Static Structural and Modal Analysis Using Isogeometric Analysis

Gondegaon, Sangamesh; Voruganti, Hari K.

doi:10.1515/jtam-2016-0020

Cited by 14 publications

(5 citation statements)

References 15 publications

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“…An excellent open source Matlab Ò implementation code for the IGA of one, two, and three-dimensional structural mechanics problems have been provided in [26]. The detailed application of B-spline based isogeometric analysis to one-and two-dimensional static structural and vibrational problems along with the implementation procedure is reported in [27]. A suite of free and open source research tool GeoPDEs, which serves as a starting tool for IGA users and is compatible with Octave, Matlab Ò programming languages, for the NURBS based isogeometric analysis of PDEs, have been included in Ref.…”

Section: Available Implementation Procedures Of Iga and Their Shortcomentioning

confidence: 99%

“…Finally, in ''Post-processing in IGA'' section, the necessary changes in post-processing stage of FEA are revised for the IGA. The reader may refer to [27] for understanding the IGA based implementation of one-dimensional structural bar problem. In this presentation, a standard infinite plate with the circular hole problem in tension, shown in Fig.…”

Section: A Detailed Stepwise Implementation Procedures For Igamentioning

confidence: 99%

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IGA: A Simplified Introduction and Implementation Details for Finite Element Users

Agrawal

Gautam

2018

J. Inst. Eng. India Ser. C

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Isogeometric analysis (IGA) is a recently introduced technique that employs the Computer Aided Design (CAD) concept of Non-uniform Rational B-splines (NURBS) tool to bridge the substantial bottleneck between the CAD and finite element analysis (FEA) fields. The simplified transition of exact CAD models into the analysis alleviates the issues originating from geometrical discontinuities and thus, significantly reduces the design-toanalysis time in comparison to traditional FEA technique. Since its origination, the research in the field of IGA is accelerating and has been applied to various problems. However, the employment of CAD tools in the area of FEA invokes the need of adapting the existing implementation procedure for the framework of IGA. Also, the usage of IGA requires the in-depth knowledge of both the CAD and FEA fields. This can be overwhelming for a beginner in IGA. Hence, in this paper, a simplified introduction and implementation details for the incorporation of NURBS based IGA technique within the existing FEA code is presented. It is shown that with little modifications, the available standard code structure of FEA can be adapted for IGA. For the clear and concise explanation of these modifications, step-by-step implementation of a benchmark plate with a circular hole under the action of in-plane tension is included.

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Section: Available Implementation Procedures Of Iga and Their Shortcomentioning

confidence: 99%

Section: A Detailed Stepwise Implementation Procedures For Igamentioning

confidence: 99%

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

Agrawal

Gautam

2018

J. Inst. Eng. India Ser. C

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“…Weeger et al (2013) also used similar methodologies to investigate static and dynamic analysis of non-linear Euler-Bernoulli beam. Gondegaon and Voruganti (2016) performed static and modal analysis of 1-D and 2-D structural problems. They considered rotation-free element for the beam formulation and excluded slope degree of freedom.…”

Section: Related Workmentioning

confidence: 99%

“…Because each control point has one degree of freedom, the IGA formulation of beam cannot capture slope as separate degrees of freedom. Therefore, in the literature related to IGA, beam analysis is carried out with either with a rotationfree element (Cottrell et al, 2006;Gondegaon and Voruganti, 2016) or a 2-D beam formulation (Li et al, 2013;Weeger et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

A novel method to apply Neumann boundary conditions in the Isogeometric Analysis (IGA) of beam with 1-D formulation

Mondal

Gondegaon

Voruganti

2017

WJE

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Purpose This paper proposes a novel approach to impose the Neumann boundary condition for isogeometric analysis (IGA) of Euler–Bernoulli beam with 1-D formulation. The proposed method is for only IGA in which it is difficult to handle the Neumann boundary conditions. The control points of B-spline are equivalent to nodes in finite element method. With 1-D formulation, it is not possible to accommodate multiple degrees of freedom in IGA. This case arises in the analysis of beams. The paper aims to propose a way to work around this issue in a simple way. Design/methodology/approach Neumann boundary conditions, which are even-order derivatives (example: double derivative) of the primary variable, are inherently satisfied in the weak form. Boundary conditions with an odd number of derivatives (example: slope) are imposed with the introduction of a new penalty matrix. Findings The proposed method can impose a slope boundary condition for IGA of a beam using 1-D formulation. Originality/value From the literature, it can be observed that the beam is formulated in 1-D by considering it as either a rotation-free element or a 2-D formulation by considering shear strain along with the normal strain. The work represents 1-D formulation of a beam while considering the slope boundary condition, which is easy and effective to formulate, compared with the slope boundary conditions reported in previous works.

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“…In IGA, both geometrical and analytical model are represented using the same B-spline basis function, thus avoiding meshing. This superiority of IGA over FEM results in less computational time and better accuracy of analysis solution [1].…”

Section: Introductionmentioning

confidence: 99%

An efficient parametrization of planar domain for isogeometric analysis using harmonic functions

Gondegaon

Voruganti

2018

J Braz. Soc. Mech. Sci. Eng.

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A recent and unified methodology of isogeometric analysis (IGA) requires the geometric model of the domain in the form of a parametric spline. Developing such a geometric model for IGA is called parameterization, and it is a challenging task. The way quality of a mesh affects the results in finite element analysis; an effective parametrization is a key for accurate results and computational efficiency. Finding a spline representation for the domain involves two sets of unknowns, namely parameter values and control points. In this work, a new method is proposed to find them in two stages for planar domains. The domain is mapped to an equivalent convex domain using harmonic functions. Here, the domain is mapped to a circle and then to a square so that the resulting parameter values are suitable for the tensor-product form of B-spline surface. The B-spline control points for the domain are computed with inverse of tensor-product B-spline. Most existing methodologies involve iterative optimization-based methods which makes them expensive. Experimental results of a few cases of complex domains are reported to demonstrate the effectiveness of the method in comparison with other methods. Moreover, metrics are developed to assess the quality of parametrization are included.

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Static Structural and Modal Analysis Using Isogeometric Analysis

Cited by 14 publications

References 15 publications

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

IGA: A Simplified Introduction and Implementation Details for Finite Element Users

A novel method to apply Neumann boundary conditions in the Isogeometric Analysis (IGA) of beam with 1-D formulation

An efficient parametrization of planar domain for isogeometric analysis using harmonic functions

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