Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications

Ding, Chensen; Cui, Xiangyang; Huang, Guanxin; Li, Guangyao; Tamma, Kumar K.

doi:10.1016/j.cma.2017.02.004

Cited by 16 publications

(8 citation statements)

References 55 publications

(44 reference statements)

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“…In this section, the basic theories of IGA are described, including parametric modelling and CAE simulation, and then the IC‐based IGR method is implemented to recalculate the incremental solution.…”

Section: Basic Theories Of Iga and Reanalysis Methodsmentioning

confidence: 99%

“…However, the cases used to validate the MGR method proposed in Reference are relatively simple and regular structures. Additionally, the cases demonstrated in Reference by the IC‐based IGR are also simple and can be constructed easily. For large and complicated modifications, it is obvious that mapping is difficult to construct directly by IC‐based IGA or MGR methods.…”

Section: Auxiliary Projection‐based Mg‐igrmentioning

confidence: 99%

See 1 more Smart Citation

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

Liu

et al. 2020

Numerical Meth Engineering

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Summary An efficient optimization framework is developed in this study by integrating auxiliary projection‐based multigrid isogeometric reanalysis (MG‐IGR) and metaheuristic searching techniques. It is well known that the inherent characteristics of isogeometric analysis (IGA) are superior in shape optimization problems. Inheriting the characteristics of IGA, an auxiliary projection‐based MG reanalysis (MGR) is proposed to construct mapping between the mesh before modification and after modification during the optimization process. Subsequently, MG‐IGR is utilized to reanalyze the modified design efficiently by reusing the initial evaluated results. Moreover, the proposed MG‐IGR also eliminates the restriction of mesh consistency. In this framework, the structure can be designed directly through parameterized control of the non‐uniform rational B‐spline (NURBS) model, and the MG‐IGR fast solver enables any metaheuristic algorithm to perform the optimization procedure. Moreover, the accuracy of the simulation can be guaranteed by the NURBS model and the convergence criterion of the MG. Finally, two geometric optimization examples are presented to validate the performance of the developed framework.

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Section: Basic Theories Of Iga and Reanalysis Methodsmentioning

confidence: 99%

Section: Auxiliary Projection‐based Mg‐igrmentioning

confidence: 99%

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

Liu

et al. 2020

Numerical Meth Engineering

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“…It avoids solving the complete set of modified equations and takes full use of their advantages in CAD/CAE integration. Until now, a large amount of reanalysis methods has been used in various classes of problems (Kirsch, 1991;Kirsch, 2003;Kirsch, 2000a;Kirsch, 2000b;Kirsch, 2008;Chen and Yang, 2004;Yang et al, 2004;Wu et al, 2003;Huang et al, 2014;Ding et al, 2018a;Ding et al, 2017). For example, the combined approximation (CA) firstly studied by Kirsch (1991) is successfully applied to many aspects and profoundly reviewed (Kirsch, 2003;Kirsch, 2000a;Kirsch, 2000b;Kirsch, 2008).…”

Section: The Reanalysis and Isogeometric Independent Coefficients Methodsmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

Self Cite

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Purpose This paper aims to provide designers/engineers, in engineering structural design and analysis, approaches to freely and accurately modify structures (geometric and/or material), and then quickly provide real-time capability to obtain the numerical solutions of the modified structures (designs). Design/methodology/approach The authors propose an isogeometric independent coefficients (IGA-IC) method for a fast reanalysis of structures with geometric and material modifications. Firstly, the authors seamlessly integrate computer-aided design (CAD) and computer-aided engineering (CAE) by capitalizing upon isogeometric analysis (IGA). Hence, the authors can easily modify the structural geometry only by changing the control point positions without tedious transformations between CAE and CAD models; and modify material characters simply based on knots vectors. Besides, more accurate solutions can be obtained because of the high order degree of the spline functions that are used as interpolation functions. Secondly, the authors advance the proposed independent coefficients method within IGA for fast numerical simulation of the modified designs, thereby significantly reducing the enormous time spent in repeatedly numerical evaluations. Findings This proposed scheme is efficient and accurate for modifying the structural geometry by simply changing the control point positions, and material characters by knots vectors. The enormous time spent in repeated full numerical simulations for reanalysis is significantly reduced. Hence, enabling quickly modifying structural geometry and material, and analyzing the modified model for practicality in design stages. Originality/value The authors herein advance and propose the IGA-IC scheme. Where, it provides designers to fasten and simple designs and modify structures (both geometric and material). It then can quickly in real-time obtain numerical solutions of the modified structures. It is a powerful tool in practical engineering design and analysis process for local modification. While this method is an approximation method designed for local modifications, it generally cannot provide an exact numerical solution and its effectiveness for large modification deserves further study.

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“…the design variables. In case of the shape parametrization of the form (22), this operator reads as:…”

Section: Shape Representation and Parametrizationmentioning

confidence: 99%

“…That is why the central FD takes twice the computational time of the forward FD (see again table 4). Of course, this computational time can surely be reduced by saving redundant quantities and by using dedicated strategies as for example structural reanalysis [22,52]. However, in this example, there are only 32 design variables.…”

Section: Typementioning

confidence: 99%

A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization

Hirschler

Bouclier

Duval

et al. 2020

Arch Computat Methods Eng

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Isogeometric shape optimization has been now studied for over a decade. This contribution aims at compiling the key ingredients within this promising framework, with a particular attention to sensitivity analysis. Based on all the researches related to isogeometric shape optimization, we present a global overview of the process which has emerged. The principal feature is the use of two refinement levels of the same geometry: a coarse level where the shape updates are imposed and a fine level where the analysis is performed. We explain how these two models interact during the optimization, and especially during the sensitivity analysis. We present new theoretical developments, algorithms, and quantitative results regarding the analytical calculation of discrete adjoint-based sensitivities. In order to highlight the versatility of this sensitivity analysis method, we perform eight benchmark optimization examples with different types of objective functions (compliance, displacement field, stress field, and natural frequencies), different types of isogeometric element (2D and 3D standard solids, and a Kirchhoff-Love shell), and different types of structural analysis (static and vibration). The numerical performances of the analytical sensitivities are compared with approximate sensitivities. The results in terms of accuracy and numerical cost make us believe that the presented method is a viable strategy to build a robust framework for shape optimization.

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Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications

Cited by 16 publications

References 55 publications

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework

Isogeometric independent coefficients method for fast reanalysis of structural modifications

A New Lighting on Analytical Discrete Sensitivities in the Context of IsoGeometric Shape Optimization

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