Bending analysis of composite and sandwich beams using Ritz method
Abstract
In the present paper, the bending behaviour of 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) are investigated by using the Timoshenko beam theory and the Ritz method. In order to solve the problem, the shape functions for axial, transverse deflections and the rotation of the cross-section are presented in polynomial forms. 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 by adding auxiliary functions to the shape functions. 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 study. The effects of fiber angle, lay-up and aspect ratio on displacements and stresses are studied.
Keywords
References
- [1] Nguyen TK, Nguyen ND, Vo TP, Thai HT. Trigonometric-series solution for analysis of laminated composite beams. Compos Struct 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. Comput Struct 1989; 33(3):755–764.
- [5] Khdeir AA, Reddy JN. An exact solution for the bending of thin and thick cross-ply laminated beams. Compos Struct 1997; 37(2):195–203.
- [6] Soldatos KP, Watson P. A general theory for the accurate stress analysis of homogeneous and laminated composite beams. Int J Solids Struct 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. Int J Solids Struct 2003; 40(6):1525–1546. [10] Murthy MVVS, Mahapatra DR, Badarinarayana K, Gopalakrishnan S. A refined higher order finite element for asymmetric composite beams. Compos Struct 2005; 67(1):27–35.
- [11] Vidal P, Polit O. A family of sinus finite elements for the analysis of rectangular laminated beams. Compos Struct 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. Compos Struct 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. Compos Struct 2017; 163:168–184.