Analytical and Numerical Modelling of the Axisymmetric Bending of Circular Sandwich Plates with the Nonlinear Elastic Core Material

الموضوعات :

A Kudin ¹ (Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine)
S Choporov ² (Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine)
Yu Tamurov ³ (Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine)
M.A.V Al Omari ⁴ (Department of Mathematics, Zaporizhzhya National University, Zhukovsky street 66, Zaporizhzhya 69600, Ukraine)

تاريخ الإرسال : 18 الخميس , رمضان, 1437 تاريخ التأكيد : 16 الجمعة , ذو القعدة, 1437 تاريخ الإصدار : 19 الثلاثاء , ذو الحجة, 1437

الکلمات المفتاحية: Circular Sandwich Plate, Nonlinear elastic material, The finite element method, Perturbation method,

ملخص المقالة :

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlinear differential equations has been described. The perturbation method for differential equations with small parameters is used to represent nonlinear differential equations as a sequence of linear equations. Linear differential equations are reduced to Bessel’s equation. It is compared results of analytical model with results of other researches using two problems: 1) the problem of axisymmetric transverse bending of a circular sandwich plate, 2) the problem of axisymmetric transverse bending of an annular sandwich plate. The effect of accounting nonlinear elastic core material on the strain state of the sandwich plate is described.

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