Flexure Analysis of Laminated Composite and Sandwich Beams Using Timoshenko Beam Theory

Year 2018, Volume: 21 Issue: 3, 633 - 643, 01.09.2018

Armağan Karamanlı

https://doi.org/10.2339/politeknik.386958

Cited By: 2

Abstract

The static behaviour of laminated
composite and sandwich beams subjected to various sets of boundary conditions
is investigated by using the Timoshenko beam theory and the Symmetric Smoothed
Particle Hydrodynamics (SSPH) method. In order to solve the problem, a SSPH
code which consists of up to sixth order derivative terms in Taylor series
expansion is developed. The validation and convergence studies are performed by
solving symmetric and anti-symmetric cross-ply composite beam problems with
various boundary conditions and aspect ratios. The results in terms of mid-span
deflections, axial and shear stresses are compared with those from previous
studies to validate the accuracy of the present method. The effects of fiber
angle, lay-up and aspect ratio on mid-span displacements and stresses are
studied. At the same time, the problems not only for the convergence analysis
but also for the extensive analysis are also solved by using the
Euler-Bernoulli beam theory for comparison purposes. 

Keywords

Meshless method, composite beam, SSPH method, Timoshenko beam theory

References

• [1] Nguyen T.K., Nguyen N.D., Vo T.P., Thai H.T., “Trigonometric-series solution for analysis of laminated composite beams”, Compos Struct, 160:142-151, (2017).
• [2] Timoshenko S.P., Goodier J.C., “Theory of Elasticity”, McGraw-Hill Co. Inc., New York, 1970.
• [3] Wang C.M., Reddy J.N., Lee, K.H., “Shear Deformable Beams and Plates Relations with Classical Solutions”, Elsevier Science Ltd., Oxford 2000.
• [4] Kant T., Manjunath B.S., “Refined theories for composite and sandwich beams with C0 finite elements”, Comput Struct, 33(3):755–764, (1989).
• [5] Khdeir A.A., Reddy J.N., “An exact solution for the bending of thin and thick cross-ply laminated beams”, Compos Struct 37(2):195–203, (1997).
• [6] Soldatos K.P., Watson P., “A general theory for the accurate stress analysis of homogeneous and laminated composite beams”, Int J Solids Struct. 34(22): 2857– 2885, (1997).
• [7] Shi G., Lam K.Y., Tay T.E., “On efficient finite element modeling of composite beams and plates using higher- order theories and an accurate composite beam element”, Compos Struct, 41(2):159–165, (1998).
• [8] Zenkour A. M., “Transverse shear and normal deformation theory for bending analysis of laminated and sandwich elastic beams”, Mechanics of Composite Materials & Structures, 6(3): 267-283 (1999).
• [9] Karama M., Afaq K.S., Mistou S., “Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity”, Int J Solids Struct., 40(6):1525– 1546, (2003).
• [10] Murthy M.V.V.S., Mahapatra D.R., Badarinarayana K., Gopalakrishnan S., “A refined higher order finite element for asymmetric composite beams”, Compos Struct, 67(1):27–35, (2005).
• [11] Vidal P., Polit O., “A family of sinus finite elements for the analysis of rectangular laminated beams”, Compos Struct, 84(1):56–72, (2008).
• [12] Aguiar R.M., Moleiro F., Soares C.M.M., “Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections”, Compos Struct, 94 (2):601–616, (2012).
• [13] Nallim L.G., Oller S., Onate E., Flores F.G., “A hierarchical finite element for composite laminated beams using a refined zigzag theory”, Compos Struct, 163:168–184, (2017).
• [14] Vo T.P., Thai H.T., Nguyen T.K., Lanc D., Karamanli A., “Flexural analysis of laminated composite and sandwich beams using a four-unknown shear and normal deformation theory”, Compos Struct, 176:388-397, (2017).
• [15] Donning B.M., Liu W.K., “Meshless methods for shear-deformable beams and plates”, Computer Methods in Applied Mechanics and Engineering, 152:47-71, (1998).
• [16] Gu Y.T., Liu G.R., “A local point interpolation method for static and dynamic analysis of thin beams”, Computer Methods in Applied Mechanics and Engineering, 190(42):5515-5528, (2001).
• [17] Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S., “Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates” Compos Struct, 66:287-293, (2004).
• [18] Ferreira A.J.M., Fasshauer G.E., “Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method”, Computer Methods in Applied Mechanics and Engineering, 196:134-146, (2006).
• [19] Moosavi M.R., Delfanian F., Khelil A., “The orthogonal meshless finite volume method for solving Euler– Bernoulli beam and thin plate problems”, Finite Elements in Analysis and Design, 49:923-932, (2011).
• [20] Wu C.P., Yang S.W., Wang Y.M., Hu H.T., “A meshless collocation method for the plane problems of functionally graded material beams and plates using the DRK interpolation”, Mechanics Research Communications, 38:471-476, (2011).
• [21] Roque C.M.C., Figaldo D.S., Ferreira A.J.M., Reddy J.N., “A study of a microstructure-dependent composite lamminated Timoshenko beam using a modified couple stress theory and a meshless method”, Compos Struct, 96:532-537, (2013).
• [22] Karamanli A., “Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method”, Compos Struct, 160:653-669, (2017).
• [23] Karamanli A., “Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory”, Compos Struct, 160:653-669, (2017).
• [24] Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S., “Radial basis functions and higher order shear deformation theories in the analysis of laminated composite beams and plates”, Compos Struct, 66:287-293, (2004).
• [25] Ferreira A.J.M., “Thick composite beam analysis using a global meshless approximation based on radial basis functions”, Mech Adv Mater Struct, 10:271–84, (2003).
• [26] Roque C.M.C., Fidalgo D.S., Ferreira A.J.M., Reddy J.N., “A study of a microstructure dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method”, Compos Struct, 96:532-537, (2013).
• [27] Liew K.M., Lim H.K., Tan M.J., He X.Q., “Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method”, Computational Mechanics, 29:486-497, (2002).