## Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory.(English)Zbl 1278.74065

Summary: In the present paper, a new improved high-order theory is presented for biaxial buckling analysis of sandwich plates with soft orthotropic core. Third-order plate theory is used for face sheets and quadratic and cubic functions are assumed for transverse and in-plane displacements of the core, respectively. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. The nonlinear Von-Karman type relations are used to obtain strains. Also, transverse flexibility and transverse normal strain and stress of the orthotropic core are considered. The equations of motion and boundary conditions are derived by principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich plates under biaxial in-plane compressive loads is presented using Navier’s solution. Effect of geometrical parameters of face sheets and core and biaxial loads ratio are studied on the overall buckling of sandwich plates. Comparison of the present results with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed theory.

### MSC:

 74G60 Bifurcation and buckling 74K20 Plates 74E30 Composite and mixture properties

### Keywords:

biaxial buckling; sandwich plate; analytical solution
Full Text:

### References:

 [1] Ambartsumian, S.A., 1958. On a theory of bending of anisotropic plates, Investiia Akad Nauk SSSR, Ot Tekh Nauk. 4. [2] Brischetto, S.; Carrera, E.; Demasi, L., Improved bending analysis of sandwich plates using a zig-zag function, Compos struct., 89, 408-415, (2009) [3] Carrera, E., Nonlinear response of asymmetrically laminated plates in cylindrical bending, Aiaa j., 31, 1953-1957, (1993) [4] Carrera, E., Mixed layerwise models for multilayered plates analysis, Compos struct., 43, 57-70, (1998) [5] Carrera, E., A priori vs a posteriori evaluation of transverse stresses in multilayered orthotropic plates, Compos struct., 48, 245-260, (2000) [6] Carrera, E., Historical review of zig-zag theories for multilayered plates and shells, Trans. ASME appl. mech. rev., 56, 287-308, (2003) [7] Carrera, E., Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking, Arch. comput. meth eng. state art rev., 10, 215-296, (2003) · Zbl 1140.74549 [8] Carrera, E., On the use of murakami’s zig-zag function in the modeling of layered plates and shells, Comput. struct., 82, 541-554, (2004) [9] Carrera, E.; Brischetto, S., Analysis of thickness locking in classical, refined and mixed multilayered plate theories, Compos struct., 82, 549-562, (2008) [10] Carrera, E.; Ciuffreda, A., Bending of composites and sandwich plates subjecetd to localized lateral loadings: a comparison of various theories, Compos struct., 68, 185-202, (2005) [11] Carrera, E.; Demasi, L., Classical and advanced multilayered plate elements based upon PVD and RMVT. part 1: derivation of finite element matrices, Int. J. numer. methods eng., 55, 191-231, (2002) · Zbl 1098.74686 [12] Carrera, E.; Demasi, L., Two benchmarks to assess two-dimensional theories of sandwich composite plates, Aiaa j., 41, 1356-1362, (2003) [13] Chakrabarti, A.; Sheikh, A.H., Buckling of laminated sandwich plates subjected to partial edge compression, Int. J. mech. sci., 47, 418-436, (2005) · Zbl 1192.74120 [14] Cho, M.; Parmerter, R.R., An efficient higher order plate theory for laminated composites, Compos struct., 20, 113-123, (1992) [15] Dafedar, J.B.; Desai, Y.M.; Mufti, A.A., Stability of sandwich plates by mixed, higher-order analytical formulation, Int. J. solids struct., 40, 4501-4517, (2003) · Zbl 1054.74581 [16] Dawe, D.J.; Yuan, W.X., Overall and local buckling of sandwich plates with laminated faceplates. part I: analysis, Comput. methods appl. mech. eng., 190, 5197-5213, (2001) · Zbl 1006.74036 [17] Demasi, L., Refined multilayered plate elements based on the murakami zig-zag functions, Compos. struct., 70, 308-316, (2005) [18] Di Sciuva, M., Bending, vibration and bucking of simply-supported thick multilayered orthotropic plates: an evaluation of a new displacement model, J. sound vib., 105, 3, 425-442, (1986) [19] Di Sciuva, M.; Gherlone, M., A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation, Compos struct., 59, 419-431, (2003) [20] Frostig, Y., Buckling of sandwich panels with a transversely flexible core: high-order theory, Int. J. solids structures, 35, 183-204, (1998) · Zbl 0927.74025 [21] Ganapathi, M.; Patel, B.P.; Makhecha, D.P., Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory, Composites B., 35, 345-355, (2004) [22] Hohe, J.; Librescu, L.; Oh, S.Y., Dynamic buckling of flat and curved sandwich panels with transversely compressible core, Compos struct., 74, 10-24, (2006) [23] Icardi, U., Layerwise mixed element with sublaminates approximation and 3D zig-zag field, for analysis of local effects in laminated and sandwich composites, Int. J. numer. methods eng., 70, 94-125, (2007) · Zbl 1194.74414 [24] Ji, W.; Waas, A.M., Global and local buckling of sandwich beam, J. eng. mech., 133, 230-237, (2007) [25] Ji, W.; Waas, A.M., 2D elastic analysis of the sandwich panel buckling problem: benchmark solutions and accurate finite element formulations, Zamp, 61, 897-917, (2010) · Zbl 1273.74106 [26] Kant, T.; Swaminathan, K., Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory, Compos struct., 56, 329-344, (2002) [27] Kardomateas, G.A., Wrinkling of wide sandwich panels/beams with orthotropic phases by an elasticity approach, J. appl. mechanics, 72, 818-825, (2005) · Zbl 1111.74471 [28] Lekhnitskii, S.G., 1935. Strength calculation of composite beams. Vestnik inzhen i tekhnikov. 9. [29] Leotoing, L.; Drapier, S.; Vautrin, A., First applications of a novel unified models for global and local buckling of sandwich columns, Eur. J. mech. solids, 21, 683-701, (2002) · Zbl 1062.74015 [30] Li, X.; Liu, D., A laminate theory based on global – local superposition, Commun. numer. methods eng., 11, 633-641, (1995) · Zbl 0870.73043 [31] Matsunaga, H., Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory, Compos struct., 68, 4, 439-454, (2005) [32] Murakami, H., Laminated composite plate theory with improved in-plane response, Trans. ASME J. appl. mech., 53, 661-666, (1986) · Zbl 0597.73069 [33] Nayak, A.K.; Shenoi, R.A.; Moy, S.S.J., Dynamic response of composite sandwich plates subjected to initial stresses, Composites: part A, 37, 1189-1205, (2006) [34] Niu, K.; Talreja, R., Modeling of wrinkling in sandwich panels under compression, J. eng. mechanics, 125, 875-883, (1999) [35] Noor, A.K.; Peters, J.M.; Burton, W.S., Three-dimensional solutions for initially stressed structural sandwiches, J. eng. mechanics, ASCE, 120, 284-303, (1994) [36] Pagano, N.J., Exact solutions for rectangular bidirectional composites and sandwich plates, J. compos mater., 4, 20-34, (1970) [37] Pandit, M.K.; Singh, B.N.; Sheikh, A.H., Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, Thin-wall struct., 46, 1183-1191, (2008) [38] Rao, M.K.; Desai, Y.M., Analytical solutions for vibrations of laminated and sandwich plates using mixed theory, Compos struct., 63, 361-373, (2004) [39] Reddy, J.N., A refined nonlinear theory of plates with transverse shear deformation, Int. J. solids struct., 20, 881-896, (1987) · Zbl 0556.73064 [40] Reddy, J.N., Mechanics of laminated composite plates and shells, theory and analysis, (2004), CRC Press New York · Zbl 1075.74001 [41] Reissner, E., On a certain mixed variational theory and a proposed application, Int. J. numer. methods eng., 20, 1366-1368, (1984) · Zbl 0535.73017 [42] Ren, J.G., A new theory of laminated plates, Compos sci. technol., 26, 225-239, (1986) [43] Shariyat, M., A generalized high-order global – local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads, Compos struct., 92, 130-143, (2010) [44] Whitney, J.M., The effects of transverse shear deformation on the bending of laminated plates, J. compos mater., 3, 534-547, (1969) [45] Yuan, W.X.; Dawe, D.J., Overall and local buckling of sandwich plates with laminated faceplates, Part applications. comput. methods appl. mech. eng., 190, 5215-5231, (2001) · Zbl 1006.74036 [46] Zhen, W.; Wanji, C., Thermomechanical buckling of laminated composite and sandwich plates using global – local higher order theory, Int. J. mech. sci., 49, 712-721, (2007) [47] Zhen, W.; Wanji, C., A C^{0}-type higher-order theory for bending analysis of laminated composite and sandwich plates, Compos struct., 92, 653-661, (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.