Size effects of basic cell in static analysis of sandwich beams

In this paper, multilayered sandwich beam structures are considered. Within the scope of static analyses and stiffness design of such type of lightweight and functional structures, size effects of the basic cell are studied both theoretically and numerically in a systematic way for the first time. The direct FE discretization method, the homogenization method and the classical beam theory are examined systematically to reveal, on one hand, the existence of the size effect, and on the other hand, the ability of each method in capturing the size effect upon the static stress distribution and structural deflection. Particularly, limitations of the homogenization method are clarified although the latter is widely applied today in the equivalent modeling and topology design of cellular materials of sandwich structures. By means of the above methods, bending problems of multilayered beams and cellular core sandwiches are solved to illustrate variations of the deflection, stress as well as the computing accuracies in terms of the size of the basic cell. It is shown that the size effect is important when the basic cell has a considerable dimension relative to the structural size and that this effect decreases rapidly with the size reduction of the basic cell. Theoretically, the homogenized result corresponds to the limit solution when the size of the basic cell tends to be infinitely small.