Isogeometric Analysis as a New FEM Formulation - Simple Problems of Steady State Thermal Analysis

Kacprzyk, Zbigniew; Ostapska-Łuczkowska, Katarzyna

doi:10.1016/j.proeng.2014.12.018

Cited by 8 publications

(6 citation statements)

References 2 publications

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“…This is accomplished by using the same function space to represent the geometry Ω and to discretize the PDE problem posed over Ω . Since its birth in 2005, IGA has been successfully applied to wide variety of problems including: thermal analysis [2], linear elasticity problems [1], structural vibrations [3], incompressible flows [4] and inviscid compressible flows [5].…”

Section: Introductionmentioning

confidence: 99%

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

Hinz

Jaeschke

Möller

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases. c

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Section: Introductionmentioning

confidence: 99%

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

Hinz

Jaeschke

Möller

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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“…An EGG-based planar parametrization framework that supports THB-splines has been proposed in [13]. Since its birth in 2005, IGA was successfully applied to wide variety of problems including: thermal analysis [14], linear elasticity problems [1], structural vibrations [15], incompressible flows [16] and inviscid compressible flows [17]. As a mature numerical method, it is ready to be used in more complex industrial processes.…”

Section: Introductionmentioning

confidence: 99%

The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications

Hinz¹,

Jaeschke²,

Möller³

et al. 2020

Preprint

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“…Some implementations depend on existing mature software, e.g. LS-DYNA (Benson et al, 2010) and Rhino (Kacprzyk and Ostapska-Łuczkowska, 2014;Kiendl et al, 2009). A framework based on PETSc for high-performance IGA was presented (Vignal et al, 2014;Collier and Calo, 2016).…”

Section: Introductionmentioning

confidence: 99%

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

Chang

Wang

Yan

et al. 2016

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Purpose As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems. Design/methodology/approach IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions. Findings Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method. Originality/value A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

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Isogeometric Analysis as a New FEM Formulation - Simple Problems of Steady State Thermal Analysis

Cited by 8 publications

References 2 publications

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

The Role of PDE-Based Parameterization Techniques in Gradient-Based IGA Shape Optimization Applications

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

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