Elastic Analysis of Multi-Layer Plates with Arbitrary Geometry and Boundary Conditions Using Layerwise Mixed Formulation

Document Type : پژوهشی

Authors

University of Hormozgan

Abstract

In this paper, a three-dimensional solution with mixed layerwise formulation is presented for multi-layer composite plates with arbitrary geometry and boundary conditions.  In this study, the displacement field the out-of plane stresses are considered as a sum of a series of functions with unknown coefficients. The boundary conditions and the continuity of the displacement field and the traction stresses between the layers are exactly satisfied. Equilibrium and compatibility equations are also applied using the Reissner's variational principle. The results show that the mixed formulation has faster convergence than displacement based formulation, and provides more accurate values of interlaminar stresses.

Keywords


[1] Carrera E., "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Archives of Computational Methods in Engineering, Vol. 9, No. 2, pp. 87–140, (2002).
[2] Reddy J.N., Robbins Jr D.H.,"Theories and computational models for composite laminates", Applied Mechanics Reviews, Vol. 47, No. 6, pp. 147–69, (1994).
[3] Noor A.K., Burton W.S., "Assessment of shear deformation theories for multilayered composite plates", Applied Mechanics Reviews, Vol. 42, No. 1, pp. 1-13, (1989).
[4] Carrera E., "Historical review of zig-zag theories for multilayered plates and shells", Applied Mechanics Reviews, Vol. 56, No. 3, pp. 287-308, (2003).
[5] Reddy J.N., "Mechanics of laminated composite plates and shells – theory and analysis", CRC Press, Boca Raton, (2004).
[6] Reddy J.N., "An introduction to the finite element method", McGraw-Hill, New York, (2006).
[7] Washizu K., "Variational methods in elasticity and plasticity", Pergamon Press, New York,
(1982).
[8] Reddy J.N., "Energy principles and variational methods in applied mechanics", John Wiley & Sons, New York, (2002).
[9] Reissner E., "On a variational theorem in elasticity", Journal of Mathematical Physics, Vol. 29, pp. 90–95, (1950).
[10] Mindlin R.D., "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", Journal of Applied Mechanics, Vol. 18, pp. 31–38, (1951).
[11] Reddy J.N., "A generalization of two-dimensional theories of laminated plates", Communications in Applied Numerical Methods, Vol. 3, pp. 173–180, (1987).
[12] Cho M. and Parmerter R.R., "An efficient higher order plate theory for laminated composites", Composite Structures, Vol. 20, pp. 113–123, (1992).
[13] Cho M. and Parmerter R.R., "Efficient higher order composite plate theory for general lamination configurations", AIAA Journal, Vol. 31, pp. 1299–1306, (1993).
[14] Shodja H.M. and Kamali M.T., "Three-dimensional analysis of piezocomposite plates with arbitrary geometry and boundary conditions", International Journal of Solids and Structures, Vol. 40, pp. 4837–4858, (2003).
[15] Kamali M.T. and Shodja H.M., "A semi-analytical method for piezocomposite structures with arbitrary interfaces", Computer Methods in Applied Mechanics and Engineering, Vol. 194, pp. 4588–4604, (2005).
[16] Kamali M.T. and Pourmoghaddam S., "Three-dimensional analysis of multi-layer composite plates of arbitrary shape and boundary conditions with shear slip interfaces", Mechanics of Advanced Materials and Structures, Vol. 23, pp. 481–493, (2016).
[17] Moleiro F., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation", Composite Structures, Vol. 119, pp. 134–149, (2015).
[18] Moleiro F., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "A layerwise mixed least-squares finite element model for static analysis of multilayered composite plates", Computers & Structures, Vol. 89, pp. 1730–1742, (2011).
[19] Moleiro F., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates", Composite Structures, Vol. 92, pp. 2328-2338, (2010).
[20] Moleiro F., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Mixed least-squares finite element models for static and free vibration analysis of laminated composite plates", Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 1848-1856, (2009).
[21] Moleiro F., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Mixed least-squares finite element model for the static analysis of laminated composite plates", Computers & Structures, Vol. 86, pp. 826-838, (2008).
[22] Garcia Lage R., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Analysis of adaptive plate structures by mixed layerwise finite elements", Composite Structures, Vol. 66, pp. 269-276, (2004).
[23] Garcia Lage R., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Analysis of laminated adaptive plate structures using layerwise finite element models", Computers & Structures, Vol. 82, pp. 1939-1959, (2004).
[24] Garcia Lage R., Mota Soares C.M., Mota Soares C.A. and Reddy, J.N., "Modelling of piezolaminated plates using layerwise mixed finite elements", Computers & Structures, Vol. 82, pp. 1849-1863, (2004).
[25] Carrera E., "Evaluation of layerwise mixed theories for laminated plates analysis," AIAA Journal, Vol. 36, pp. 830-839, (1986).
[26] Reissner E., "On a certain mixed variational theory and proposed applications," International Journal of Numerical Methods in Engineering, Vol. 20, pp. 1366-1368, (1984).
[27] Reissner E., "On a mixed variational theorem and on a shear deformable plate theory," International Journal of Numerical Methods in Engineering, Vol. 23, pp. 193-198, (1986).
[28] Pagano N.J., "Exact solutions for rectangular bidirectional composites and sandwich plates", Journal of Composite Materials, Vol. 4, pp. 20-34, (1970).
CAPTCHA Image