A Step by Step Procedure to Perform Isogeometric Analysis of Beam and Bar Problems in Civil Engineering Including Sizing Optimisation of a Beam

K. N. V. Chandrasekhar*, N. S. S. Sahithi**
* Assistant Professor, Department of Civil Engineering, CVR College of Engineering, Hyderabad, India.
** PG Scholar, Department of Civil Engineering, CVR College of Engineering, Hyderabad, India.
Periodicity:March - May'2018
DOI : https://doi.org/10.26634/jste.7.1.14283


The integration of CAD geometry and analysis is really a big advantage of using Isogeometric analysis. The Galerkin weak formulation is used to solve the governing differential equations using the B-splines and NURBS functions. The main focus of this paper is to present a detailed step by step procedure to solve beam and bar problems in Civil Engineering. The beam is analysed for static and dynamic loading, and the bar problem is analysed to find the natural frequency of vibration. The sizing optimization of the beam is also perfomed to determine the optimal cross section dimensions of the beam. The results from the Isogeometric analysis are then compared with the theoretical results. The results from Isogeometric analysis shows a good agreement with those obtained by using the analytical methods. The solution from the Isogeometric analysis has better precision over other standard methods. The structures are designed with a basic set of criteria, which include minimum weight, frequency, compliance, and volume. In this paper, the problems related to the weight and frequency are presented, and this paper provides a few basic examples to discuss in a classroom.


Isogeometric, beam, bar, vibration, sizing optimization, frequency

How to Cite this Article?

Chandrasekhar, K.N.V., and Sahithi, N.S.S. (2018). A Step By Step Procedure to Perform Isogeometric Analysis of Beam and Bar Problems In Civil Engineering Including Sizing Optimisation of a Beam. i-manager’s Journal on Structural Engineering, 7(1), 13-27. https://doi.org/10.26634/jste.7.1.14283


[1]. Clough, R. W., & Penzien, J. (1993). Dynamics of Structures, McGraw Hill.
[2]. De Lorenzis, L. (2012). Some recent results and open issues on interface modeling in civil engineering structures. Materials and Structures, 45(4), 477-503.
[3]. Espath, L. F. R., Braun, A. L., & Awruch, A. M. (2011). An introduction to isogeometric analysis applied to solid mechanics. Mecánica Computacional, 30, 1955-1975.
[4]. Gondegaon, S., Ahmada,R., & Voruganti, H. K. (2014). Geometric Modeling for Isogeometric analysis. Proceedings of ICTACEM 2014 International Conference On Theoretical, Applied, Computational And Experimental Mechanics.
[5]. Gondegaon, S., & Voruganti, H. K. (2016). Static structural and modal analysis using Isogeometric analysis. Journal of Theoretical and Applied Mechanics, 46(4), 36- 75.
[6]. Hartmann, S., Benson, D. J., & Lorenz, D. (2011). About Isogeometric analysis and the new NURBS-based Finite th Elements in LS-DYNA. In 8 European LS-DYNA Users Conference, Strasbourg, France.
[7]. Hassani, B., Khanzadi, M., & Tavakkoli, S. M. (2012). An isogeometrical approach to structural topology optimization by optimality criteria. Structural and Multidisciplinary Optimization, 45(2), 223-233.
[8]. Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39-41), 4135- 4195.
[9]. Jockovic, M. (2016, April). Free vibration analysis of t h beam element using Isogeometric analysis. 4 I n t e r n a t i o n a l C o n f e r e n c e o n C o n t e m p o r a r y Achievements in Civil Engineering.
[10]. Lee, J. S., An, Y. N., & Chang, K. (2010). Optimum structural design based on isogeometric analysis method. In Strategic Technology (IFOST), 2010 International Forum on (pp. 377-381). IEEE.
[11]. Nagy, A. P., Abdalla, M. M., & Gürdal, Z. (2010). On the variational formulation of stress constraints in isogeometric design. Computer Methods in Applied Mechanics and Engineering, 199(41-44), 2687-2696.
[12]. Nguyen, V. P., Anitescu, C., Bordas, S. P., & Rabczuk, T. (2015). Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 117, 89-116.
[13]. Rauen, M., Machado, R. D., & Arndt, M. (2013, November). Isogeometric Analysis of Free Vibration of Bars. nd 22 International Congress of Mechanical Engineering.
[14]. Shah, M., & Katukam, R. (2015a). Stress Analysis without Meshing Iso-Geometric Analysis Finite Element Method (IGAFEM). Boeing Summer Internship Project.
[15]. Shah, M., & Katukam, R. (2015b). Stress Analysis without Meshing Isogeometric Analysis Finite Element Method. International Conference on Innovations in Computer Science and Technology, ICICSIT.

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

If you have access to this article please login to view the article or kindly login to purchase the article
Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.