Static Structural and Modal Analysis Using Isogeometric Analysis

Open access

Abstract

Isogeometric Analysis (IGA) is a new analysis method for unification of Computer Aided Design (CAD) and Computer Aided Engineering (CAE). With the use of NURBS basis functions for both modelling and analysis, the bottleneck of meshing is avoided and a seamless integration is achieved. The CAD and computational geometry concepts in IGA are new to the analysis community. Though, there is a steady growth of literature, details of calculations, explanations and examples are not reported. The content of the paper is complimentary to the existing literature and addresses the gaps. It includes summary of the literature, overview of the methodology, step-by-step calculations and Matlab codes for example problems in static structural and modal analysis in 1-D and 2-D. At appropriate places, comparison with the Finite Element Analysis (FEM) is also included, so that those familiar with FEM can appreciate IGA better.

[1] HUGHES, T. J., J. A. COTTRELL, Y. BAZILEVS. Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement. Computer Methods in Applied Mechanics and Engineering, 194 (2005), No. 39, 4135-4195.

[2] KAGAN, P., A. FISCHER. Integrated Mechanically Based CAE System using B-Spline Finite Elements. Computer-Aided Design, 32 (2000), No. 8, 539-552.

[3] KAGAN, P., A. FISCHER, P. Z. BAR-YOSEPH. New B-Spline Finite Element Approach for Geometrical Design and Mechanical Analysis. International Journal for Numerical Methods in Engineering, 41 (1998), No. 3, 435-458.

[4] COTTRELL, J. A., T. J. R. HUGHES, A. REALI. Studies of Refinement and Continuity in Isogeometric Structural Analysis. Computer Methods in Applied Mechanics and Engineering, 196 (2007), No. 41, 4160-4183.

[5] DENG, J., F. CHEN, X. LI, C. HU, W. TONG, Z. YANG, Y. FENG. Polynomial Splines over Hierarchical T-meshes. Graphical Models, 70 (2008), No. 4, 76-86.

[6] SCHILLINGER, D., L. DEDE, M. A. SCOTT, J. A. EVANS, M. J. BORDEN, E. RANK, T. J. HUGHES. An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS, immersed Boundary Methods, and T-spline CAD Surfaces. Computer Methods in Applied Mechanics and Engineering, 249 (2012), 116-150.

[7] WALL, W. A., M. A. FRENZEL, C. CYRON. Isogeometric Structural Shape Optimization. Computer Methods in Applied Mechanics and Engineering, 197 (2008), No. 33, 2976-2988.

[8] HASSANI, BEHROOZ, S. M. TAVAKKOLI, N. Z. MOGHADAM. Application of Isogeometric Analysis in Structural Shape Optimization. Scientia Iranica, 18 (2011), No. 4, 846-852. SIMPSON, R. N., S. P. BORDAS, J. TREVELYAN, T. RABCZUK, (2012).

[9] KIENDL, J., K. U. BLETZINGER, J. LINHARD, R. W¨U CHNER. Isogeometric Shell Analysis with Kirchhoff-Love Elements. Computer Methods in Applied Mechanics and Engineering, 198 (2009), No. 49, 3902-3914.

[10] NIELSEN, P. N., A. R. GERSBORG, J. GRAVESEN, N. L. PEDERSEN. Discretizations in Isogeometric Analysis of Navier-Stokes Flow. Computer Methods in Applied Mechanics and Engineering, 200 (2011), No. 45, 3242-3253.

[11] G´OMEZ, H., V. M. CALO, Y. BAZILEVS, T. J. HUGHES. Isogeometric Analysis of the Cahn-Hilliard Phase-field Model. Computer Methods in Applied Mechanics and Engineering, 197 (2008), No. 49, 4333-4352.

[12] MASUD, A., R. KANNAN. B-splines and NURBS based Finite Element Methods for Kohn-Sham Equations. Computer Methods in Applied Mechanics and Engineering, 241 (2012), 112-127.

[13] COTTRELL, J. A., A. REALI, Y. BAZILEVS, T. J. HUGHES. Isogeometric Analysis of Structural Vibrations. Computer Methods in Applied Mechanics and Engineering, 195 (2006), No. 41, 5257-5296.

[14] SHOJAEE, S., E. IZADPANAH, N. VALIZADEH, J. KIENDL. Free Vibration Analysis of Thin Plates by using a NURBS-based Isogeometric Approach. Finite Elements in Analysis and Design, 61 (2012), 23-34.

[15] PIEGL, L., W. TILLER. The NURBS Book, Springer Science & Business Media, 2012.

Journal of Theoretical and Applied Mechanics

The Journal of Institute of Mechanics of Bulgarian Academy of Sciences

Journal Information

CiteScore 2017: 1.14

SCImago Journal Rank (SJR) 2017: 0.217
Source Normalized Impact per Paper (SNIP) 2017: 0.583

Mathematical Citation Quotient (MCQ) 2017: 0.01

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 280 280 36
PDF Downloads 147 147 30