A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method

Chang, Fi‐John; Wang, Weiqiang; Yan, Liang; Qu, Yi-Qing

doi:10.1108/ec-10-2015-0306

Cited by 4 publications

(4 citation statements)

References 40 publications

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“…Hughes et al (2005) and Cottrell et al (2009) firstly introduced the concept of IGA by using the spline basis functions [such as non-uniform rational B-splines (NURBSs)] constructing the exact geometric models as interpolation functions in CAE analysis. Up to now, this approach has also gained widespread reception from the scientific community and many applications have been verified, for example, structural optimization (Cho and Ha, 2009;Qian, 2010;Ding et al, 2016;Ding et al, 2018c;Lian et al, 2017;Lian et al, 2016;Hao et al, 2018a;Hao et al, 2019;Hao et al, 2018b), plate and composite structures (Thai et al, 2014;Yu et al, 2018;Thai et al, 2015;Nguyen-Xuan et al, 2014;Chang et al, 2016;Yin et al, 2015;Thanh et al, 2019b;Phung-Van et al, 2019;Thanh et al, 2019a;Thanh et al, 2018;Phung-Van et al, 2018;Thai et al, 2018b;Thai et al, 2018a;Tran et al, 2017;Thai et al, 2016), isogeometric boundary methods (Simpson et al, 2013;Simpson et al, 2012;Peng et al, 2017;Scott et al, 2013), stochastic analysis (Ding et al, 2019a;Ding et al, 2018b;Ding et al, 2019b;Ding et al, 2019c), other splines based methods (Atroshchenko et al, 2018;Nguyen-Thanh et al, 2011;Gu et al, 2018a;Gu et al, 2018b), and especially the severa...…”

Section: Cae Modelmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

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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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Section: Cae Modelmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

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“…In addition, many works on other dimensions of IGA have been conducted, including topology optimization (Dedè et al , 2012), fluid mechanics (Nielsen et al , 2011), plate structures (Yin et al , 2015; Rauen et al , 2017) and various significant reviews (Nguyen et al , 2015; Chang et al , 2016).…”

Section: Introductionmentioning

confidence: 99%

Fuzzy combinatorial optimization in four-dimensional tradeoff problem of cost-time-quality-risk in one dimension and in the second dimension of risk context in ambiguous mode

Hosseinzadeh¹,

Paryzad

Pour

et al. 2020

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Purpose The optimization and tradeoff of cost-time-quality-risk in one dimension and this four-dimensional problem in ambiguous mode and risk can be neither predicted nor estimated. This study aims to solve this problem and rank fuzzy numbers using an innovative algorithm “STHD” and a special technique “radius of gyration” (ROG) for fuzzy answers, respectively. Design/methodology/approach First, it is the optimization of a fully fuzzy four-dimensional problem which has never been dealt with in regard to risk in ambiguous mode and complexities. Therefore, the risk is a parameter which has been examined neither in probability and estimableness mode nor in the ambiguous mode so far. Second, it is a fully fuzzy tradeoff which, based on the principle of incompatibility “Zadeh, 1973”, proposes that when the complexity of a system surpasses the limited point, it becomes impossible to define the performance of that system accurately, precisely and meaningfully. The authors believe that this principle is the source of fuzzy logic. Third, for calculating and ranking fuzzy numbers of answers, a special technique for fuzzy numbers has been used. Fourth, For the sake of ease, precision and efficiency, an innovative algorithm called the technique of hunting dolphins “STHD” has been used. Finally, the problem is very close to reality. By applying risk in ambiguous mode, the problem has been realistically looked at. Findings The results showed that the algorithm was highly robust, with its performance depending very little on the regulation of the parameters. Ranking fuzzy numbers using the ROG indicated the flexibility of fuzzy logic, and it was also determined that the most appropriate regulations were to ensure low time, risk and cost but maximum quality in calculations, which were produced non-uniformly based on the levels of Pareto answers. Originality/value The ROG and Chanas Fuzzy Critical Path Method as developed by other researchers have been used. Despite the increase in limitations, parameters can develop. The originality of this study with regard to evaluating the results of tradeoff combinatorial optimization is upon decision-making which has a special and highly strategic role in the fate of the project, with the research been conducted with a special approach and different tools in a fully fuzzy environment.

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“…If pure numerical efficiency is the only criterion for qualifying an implementation of IGA, the best approach would certainly be to rewrite everything into a dedicated piece of code written using a low-level language (e.g. PetIGA (Dalcin et al , 2016) for high performance IGA based on the PETSc library, (Chang et al , 2016) for an implementation using Fortran and (Nguyen et al , 2015) for global implementation aspects). In addition, let us mention that recent works to implement IGA efficiently start with a modification of the standard looping over elements in the assembly process (Calabro et al , 2017), which is incompatible with the use of standard FE codes.…”

Section: Introductionmentioning

confidence: 99%

Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software

Tirvaudey

Bouclier

Passieux

et al. 2019

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Purpose The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward with respect to the elementary structure of finite element (FE) codes. This often discourages industrial engineers from adopting isogeometric capabilities in their well-established simulation environment. Design/methodology/approach Based on the concept of Bézier and Lagrange extractions, a novel method is proposed to implement IGA from an existing industrial FE code with the aim of bringing human implementation effort to the minimal possible level (only using standard input-output of finite element analysis (FEA) codes, avoid code-dependent subroutines implementation). An approximate global link to go from Lagrange polynomials to non-uniform-rational-B-splines functions is formulated, which enables the whole FE routines to be untouched during the implementation. Findings As a result, only the linear system resolution step is bypassed: the resolution is performed in an external script after projecting the FE system onto the reduced, more regular and isogeometric basis. The novel procedure is successfully validated through different numerical experiments involving linear and nonlinear isogeometric analyses using the standard input/output of the industrial FE software Code_Aster. Originality/value A non-invasive implementation of IGA into FEA software is proposed. The whole FE routines are untouched during the novel implementation procedure; a focus is made on the IGA solution of nonlinear problems from existing FEA software; technical details on the approach are provided by means of illustrative examples and step-by-step implementation; the methodology is evaluated on a range of two- and three-dimensional elasticity and elastoplasticity benchmarks solved using the commercial software Code_Aster.

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A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method

Cited by 4 publications

References 40 publications

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Fuzzy combinatorial optimization in four-dimensional tradeoff problem of cost-time-quality-risk in one dimension and in the second dimension of risk context in ambiguous mode

Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software

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