A nonlinear dynamical theory of non-classical plates

Abstract

In this paper, a new nonlinear formulation of plates, including shear and rotatory inertia and transverse normal stress effects, is developed by means of general assumptions, of which the yon Karman-type fornmlation and some thick plate theories are special cases. To keep the formulation fairly general, the problem addressed in this paper simultaneously includes: the effects of shear deformation according to the geometric deformation similarity of the crosssection, the rotatory inertia, and the transverse normal stress. The three-dimensional compatible equations are applied to derive the basic equations. Numerical results are given for linear and non-linear analysis of plates. Nomenclature h It, V. IV It O, V O, WO fo q(x,y,t) P D E G V J P(:) B(:) k,,ko thic~less of the plate displacements at any point (x, y, z) in the x-, y-, and z-direction, respectively The middle-surface displacement components in the x-, y-, and =-direction, respectively shear rotations in addition to the usual flexural rotations deformation distribution fnnction of thickness transverse distributed loading mass density flexural rigidity of the plate, D = Eh 3 / 12(1 -v 2) Young's modulus modulus of elasticity in shear Poission's ratio inertia moment displacement distribution fnnction of shear function of transverse normal deformation angle fimctions of rotation at x-and ),-directions influence coefficients of shear and transverse normal stress, respectively This

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