Mathematical modelling of a rectangular sandwich plate with a metal foam core

The subject of the paper is a simply supported rectangular sandwich plate. The plate is compressed in plane. It is assumed that the plate under consideration is symmetrical in build and consists of two isotropic facings and a core. The middle plane of the plate is its symmetry plane. The core is made of a metal foam with properties varying across its thickness. The porous-cellular metal as a core of the three layered plate is of continuous structure, while its mechanical properties are isotropic. Dimensionless coefficients are introduced to compensate for this.

The field of displacements and geometric relationships are assumed. This non-linear hypothesis is generalization of the classical hypotheses, in particular, the broken-line hypothesis. The principle of stationarity of the total potential energy of the compressed sandwich plate is used and a system of differential equations is formulated. This system is approximately solved. The forms of unknown functions are assumed, which satisfy boundary conditions for supports of the plate. Critical loads for a family of sandwich plates are numerically determined. Results of the calculation are shown in figures.