BENDING BEHAVIOR OF FUNCTIONALLY GRADED MATERIAL SANDWICH BEAMS UNDER GENERALLY RESTRAINED BOUNDARY CONDITIONS WITH SIX-PARAMETER

A constraint model with six-parameter is presented to study the static bending behavior of functionally graded material (FGM) sandwich beams with general boundary conditions. The beams are assumed to be composed of an upper panel layer, a sandwich layer and a lower panel layer, in which the core layers are ceramic single-phase (hard core), ceramic-metal composite (FGM core) and metal single-phase (soft core) materials, respectively. The effective material properties for FGM layer across the depth of sandwich beams are described by the mixture power-law distributions according to Voigt model. The general elastic constraints at both ends of a beam is simulated by two sets of translational springs and one set of rotational springs. Based on Timoshenko beam theory, the governing differential equations and general elastic boundary conditions can be obtained by energy variational principle for the structure. The displacement method is used to solve the problem, and the bending response of the structure is obtained by writing the MATLAB calculation program of differential quadrature method. The significant influences of constraining spring stiffness, layer thickness ratio, sandwich type, material graded index, and slenderness ratios on the static bending characteristic of FGM sandwich beams are mainly discussed by several numerical examples. The results show that the method is feasible and the numerical results are reliable and accurate. Moreover, the universality and superiority for the constraint model with six-parameter are demonstrated by comparing with those of various classical boundary conditions. This research can provide theoretical basis and reference for both strength and stiffness design of FGM sandwich beam.