Buckling Analysis of Orthotropic and Anisotropic Rectangular Plates by GDQ Method

الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک

محسن فتاحی ¹ (کارشناس ارشد، مهندسی مکانیک دانشگاه آزاد اسلامی واحد خمینی‌شهر)
فاطمه فرهت نیا ² (استادیار، دانشگاه آزاد اسلامی واحد خمینی‌شهر)
منصور درویزه ³ (استاد، دانشگاه گیلان)

تاريخ الإرسال : 21 الأحد , ذو الحجة, 1436 تاريخ التأكيد : 21 الأحد , ذو الحجة, 1436 تاريخ الإصدار : 12 الخميس , ربيع الأول, 1429

الکلمات المفتاحية: Buckling - Orthotropic Plate - Anisotropic - Generalized Differential Quadrature Method,

ملخص المقالة :

In this paper, buckling of orthotropic rectangular plates under different loadings was investigated. For this reason, governing buckling equations for an isotropic plate were modified by applying constitutive equations of orthotropic materials. After obtaining the equations of orthotropic plates, Generalized Differential Quadrature method (GDQM) was applied on buckling equations and thus a set of Eigen value equations resulted. In order to solve this Eigen value problem, a computer program was developed using MATLAB software in a way that the influence of different parameters such as length to width ratio (aspect ratio), the number of layers, the angle of layers arrangement, material of layers, kind of loading and boundary conditions were included. A buckling load factor was calculated for simply supported and clamped supported plates. The results of GDQ method were compared with reported results from Rayleigh – Ritz method and with results from solving the Finite element using ANSYS 8.0 software. The comparison showed the accuracy of obtained result clearly.

المصادر:

[1]            Perry, C . L., “ The bending of thin elliptical plates”, Int Proc, Symp, Applied Mathematics, (1950), Vol. III, Elasticity, McGraw-Hill, New York, pp. 131-139

[2]            Nash, W . A., and Cooly, I . D., “Large deflection of a clamped elliptical plate subjected to Uniform pressure, Journal of Applied Mechanics, (1959), Vol. pp. 26, pp. 291-293.

[3]            Timoshenko, S . P ., and Gere, J . M., “Theory of elastic stability”, (1961), 2^nd , Ed, McGraw-Hill, New York, N . Y.

[4]            Bellman, R. E., and Casti, J. "Differential quadrature and long-term integration." J. Math. Anal. And applications, Vol. 34, 235-238. (1971) 

[5]            Mingle, J . O., “Computational consideration in nonlinear diffusion”, Int. J. Numrn. Methods Eng (1973), 7: 103-116.

[6]            Bellman, R. E., Kashef, B.G., and Casti, J. "Differential quadrature: a technique for the aroid solution for nonlinear partial differential equations." J. Computational Phys., Vol. 10, 45-52. (1972).

[7]            Bellman, R. E., and Kashef, B.G., "Solution of the partial differential equation of Hodgkins-Huxley model using differential quadrature", Math. Anal. Biosci., 19, 1-8(1974).

[8]            Civan, F., and Sliepcevich C. M. "Application of differentioal quadrature to transport processes", J. M ath. Anal. Appl., 93, 206-221. (1983).

[9]            Striz, A . G ., Chen, W . L., Bert C . W., “Free vibration of plates by the accuracy quadrature element method”, Journal of sound and Vibration, Vol. 202(5), pp. 698-702, copyright (1997), with permission from Academic press.

[10]        Striz, A . G ., Wang, X., and Bert C . W., “Harmonic differential quadrature method and Application to analysis of structural components”, (1995), Acta. Mech. III. 84-94.

[11]        Sherbourne, A . N., and Pandey, M . D, Differential quadrature method in the buckling analysis of beams and composite plates, Comput ans structures, (1991), 40: 903-913.

[12]        Shu, C ., Free vibration analysis of composite laminated conical shells, Journal of sound and vibration , Vol. 194(4), pp. 587-604, copyright (1996), with permission from academic press.

[13]        Shu, C ., and Chew, Y . T., and Khoo, B . C., and Yeo, K . S., “Application GDQ scheme to simulate incompressible viscous flows around complex geometries”, Mechanics Research communication, (1995), Vol.22(4), pp. 319-325.

[14]        Shu, C ., and Chew, Y . T., and Khoo, B . C., and Yeo, K . S., “Solution of three-dimensional boundary layer equation by global methods of generalized differential-integral quadrature”, International journal numerical methods for heat and flow, (1996), Vol. 6(2), pp. 61-75.

Shu, C ., and Richards, B . E., “Generalized differential and integral quadrature and their application to solve boundary –layer equation”, International journal for numerical