i-manager Publications

Cubic Basis Splines to Perform Topology Optimization of Laminated Composite Regular Cylindrical and Elliptical and Hyperbolic Thin Shell Structures using Inverse Buckling Formulation

K. N. V. Chandrasekhar*, V. Bhikshma**

* Mahaveer Institute of Science and Technology, Vyasapuri, Keshavagiri, Hyderabad, Telangana, India.

** University College of Engineering, Osmania University, Amberpet, Hyderabad, Telangana, India.

Periodicity:March - May'2022
DOI : https://doi.org/10.26634/jce.12.2.18856

Abstract

Laminated composites are increasingly being used in civil engineering structures. The light weight coupled with high strength has paved the way for using laminated composites in important structures such as bridges and roof shells. Isogeometric analysis using splines has been of immense interest to a structural engineer to model and analyse the structure in three dimensions. The present study is focused on using basis splines to perform topology optimisation of laminated composite thin shell structures. Three different shell have been considered elliptical, cylindrical and hyperbolic structures having simply supports on all four edges. Two different lamina have been considered 0/90/0/90, 45- 45/45/-45 for each type of simply supported shells. Inverse buckling formulation with the inverse of the buckling load is taken as the objective function to perform topology optimisation. Strength and stability criteria are included in the analysis. Deformed profile of laminates is presented here for each case of lamina using isogeometric analysis. The results of cubic basis spline based analysis are in good agreement with the results given in the literature obtained using finite element analysis.

Keywords

Thin Shell, Cubic Basis Splines, Laminated Composites, Topology Optimisation, Inverse Buckling.

How to Cite this Article?

Chandrasekhar, K. N. V., and Bhikshma, V. (2022). Cubic Basis Splines to Perform Topology Optimization of Laminated Composite Regular Cylindrical and Elliptical and Hyperbolic Thin Shell Structures using Inverse Buckling Formulation. i-manager’s Journal on Civil Engineering, 12(2), 41-52. https://doi.org/10.26634/jce.12.2.18856

References

[1]. Behshad, A., & Ghasemi, M. R. (2013). Isogeometricbased modeling and analysis of laminated composite plates under transverse loading. Journal of Solid Mechanics, 5(4), 380-390.

[2]. Behshad, A., & Ghasemi, M. R. (2014). Nurbs-igabased modelling: Analysis and optimization of laminated plates. Tehnički Vjesnik, 21(4), 789-797.

[3]. Bendsøe, M. P., & Kikuchi, N. (1988). Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2

[4]. Benson, D. J., Bazilevs, Y., Hsu, M. C., & Hughes, T. (2011). A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering, 200(13-16), 1367-1378. https://doi.org/10.1016/j.cma.2010.12.003

[5]. Camp, C. V., Pezeshk, S., & Hansson, H. (2003). Flexural design of reinforced concrete frames using a genetic algorithm. Journal of Structural Engineering, 129(1), 105-115. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:1(105)

[6]. Chandrasekhar, K. N. V. Sahithi, N. S. S., & Rao, M. (2017). A Detailed Stepwise Procedure to Perform Isogeometric Analysis of a Two Dimensional Continuum Plate Structure-II. Journal of Aerospace Engineering & Technology, 7(3), 19–37.

[7]. Chandrasekhar, K. N. V., Bhikshma, V., & Reddy, K. U. B. (2022). Topology optimisation of laminated composite shellsusing Optimality Criteria. Journal of Applied and Computational Mechanics, 8(2), 405-415. https://doi.org/10.22055/JACM.2019.31296.1858

[8]. Cottrell, J. A., Hughes, T. J., & Bazilevs, Y. (2009). Isogeometric Analysis: Toward Integration of CAD and FEA. John Wiley & Sons.

[9]. Gao, J., Gao, L., Luo, Z., & Li, P. (2019). Isogeometric topology optimization for continuum structures using density distribution function. International Journal for Numerical Methods in Engineering, 119(10), 991-1017. https://doi.org/10.1002/nme.6081

[10]. Gebremedhen, H. S., Woldemicahel, D. E., & Hashim, F. M. (2019). Three-dimensional stress-based topology optimization using SIMP method. International Journal for Simulation and Multidisciplinary Design Optimization, 10. https://doi.org/10.1051/smdo/2019005

[11]. Hassani, B., Khanzadi, M., & Tavakkoli, S. M. (2012). An isogeometrical approach to structural topology optimization by optimality criteria. Structural and Multidisciplinar y Optimization, 45(2), 223-233. https://doi.org/10.1007/s00158-011-0680-5

[12]. Hoang, C. T., Rabczuk, T., & Nguyen-Xuan, H. (2013). A rotation-free isogeometric analysis for composite sandwich thin plates. International Journal of Composite Materials, 3(6A), 10-18.

[13]. 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. https://doi.org/10.1016/j.cma.2004.10.008

[14]. Hughes, T. J., Reali, A., & Sangalli, G. (2010). Efficient quadrature for NURBS-based isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 199(5-8), 301-313. https://doi.org/10.1016/j.cma.2008.12.004

[15]. Jeong, S. H., Park, S. H., Choi, D. H., & Yoon, G. H. (2012). Topology optimization considering static failure theories for ductile and brittle materials. Computers & structures, 110, 116-132. https://doi.org/10.1016/j.compstruc.2012.07.007

[16]. Kant, T., & Swaminathan, K. (2001). Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite Structures, 53(1), 73-85. https://doi.org/10.1016/S0263-8223(00)00180-X

[17]. Kant, T., & Swaminathan, K. (2002). Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Composite Structures, 56(4), 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X

[18]. Kazemi, H. S., Tavakkoli, S. M., & Naderi, R. (2016). Isogeometric topology optimization of structures considering weight minimization and local stress constraints. International Journal of Optimization in Civil Engineering, 6(2), 303-317.

[19]. Khani, A., Abdalla, M. M., & Gürdal, Z. (2012). Circumferential stiffness tailoring of general cross section cylinders for maximum buckling load with strength constraints. Composite Structures, 94(9), 2851-2860. https://doi.org/10.1016/j.compstruct.2012.04.018

[20]. Liu, H., Yang, D., Hao, P., & Zhu, X. (2018). Isogeometric analysis based topology optimization design with global stress constraint. Computer Methods in Applied Mechanics and Engineering, 342, 625-652. https://doi.org/10.1016/j.cma.2018.08.013

[21]. Luo, Y., & Kang, Z. (2012). Topology optimization of continuum structures with Drucker–Prager yield stress constraints. Computers & Structures, 90, 65-75. https://doi.org/10.1016/j.compstruc.2011.10.008

[22]. Nguyen, H. X., Atroshchenko, E., Nguyen-Xuan, H., & Vo, T. P. (2017). Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory. Computers & Structures, 193, 110-127. https://doi.org/10.1016/j.compstruc.2017.07.017

[23]. Nguyen-Van, H., Mai-Duy, N., Karunasena, W., & Tran-Cong, T. (2011). Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations. Computers & Structures, 89(7-8), 612-625. https://doi.org/10.1016/j.compstruc.2011.01.005

[24]. Panahandeh-Shahraki, D., & Mirdamadi, H. R. (2014). Shell–tensionless foundation interaction and nonlinear thermoelastic stability analysis of laminated composite cylindrical panels. Acta Mechanica, 225(1), 131-149.https://doi.org/10.1007/s00707-013-0943-x

[25]. Ram, K. S., & Sinha, P. K. (1991). Hygrothermal effects on the bending characteristics of laminated composite plates. Computers & Structures, 40(4), 1009-1015. https://doi.org/10.1016/0045-7949(91)90332-G

[26]. Sahithi, N. S. S., & Chandrasekhar, K. N. V. (2019). Isogeometric topology optimization of continuum structures using an evolutionary algorithm. Journal of Applied and Computational Mechanics, 5(2), 414-440. https://doi.org/10.22055/JACM.2018.26398.1330

[27]. Somireddy, M., & Rajagopal, A. (2014). Meshless natural neighbor Galerkin method for the bending and vibration analysis of composite plates. Composite Structures, 111, 138-146. https://doi.org/10.1016/j.compstruct.2013.12.023

[28]. Tiwari, N. (2022). Introduction to Composites. Indian Institutes of Technology, Kanpur, National Programme on Technology Enhanced Learning.

[29]. Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O. A., Rabczuk, T., Bui, T. Q., & Bordas, S. P. (2013). NURBSbased finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter. Composite Structures, 99, 309-326. https://doi.org/10.1016/j.compstruct.2012.11.008

[30]. Wang, X., Zhu, X., & Hu, P. (2015). Isogeometric finite element method for buckling analysis of generally laminated composite beams with different boundary conditions. International Journal of Mechanical Sciences, 104, 190-199. https://doi.org/10.1016/j.ijmecsci.2015.10.008

Cubic Basis Splines to Perform Topology Optimization of Laminated Composite Regular Cylindrical and Elliptical and Hyperbolic Thin Shell Structures using Inverse Buckling Formulation

Abstract

Keywords

How to Cite this Article?

References

If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Options for accessing this content:

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