Static Analysis of Reddy-Bickford Composite and Sandwich Beams via Ritz Method

This paper is dedicated to present static behaviour of Reddy-Bickford laminated composite and sandwich beams subjected to various sets of boundary conditions which are simply supported (SS), clamped-simply supported (CS), clamped-clamped (CC) and clamped-free (CF) by using Ritz method. An analytical solution based on polynomial series including auixiliary functions which are used to satisfy the boundary conditions is developed to solve the studied problem. The polynomial shape functions for axial, transverse deflections and the rotation of the crosssection are presented. The validation and convergence studies are performed by solving symmetric and antisymmetric cross-ply composite beam problems with various boundary conditions and aspect ratios. The numerical results in terms of mid-span deflections, axial and shear stresses are obtained to make comparison with previous studies and to investigate the accuracy of the present study. The effects of fiber angle, lay-up and aspect ratio on displacements and stresses are studied. The static response of the various laminated composite sandwich structures which have symmetric lay-up based on the various boundary conditions, fiber angles and thickness ratios is also studied. It is found that the polynomial series with auxiliary functions can be used for the static analysis of the composite and sandwich beams via Ritz method

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1. Nguyen, TK, Nguyen, ND, Vo, TP, Thai HT, Trigonometric-series solution for analysis of laminated composite beams, Composite Structures, 2017,160, 142-151.
2. Timoshenko, SP, Goodier, JC, Theory of Elasticity, New York, NY, USA: McGraw-Hill Co. Inc., 1970.
3. Wang, CM, Reddy, JN, Lee, KH, Shear Deformable Beams and Plates Relations with Classical Solutions. Oxford: Elsevier Science Ltd., 2000.
4. Kant, T, Manjunath, BS, Refined theories for composite and sandwich beams with C0 finite elements, Composite Structures, 1989, 33(3), 755–764.
5. Khdeir, AA, Reddy, JN, An exact solution for the bending of thin and thick cross-ply laminated beams, Composite Structures 1997, 37(2), 195–203.
6. Soldatos, KP, Watson, P, A general theory for the accurate stress analysis of homogeneous and laminated composite beams, International Journal of Solids and Structures, 1997, 34(22), 2857–2885.
7. Shi G, Lam, KY, Tay, TE, On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element, Compos Struct, 1998, 41(2),159–165.
8. Zenkour, AM, Transverse shear and normal deformation theory for bending analysis of laminated and sandwich elastic beams, Mechanics of Composite Materials & Structures, 1999, 6(3), 267-283.
9. Karama, M, Afaq, KS, Mistou, S, Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity, International Journal of Solids and Structures, 2003, 40(6),1525–1546.
10. Murthy, MVVS, Mahapatra, DR, Badarinarayana, K, Gopalakrishnan, S, A refined higher order finite element for asymmetric composite beams, Composite Structures, 2005, 67(1), 27–35.
11. Vidal, P, Polit, O, A family of sinus finite elements for the analysis of rectangular laminated beams, Composite Structures, 2008, 84(1),56- 72.
12. Aguiar, RM, Moleiro, F, Soares CMM, Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections, Composite Structures, 2012, 94 (2),601–616.
13. Nallim, LG, Oller, S, Onate, E, Flores, FG, A hierarchical finite element for composite laminated beams using a refined zigzag theory, Composite Structures, 2017, 163,168–184.
14. Vo, TP, Thai, HT, Nguyen, TK, Lanc, D, Karamanli, A, Flexural analysis of laminated composite and sandwich beams using a four-unknown shear and normal deformation theory, Composite Structures, 2017, 176,388-397.
15. Yuan, FG, Miller, RE, A higher order finite element for laminated beams, Composite Structures, 1990, 14(2), 125–150.
16. Yu, H, A higher-order finite element for analysis of composite laminated structures, Composite Structures, 1994, 28(4), 375–383.
17. Chandrashekhara, K, Bangera, K, Free vibration of composite beams using a refined shear flexible beam element, Composite Structures, 1992, 43(4), 719–727.
18. Marur, S, Kant, T, Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modelling, Journal of Sound and Vibration, 1996, 194(3), 337–351.
19. Karama, M, Harb, BA, Mistou, S, Caperaa, S, Bending, buckling and free vibration of laminated composite with a transverse shear stress continuity model, Composites Part B: Engineering, 1998, 29(3), 223– 234.
20. Shi G, Lam K, Tay T, On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element, Composite Structures, 1998, 41(2), 159- 165.
21. Shi, G, Lam, K, Finite element vibration analysis of composite beams based on higher-order beam theory, Journal of Sound and Vibration, 1999, 219(4),707–721.
22. Murthy, M, Mahapatra, DR, Badarinarayana K, Gopalakrishnan S, A refined higher order finite element for asymmetric composite beams, Composite Structures, 2005, 67(1), 27–35.
23. Subramanian, P, Dynamic analysis of laminated composite beams using higher order theories and finite elements, Composite Structures, 2006, 73 (3),342–353.
24. Vidal, P, Polit, O, A family of sinus finite elements for the analysis of rectangular laminated beams, Composite Structures, 2008, 84(1), 56– 72.
25. Vo, TP, Thai, H-T, Static behavior of composite beams using various refined shear deformation theories, Composite Structures, 2012, 94(8), 2513–2522.
26. Vo, TP, Thai, H-T, Vibration and buckling of composite beams using refined shear deformation theory, International Journal of Mechanical Sciences, 2012, 62(1), 67–76.
27. Mantari, J, Canales, F, Finite element formulation of laminated beams with capability to model the thickness expansion, Composites Part B: Engineering, 2016, 101, 107–115.
28. Li, J, Wu, Z, Kong, X, Li, X, Wu, W, Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups, Composite Structures, 2014, 108, 767–778.
29. Ferreira, AJM, Roque, CMC, Martins, PALS, Radial basis functions and higher order shear deformation theories in the analysis of laminated composite beams and plates, Composite Structures, 2004, 66, 287-293.
30. Ferreira, AJM, Thick composite beam analysis using a global meshless approximation based on radial basis functions, Mechanics of Advanced Materials and Structures, 2003, 10, 271–284.
31. Roque, CMC, Fidalgo, DS, Ferreira, AJM, Reddy, JN, A study of a microstructure dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method, Composite Structures, 2013, 96, 532-537.
32. Liew, KM, Lim, HK, Tan, MJ, He, XQ, Analysis of laminated composite beams and plates with piezoelectric patches using the elementfree Galerkin method, Computational Mechanics, 2002, 29, 486-497.
33. Karamanli, A, Flexure Analysis of Laminated Composite and Sandwich Beams Using Timoshenko Beam Theory, (Accepted for publication),
34. [34] Matsunaga H, Vibration and buckling of multilayered composite beams according to higher order deformation theories, Journal of Sound and Vibration, 2001, 246 (1), 47–62,
35. Mantari,J, Canales, F, A unified quasi-3D HSDT for the bending analysis of laminated beams, Aerospace Science and Technology, 2016, 54, 267–275.
36. Kant, T, Marur, S, Rao, G, Analytical solution to the dynamic analysis of laminated beams using higher order refined theory, Composite Structures, 1997,40 (1),1–9,
37. Aydogdu, M, Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method, International Journal of Mechanical Sciences, 2005, 47(11), 1740–1755.
38. Aydogdu, M, Buckling analysis of cross-ply laminated beams with general boundary conditions by ritz method, Composite Science and Technology, 2006, 66(10), 1248–1255.
39. Aydogdu, M, Free vibration analysis of angle-ply laminated beams with general boundary conditions, Journal of Reinforced Plastics and Composites, 2006, 25(15), 1571–1583.
40. Mantari, J, Canales, F, Free vibration and buckling of laminated beams via hybrid Ritz solution for various penalized boundary conditions, Composite Structures, 2016, 152, 306–315.
41. Karamanli, A, Bending analysis of composite and sandwich beams using Ritz method, (Accepted for publication).
42. Rehfield, LW, Valisetty, RR, A Comprehensive Theory for Planar Bending of Composite Laminates, Computures and Structures, 1983, 15, 441-447.
43. Mau, ST, A Refined Laminate Plate Theory, Journal of Applied Mechanics, 1973, 40, 606-607.
44. Walts, TL, Vinson, JR, Interlaminar Stress in Laminated Cylindirical Shells of Composite Materials, AIAA Journal, 1976, 14, 1213-1218.