EFFECT OF SHEAR DEFORMATION ON LARGE DEFLECTIONS OF CIRCULAR SANDWICH PLATES

Abstract

C. V. Smith, Jr. Assistant Professor Georgia Institute of Technology Atlanta, Georgia W = measure of effect of shear deformation Differential equations are presented which describe axisymmetric, large deflections of circular sandwich plates, including the effect of transverse shear deformation. The equations are solved for the following states of loading and boundary conditions: tributed around a simply supported, movable boundary, 2) uniform lateral load with a clamped, immovable boundary, a clamped, movable boundary. For each load state, the differential equations are first nondimensionalized. Then a power series solution is assumed, with the coefficients determined by an iteration technique which insures satisfaction of the boundary conditions. Numerical results are presented which show that transverse shear deformation has a significant effect on the large deflections of sandwich plates. One of the new and most interesting results appears in the case of the uniform edge moment loading, where including r e 1) moments uniformly dis3) uniform lateral load with M* = nondimensionalized applied edge moment; see M = applied edge moment M ,M = bending moments in a circular plate Eq. (38) 0 1 ($)2 6E 5GZ 2 1211.-v ) for transversely orthotropic, homogeneous plates for isotropic, homogeneous plates t 2 Eftf 1 , for sandwich plates. transverse shear deformation causes a decrease of ~ N ,N = in-plane forces in a circular plate deflection at the center of the plate. r e Nomenclature in-plane rigidity Eh., for homogeneous plates 2Eftf, for sandwich plates bendifig rigidity Eh.3 , for homogeneous plates 12( l-v2) E t t 2 =-, for sandwich plates 2(1-vy ) E = modulus of elasticity E = modulus of elasticity for face material F = nondimensional radial in-plane force; see f Eqs. (36) and (68). G = transverse shear'modulus G = shear modulus for core material . R = radius of a circular plate S = nondimensiohalized applied transverse load; see Eq. (68) Vr h q = applied transverse load r = radial coordinate = transverse shear in a circular plate = thickness of homogeneous plate = thickness of core in a sandwich plate = thickness of the identical face layers in = radial displacement of the midplane tc tf u a sandwich plate 0 W = transverse displacement w1 = slope of the deformed midsurface; see Z = transverse coordinate measured from the Eq. (6) midplane CY crrn,eem = midsurface strains, see Eq. (5) = slope of the deformed cross sectim = transverse shearing strain; see Eq. (4) = curvatures of the deformed midsurface; see Eq. (5) * 'P = nondimensionalized radial coordinate; This paper presents a portion of a dissertation submitted to the Department of Civil and Sanitary Engineering, Massachusetts Institute of Technology, in partial fulfillment of the requirements for the see Eq. (36) midsurface; see Eqs. (36) and (68) cp = nondimensionalized slope of the deformed degree of Doctor of Science. 7ax V = Poisson's ratio