Effect of geometrical and mechanical properties on behaviour of sandwich beams with functionally graded face sheets under indentation loading

Abstract

Improved high-order sandwich beam theory is used to model the local deformation ofsandwich beams with aluminium/alumina functionally graded (FG) face sheets loaded by central indentor. First-order shear deformation theory is used for the FG face sheets while three-dimensional elasticity is used for the flexible core. Using the model to consider the way in which different wavelengths of sinusoidal pressure loading on the upper FG face sheet are transmitted to the core and lower FG face sheet, two spreading length scales λt and λb are introduced and calculated; λt and λb, which are two functions of the beam material and geometrical properties, characterize the length over which a load on the upper surface of a beam is spread out by the face sheets and the core. Comparison of the semi-wavelength of the sinusoidal pressure loading ( L/m) on the upper FG face sheet with length scales λt and λb illustrate the importance of these length scales in describing whether the face sheets act in a rigid or a flexible manner. When the semi-wavelength ( L/m) of the applied load in the present example is higher than λt (or λb), 10–90 per cent (or 5–70 per cent) of the contact load is transmitted locally to the core (or from the core to the lower FG face sheet) for the geometries and materials analysed. Conversely, when L/m is lower than λt (or λ1b), the contact load from the upper FG face sheet with a maximum of 58 per cent (or 70 per cent) is spread out over a wider area of the core (or from the core is spread out over a wider area of the lower FG face sheet). Reasonable agreement is found between the theoretical predictions in this study and finite element method results by ANSYS and the results published in literature for special cases.