Stability analysis of rectangular sandwich plate kormanikova E., Kotrasova K
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STABILITY ANALYSIS OF RECTANGULAR SANDWICH PLATE Kormanikova E., Kotrasova K. Department of Structural Mechanics, Technical University of Kosice SK-04200 Kosice, Slovak Repablic To formulate the governing differential equations for sandwich plates we define the similarity of the elastic behaviour between laminates and sandwiches in the first order shear deformation theory that all results for laminates can be applied to sandwich plates. We restrict our considerations to symmetric sandwich plates with laminate thin cover sheets. There are differences in the expressions for the flexural stiffness and the transverse shear stiffness of laminates and sandwiches. Furthermore there are essential differences in the stress distributions. M (1) ost sandwich structures can be modelled and analyzed using the shear deformation theory for laminated plates. The constitutive equation in hypermatrix form is written bellow:   with the stiffness coefficients: (2)  where:  (3) n1 and n2 are the number of layers in the lower and the upper sheet respectively and   are the transverse shear moduli of the core. The constitutive equations for a sandwich composite has a form similar to the constitutive equation for laminates including transverse shear. It differs only by the terms  instead of  which induce an asymmetry in the stiffness matrix. In the case of symmetric sandwiches with identical sheets h1= h3 = hf,  =  =  ,  = -  =  we can calculate the stiffness coefficients like: (4) As developed for laminates including shear deformations, the coefficients  can be corrected by shear correction factors  and replaced by shear parameters   to improve the modelling.In the case of symmetric sandwiches there is no coupling between stretching and bending and the form of the constitutive equation is identical to the constitutive equation for symmetric laminates including transverse shear. In the general case of a symmetric laminate with p3 = 0, the plate equation can be expressed by: For a coupling of in-plane loads and lateral deflection, the equilibrium equations will be formulated for the deformed plate element and are modified to:  (5)  T (6) he buckling load is like natural vibration independent of the lateral load and p3 is taken to be zero. Table 1 The material properties of facings For a rectangular sandwich plate consisting of 5 layers with the given material constants a buckling analysis is carried out. The plate is simply supported at all boundaries and loaded by a uniaxial uniform load (Fig. 1). Material characteristics for laminate facings and sandwich core are listed in Table 1 and Table 2, respectively.    Table 2 The material properties of sandwich core  For the stacking structure a symmetric sandwich structure is considered (Fig. 2). The fibre angle is varied: a = 0°, 30 °, 45 °, 60 °, 90 °. For the buckling analysis in COSMOS/M a unit pressure loading must be created, and the program calculates a factor to multiply the unit loading for obtaining the optimal buckling load. In the Fig. 3 there are buckling modes for asymmetric sandwich plate a = 30 °, 45 °, 60°, 90 °, respectively.   The paper deals with a modeling of buckling analysis of sandwich plates. To predict the inception of buckling for plates in-plane resultant forces must be included. For fibre angles a = 30 °, 45 °, 60 °, 90 ° the buckling modes have different shapes, they are shown in the Fig. 3. The buckling multipliers are 1.75219, 3.04541, 3.35257, 2.92635, 1.72399 for fibre angles a = 0 °, 30 °, 45 °, 60 °, 90 °, respectively. A fibre angle near 45 ° leads to the highest buckling load for a sandwich plate. |
