Computational Models for the Static and Dynamic Analyses of Laminated Composite Plates

Abstract:

The present study is to assess the accuracy of the few computational models based on various shear deformation theories in predicting the static and dynamic behaviour of antisymmetric angle-ply laminated composite plates. In the present investigation two higher order refined computational models incorporate the laminate deformations which account for the effects of both transverse shear and normal deformation and a non-linear variation of in-plane displacements are used. In addition to above, few higher order models and the first order model developed by other investigators and available in the literature are also considered for the evaluation. The equations of equilibrium are obtained using Principle of Minimum Potential Energy and the equations of motion using Hamilton’s principle. Solutions are obtained in closed-form using Navier’s solution technique. The solutions of the static analysis are obtained by solving the boundary value problem and the natural frequencies are obtained by solving the eigenvalue problem. The accuracy of the solutions obtained from the different models are established by comparing the results with the solutions wherever available in the literature. Results generated independently using the various models are presented for antisymmetric angle ply composite plates which will serve as benchmark solutions for future investigations.

• Periodical: Advanced Materials Research (Volumes 383-390)
• Pages: 5381-5386
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.383-390.5381
• Online since: November 2011
• Authors: S. Shantharam Patil
• Keywords: Analytical Solution, Angle-Ply Plates, Composite Laminate, Computational Model, Higher Order Theory, Shear Deformation

References

[1] Noor, A. K. and Burton, W.S., Assessment of shear deformation theories for multilayered composite plates, Appl. Mech. Rev. 42(1), 1-13 (1989).

DOI: 10.1115/1.3152418

[2] Kant, T. and Swaminathan, K., Estimation of transverse/interlaminar stresses in laminated composites - A selective review and survey of current developments, Compos. Struct. 49(1), 65-75 (2001).

DOI: 10.1016/s0263-8223(99)00126-9

[3] Kant, T., Numerical analysis of thick plates, Comput. Methods in Appl. Mech. and Engg. 31, 1-18 (1982).

[4] Pandya, B. N. and Kant, T., A refined higher order generally orthotropic C° plate bending element, Comput. and Struct. 28, 119-133 (1988).

DOI: 10.1016/0045-7949(88)90031-4

[5] Pandya, B. N. and Kant, T., Finite element stress analysis of laminated composites using higher order displacement model, Compos. Sci. and Technol. 32, 137-155 (1988).

DOI: 10.1016/0266-3538(88)90003-6

[6] Kant, T. and Manjunatha, B. S., An unsymmetric FRC laminate Co finite element model with 12 degrees of freedom per node, Engg. Comput. 5(3), 300-308 (1988).

DOI: 10.1108/eb023749

[7] Kant, T. and Swaminathan, K., Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher order refined theory, Compos. Struct. 53(1), 73-85 (2001).

DOI: 10.1016/s0263-8223(00)00180-x

[8] Kant, T. and Swaminathan, K., Analytical solutions for static analysis of laminated composite and sandwich plates based on a higher order refined theory, Compos. Struct. 56(4), 329-344 (2002).

DOI: 10.1016/s0263-8223(02)00017-x

[9] Swaminathan, K. and Patil, S. S., Higher order refined computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle ply plates – analytical solutions, Compos. Struct. 80(4), 595-608 (2007).

DOI: 10.1016/j.compstruct.2006.07.006

[10] Swaminathan, K. and Patil, S. S., Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle ply plates, Compos. Struct. 82(2), 209-216 (2008).

DOI: 10.1016/j.compstruct.2007.01.001

[11] Swaminathan, K. and Patil, S. S., Higher order refined computational models for the free vibration analysis of antisymmetric angle ply plates, J. of Reinf. Plast. and Compos. 27(5), 541-553 (2008).

DOI: 10.1177/0731684407084125

[12] Reddy, J. N., A simple higher order theory for laminated composite plates, ASME J. of Appl. Mech., 51, 745-752 (1984).

DOI: 10.1115/1.3167719

[13] Senthilnathan, N. R., Lim, K. H., Lee, K. H. and Chow, S. T., Buckling of shear-deformable plates, AIAA J. 25(9), 1268-1271 (1987).

DOI: 10.2514/3.48742

[14] Whitney, J. M. and Pagano, N. J., Shear deformation in heterogeneous anisotropic plates, ASME J. of Appl. Mech. 37(4), 1031-1036 (1970).

DOI: 10.1115/1.3408654

[15] Ren, J. G., Bending, vibration and buckling of laminated plates, In: Cheremisinoff NP, editor. Handbook of Ceramics and Composites, New York: Marcel Dekker; 1, 413-450 (1990).

DOI: 10.1201/9781003210085-14

[16] Reddy, J. N. and Phan, N. D., Stability and vibration of isotropic, orthotropic and laminated plates according to higher-order shear deformation theory, J. of Sound and Vib. 98(2), 157-170 (1985).

DOI: 10.1016/0022-460x(85)90383-9