Size effects of basic cell in static analysis of sandwich beams

Abstract

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.

Effective couple-stress continuum model of cellular solids and size effects analysis

“…Only a brief description is given here and more examples may refer to Dai and Zhang (2008). Moreover, our motivation is to explain the mechanism of these size effects.…”

“…The second one, named Cosserat effect or micropolar effect, arises from the violation of the classical mechanical assumption. For example, Burgueno et al (2005); Dai and Zhang (2008) found that the flexural rigidity of the multilayered sandwich beams can not be obtained correctly by the classical homogenization method when the base cell of the cellular materials has a considerable dimension relative to the structural size, and this effect decreases rapidly with the size reduction of the base cell. In fact, both the edge effect and the micropolar effect are usually present simultaneously and it is possible to observe weakening or strengthening behavior depending on which one is more dominant (Anderson and Lakes, 1994;Tekoglu, 2007).…”

Interface shape optimization of designing functionally graded sandwich structures

“…Designs of lighter, safer and efficient sandwich structures with multi-functionality have been a hotpot for research since a long time ago [8][9][10][11][12][13][14][15]. FG sandwich structures with two different materials are offered to fulfill the lighter and safer structures.…”

Cell size effects for vibration analysis and design of sandwich beams

“…This effect results in an increase of the in-plane elastic constants with an increasing ratio of the specimen size to the cell size, up to a plateau level in the limit case. Recently, Dai and Zhang [11] investigated further the size effects in static analysis of sandwich beam bending problems with given cell geometry. Zhang and Sun [12][13][14] studied the scale-related topology optimization of plane and cylindrical sandwich panels to investigate the cell size effect upon the optimum configuration.…”