Free vibration analysis of variable stiffness composite laminated thin skew plates using IGA

Document Type: Invited by Hamid Ahmadian

Authors

Aerospace research institute, Mahestan St., Tehran, Iran

10.22064/tava.2018.81281.1100

Abstract

A NURBS-based isogeometric finite element formulation is developed and adopted to the free vibration analysis of finite square and skew laminated plates. Variable stiffness plies are assumed due to implementation of curvilinear fiber
reinforcements. It is assumed due to employment of tow placement technology, in each ply of variable stiffness composite laminated plate the fiber reinforcement orientation angle is changed linearly with respect to longitudinal geometry coordinate. The classic plate theory is utilized for structural model description. The cubic NURBS basis functions are employed to approximate the geometry of the plate while simultaneously serve as the shape functions for solution field approximation in the analysis. To show the effectiveness and accuracy of the developed formulation, some representative
results are extracted and compared to similar items available in the literature. The effects of curvilinear fiber angles, different geometries and various end constraints are evaluated on the variable stiffness composite laminated skew panel behavior.

Highlights

  • Dynamic characteristics of variable stiffness laminated composite skew plates are extracted.
  • An Isogeometric Analysis formulation based on NURBS approximation functions is developed.
  • The first implementation of IGA in analyzing skew panels made from VSCL materials.
  • Cubic NURBS basis functions are employed to build both geometry and its numerical model.
  • The effects of skew angle on the natural frequencies are clarified for different constraint sets

Keywords

Main Subjects


[1] T.J.R. Hughes, 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) 4135-4195.

[2] Y. Bazilevs, V.M. Calo, T.J.R. Hughes, Y. Zhang, Isogeometric fluid-structure interaction: theory, algorithms, and computations, Computational mechanics, 43 (2008) 3-37.

[3] F. Auricchio, L.B. Da Veiga, C. Lovadina, A. Reali, The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 314-323.

[4] J.A. Cottrell, T.J.R. Hughes, A. Reali, Studies of refinement and continuity in isogeometric structural analysis, Computer methods in applied mechanics and engineering, 196 (2007) 4160-4183.

[5] S. Shojaee, N. Valizadeh, E. Izadpanah, J. Kiendl, Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric approach, Finite Elements Analysis Design, 61 (2012) 23-34.

[6] S. Shojaee, N. Valizadeh, E. Izadpanah, T. Bui, T.-V. Vu, Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method, Composite Structures, 94 (2012) 1677-1693.

[7] X.C. Qin, C.Y. Dong, F. Wang, X.Y. Qu, Static and dynamic analyses of isogeometric curvilinearly stiffened plates, Applied Mathematical Modelling, 45 (2017) 336-364.

[8] Y. Xue, G. Jin, H.u. Ding, M. Chen, Free vibration analysis of in-plane functionally graded plates using a refined plate theory and isogeometric approach, Composite Structures, 192 (2018) 193-205.

[9] K. Kozaczuk, Automated fiber placement systems overview, Prace Instytutu Lotnictwa, 4 (2016) 52-59.

[10] M.W. Hyer, R.F. Charette, Use of curvilinear fiber format in composite structure design, AIAA journal, 29 (1991) 1011-1015.

[11] Z. Gurdal, R. Olmedo, In-plane response of laminates with spatially varying fiber orientations-variable stiffness concept, AIAA journal, 31 (1993) 751-758.

[12] R. Olmedo, Z. Gurdal, Buckling response of laminates with spatially varying fiber orientations, in:  Proceedings of the 34th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials (SDM) Conference, La Jolla, CA 1993.

[13] H. Akhavan, P. Ribeiro, Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers, Composite Structures, 93 (2011) 3040-3047.

[14] S. Honda, Y. Narita, Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers, Composite Structures, 93 (2011) 902-910.

[15] S. Honda, Y. Narita, Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths, Journal of Sound and Vibration, 331 (2012) 180-191.

[16] J. Fazilati, Stability analysis of variable stiffness composite laminated plates with delamination using spline-FSM, Latin American Journal of Solids and Structures, 14 (2017) 528-543.

[17] J. Fazilati, Panel flutter of curvilinear composite laminated plates in the presence of delamination, Journal of Composite Materials, (2018).

[18] K.M. Liew, C.M. Wang, Vibration studies on skew plates: treatment of internal line supports, Computers & structures, 49 (1993) 941-951.

[19] R.K. Kapania, S. Singhvi, Free vibration analyses of generally laminated tapered skew plates, Composites Engineering, 2 (1992) 197-212.

[20] K. Hosokawa, Y. Terada, T. Sakata, Free vibrations of clamped symmetrically laminated skew plates, Journal of sound and vibration, 189 (1996) 525-533.

[21] C.M. Wang, K.K. Ang, L. Yang, E. Watanabe, Free vibration of skew sandwich plates with laminated facings, Journal of sound and vibration, 235 (2000) 317-340.

[22] P. Malekzadeh, A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates, Thin-walled structures, 45 (2007) 237-250.

[23] A. Houmat, Nonlinear free vibration analysis of variable stiffness symmetric skew laminates, European Journal of Mechanics-A/Solids, 50 (2015) 70-75.

[24] L. Piegl, W. Tiller, The NURBS Book

in, Springer, Berlin Heidelberg, 1995.

[25] V. Khalafi, J. Fazilati, Supersonic Flutter Analysis of Curvilinear Fiber Variable Stiffness Composite Laminated Plates, in:  5th International Conference on Composites: Characterization, Fabrication and Application, CCFA-5 2016.

[26] S. Wang, Vibration of thin skew fibre reinforced composite laminates, Journal of sound and vibration, 201 (1997) 335-352.

[27] W. Han, S.M. Dickinson, Free vibration of symmetrically laminated skew plates, Journal of sound and vibration, 208 (1997) 367-390.