiffness composite panels with varying fiber orientation and curvilinear fiber path. Non-uniform rational B-Splines (NURBS) based Isogeometric analysis (IGA) is utilized for the numerical computation of the general minimum compliance problem. The sensitivity analysis of the structure compliance function for the density and bi-layer orientation is conducted. The bi-layer fiber paths in the design domain are generated using streamline method and updated by divided pieces reselection method after the optimization process. Several common examples are tested to demonstrate the effectiveness of the method. The results show that the proposed method can… More
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  • Parametric Structural Optimization of 2D Complex Shape Based on Isogeometric Analysis
  • Abstract The geometric model and the analysis model can be unified together through the isogeometric analysis method, which has potential to achieve seamless integration of CAD and CAE. Parametric design is a mainstream and successful method in CAD field. This method is not continued in simulation and optimization stage because of the model conversion in conventional optimization method based on the finite element analysis. So integration of the parametric modeling and the structural optimization by using isogeometric analysis is a natural and interesting issue. This paper proposed a method to realize a structural optimization of parametric complex shapes by using isogeometric… More
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  • T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains
  • Abstract In this paper, a new isogeometric topology optimization (ITO) method is proposed by using T-splines based isogeometric analysis (IGA). The arbitrarily shaped design domains, directly obtained from CAD, are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline (NURBS). The coefficients correlated with control points are directly used as design variables. Therefore, the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution. Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures. The… More
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  • T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems
  • Abstract Nonlinear behaviors are commonplace in many complex engineering applications, e.g., metal forming, vehicle crash test and so on. This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems, to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials. By applying the adaptive refinement capability of T-splines during the iteration process of analysis, the numerical simulation accuracy of the nonlinear model could be increased dramatically. The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be… More
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  • Multiscale Isogeometric Topology Optimization with Unified Structural Skeleton
  • Abstract This paper proposes a multiscale isogeometric topology optimization (ITO) method where the configuration and layout of microstructures are optimized simultaneously. At micro scale, a shape deformation method is presented to transform a prototype microstructure (PM) for obtaining a series of graded microstructures (GMs), where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability. For the macro scale calculation, the effective mechanical properties can be estimated by means of the numerical homogenization method. By adopting identical non-uniform rational basis splines (NURBS) as basis functions for both parameterized level set model and… More
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  • Multiresolution Isogeometric Topology Optimisation Using Moving Morphable Voids
  • Abstract A general and new explicit isogeometric topology optimisation approach with moving morphable voids (MMV) is proposed. In this approach, a novel multiresolution scheme with two distinct discretisation levels is developed to obtain high-resolution designs with a relatively low computational cost. Ersatz material model based on Greville abscissae collocation scheme is utilised to represent both the Young’s modulus of the material and the density field. Two benchmark examples are tested to illustrate the effectiveness of the proposed method. Numerical results show that high-resolution designs can be obtained with relatively low computational cost, and the optimisation can be significantly improved without introducing… More
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  • Data-Driven Structural Design Optimization for Petal-Shaped Auxetics Using Isogeometric Analysis
  • Abstract Focusing on the structural optimization of auxetic materials using data-driven methods, a back-propagation neural network (BPNN) based design framework is developed for petal-shaped auxetics using isogeometric analysis. Adopting a NURBS-based parametric modelling scheme with a small number of design variables, the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method, and demonstrated in this work to give high accuracy and efficiency. Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis, in contrast to the generally complex procedures of typical shape and size sensitivity approaches. More
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