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
Summary
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
Keywords
Isogeometric Analysis; Shape Optimization; Topology Optimization; Numerical method; Optimization Algorithm
Published Papers
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Open Access
EDITORIAL
Introduction to the Special Issue on Recent Developments of Isogeometric Analysis and Its Applications in Structural Optimization
Yingjun Wang, Zhenpei Wang, Xiaowei Deng, David J. Benson, Damiano Pasini, Shuting Wang
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 783-785, 2020, DOI:10.32604/cmes.2020.013234
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract This article has no abstract.
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Open Access
ARTICLE
Isogeometric Analysis and Shape Optimization of Holed Structures via the Patch Removing Technique
Daoyuan Yu, Shouyu Cai, Wenya Fan, Lan Zhang
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 787-806, 2020, DOI:10.32604/cmes.2020.09936
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract In this study, a patch removing based Isogeometric analysis (PR-IGA)
method is proposed to conduct the holed structural analysis with only one parametric domain, in which there are also no trimmed elements. The theoretical foundation of this novel patch removing approach is that any holed structure can be
obtained by removing sub-patches (i.e., the holes) from an intact base patch. Since
the parametric domains of these patches are all meshed by rectangular grids, the
elements in the resulted holed structural parametric domain could all be
untrimmed rectangles under certain mapping conditions. To achieve the special
condition, a systematic technique consisting…
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Open Access
ARTICLE
Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space
Hongyin Yang, Jiwei Zhong, Ying Wang, Xingquan Chen, Xiaoya Bian
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.3, pp. 807-824, 2020, DOI:10.32604/cmes.2020.010936
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract In this paper, general interpolating isogeometric boundary node method
(IIBNM) and isogeometric boundary element method (IBEM) based on parameter
space are proposed for 2D elasticity problems. In both methods, the integral cells
and elements are defined in parameter space, which can reproduce the geometry
exactly at all the stages. In IIBNM, the improved interpolating moving leastsquare method (IIMLS) is applied for field approximation and the shape functions
have the delta function property. The Lagrangian basis functions are used for field
approximation in IBEM. Thus, the boundary conditions can be imposed directly
in both methods. The shape functions are defined in…
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Open Access
ARTICLE
Resolving Domain Integral Issues in Isogeometric Boundary Element Methods via Radial Integration: A Study of Thermoelastic Analysis
Shige Wang, Zhongwang Wang, Leilei Chen, Haojie Lian, Xuan Peng, Haibo Chen
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 585-604, 2020, DOI:10.32604/cmes.2020.09904
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract The paper applied the isogeometric boundary element method (IGABEM) to thermoelastic problems. The Non-Uniform Rational B-splines (NURBS)
used to construct geometric models are employed to discretize the boundary integral formulation of the governing equation. Due to the existence of thermal stress,
the domain integral term appears in the boundary integral equation. We resolve
this problem by incorporating radial integration method into IGABEM which
converts the domain integral to the boundary integral. In this way, IGABEM
can maintain its advantages in dimensionality reduction and more importantly,
seamless integration of CAD and numerical analysis based on boundary representation. The algorithm is verified…
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Open Access
ARTICLE
Analysis-Aware Modelling of Spacial Curve for Isogeometric Analysis of Timoshenko Beam
Yang Xia, Luting Deng, Jian Zhao
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 605-626, 2020, DOI:10.32604/cmes.2020.010204
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
A High-Accuracy Single Patch Representation of Multi-Patch Geometries with Applications to Isogeometric Analysis
Jinlan Xu, Ningning Sun, Gang Xu
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 627-642, 2020, DOI:10.32604/cmes.2020.010341
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications. In isogeometric analysis, multi-patch structure
is not easy to achieve high continuity between neighboring patches which will reduce
the advantage of isogeometric analysis in a sense. The proposed method can achieve
high continuity at surface stitching region with low geometric error, and this technique exploits constructing the approximate surface with several control points are
from original surfaces, which guarantees the local feature of the surface can be
well-preserved with high precision. With the proposed approximating method,
isogeometric analysis…
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Open Access
ARTICLE
IGA Based Bi-Layer Fiber Angle Optimization Method for Variable Stiffness Composites
Chao Mei, Qifu Wang, Chen Yu, Zhaohui Xia
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 179-202, 2020, DOI:10.32604/cmes.2020.09948
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
Parametric Structural Optimization of 2D Complex Shape Based on Isogeometric Analysis
Long Chen, Li Xu, Kai Wang, Baotong Li, Jun Hong
CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 203-225, 2020, DOI:10.32604/cmes.2020.09896
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains
Gang Zhao, Jiaming Yang, Wei Wang, Yang Zhang, Xiaoxiao Du, Mayi Guo
CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 1033-1059, 2020, DOI:10.32604/cmes.2020.09920
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
T-Splines for Isogeometric Analysis of Two-Dimensional Nonlinear Problems
Mayi Guo, Gang Zhao, Wei Wang, Xiaoxiao Du, Ran Zhang, Jiaming Yang
CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 821-843, 2020, DOI:10.32604/cmes.2020.09898
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
Multiscale Isogeometric Topology Optimization with Unified Structural Skeleton
Chen Yu, Qifu Wang, Chao Mei, Zhaohui Xia
CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 779-803, 2020, DOI:10.32604/cmes.2020.09363
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
Multiresolution Isogeometric Topology Optimisation Using Moving Morphable Voids
Bingxiao Du, Yong Zhao, Wen Yao, Xuan Wang, Senlin Huo
CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 1119-1140, 2020, DOI:10.32604/cmes.2020.08859
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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…
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Open Access
ARTICLE
Data-Driven Structural Design Optimization for Petal-Shaped Auxetics Using Isogeometric Analysis
Yingjun Wang, Zhongyuan Liao, Shengyu Shi, Zhenpei Wang, Leong Hien Poh
CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.2, pp. 433-458, 2020, DOI:10.32604/cmes.2020.08680
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
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.
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Open Access
ARTICLE
Reusing the Evaluations of Basis Functions in the Integration for Isogeometric Analysis
Zijun Wu, Shuting Wang, Wenjun Shao, Lianqing Yu
CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.2, pp. 459-485, 2020, DOI:10.32604/cmes.2020.08697
（This article belongs to this Special Issue:
Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)
Abstract We propose a new approach to reuse the basis function evaluations in the
numerical integration of isogeometric analysis. The concept of reusability of the basis
functions is introduced according to their symmetrical, translational and proportional
features on both the coarse and refined levels. Based on these features and the parametric
domain regularity of each basis, we classify the bases on the original level and then reuse
them on the refined level, which can reduce the time for basis calculations at integration
nodes. By using the sum factorization method and the mean value theorem for the
integrals, a new integration method…
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