Verma, Vipin K.; Singh, B. N. Thermal buckling of laminated composite plates with random geometric and material properties. (English) Zbl 1271.74105 Int. J. Struct. Stab. Dyn. 9, No. 2, 187-211 (2009). Summary: In this paper, a C\(^\circ\) finite element has been employed for deriving an eigenvalue problem using higher order shear deformation theory. The uncertain material and geometric properties are modeled as basic random variables. A mean-centered first order perturbation technique is used to find the mean and standard derivation of the buckling temperature of laminated composite plates – subjected to a uniform temperature rise – with random material and geometric properties. The effects of the modulus ratio, fiber orientation, length-to-thickness ratio, aspect ratio and various boundary conditions on the critical temperature are examined. It is found that small variations in material and geometric properties of the composite plate significantly affect the buckling temperature of the laminated composite plate. The results have been validated with independent Monte Carlo simulation and those available in the literature. Cited in 6 Documents MSC: 74G60 Bifurcation and buckling 74K20 Plates 74F05 Thermal effects in solid mechanics 74E30 Composite and mixture properties 74E35 Random structure in solid mechanics Keywords:finite element method; composite laminated plate; thermal buckling; random variables; standard deviation PDFBibTeX XMLCite \textit{V. K. Verma} and \textit{B. N. Singh}, Int. J. Struct. Stab. Dyn. 9, No. 2, 187--211 (2009; Zbl 1271.74105) Full Text: DOI References: [1] DOI: 10.1115/1.3256386 · doi:10.1115/1.3256386 [2] DOI: 10.1016/0045-7949(89)90413-6 · Zbl 0704.73051 · doi:10.1016/0045-7949(89)90413-6 [3] Chang J. S., Comput. Struct. 37 pp 925– [4] DOI: 10.1016/S0045-7949(00)00005-5 · doi:10.1016/S0045-7949(00)00005-5 [5] DOI: 10.1061/(ASCE)0893-1321(1999)12:1(1) · doi:10.1061/(ASCE)0893-1321(1999)12:1(1) [6] DOI: 10.1016/j.compstruct.2004.04.003 · doi:10.1016/j.compstruct.2004.04.003 [7] DOI: 10.1016/j.compstruct.2003.10.018 · doi:10.1016/j.compstruct.2003.10.018 [8] DOI: 10.1016/S0263-8223(99)00127-0 · doi:10.1016/S0263-8223(99)00127-0 [9] DOI: 10.1016/0045-7949(91)90176-M · Zbl 0850.73302 · doi:10.1016/0045-7949(91)90176-M [10] DOI: 10.1016/0045-7949(94)90166-X · Zbl 0875.73064 · doi:10.1016/0045-7949(94)90166-X [11] Nakagiri S., Compos. Struct. 14 pp 9– [12] DOI: 10.1016/S0263-8223(01)00065-4 · doi:10.1016/S0263-8223(01)00065-4 [13] DOI: 10.1016/0266-3538(94)90129-5 · doi:10.1016/0266-3538(94)90129-5 [14] Chen S., Compos. Struct. 43 pp 247– [15] Yadav D., Compos. Struct. 41 pp 385– [16] Graham L. L., ASCE J. Eng. Mech. 12 pp 91– [17] DOI: 10.1061/(ASCE)0733-9399(2001)127:9(873) · doi:10.1061/(ASCE)0733-9399(2001)127:9(873) [18] DOI: 10.1115/1.3167719 · Zbl 0549.73062 · doi:10.1115/1.3167719 [19] Reddy J. N., An Introduction to Finite Element Methods (1993) [20] Kareem A., Eng. Struct. 12 pp 1– [21] Cook R. D., Concept and Applications of Finite Element Analysis (2000) [22] DOI: 10.1002/nme.1620231004 · Zbl 0597.73075 · doi:10.1002/nme.1620231004 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.