A simple analytic theory for the effect of cell geometry on both the shear modulus and the density of sandwich panel core is presented. The core shear modulus in different directions is analyzed to include the effects of the angle α and the aspect ratio b/a of the cell. It is also found that the minimum cell weight of the sandwich core depends both on the cell angle α and the cell aspect ratio b/a. The theory compares fairly well with some available experiments. The cell geometry chosen is so general that the regular hexagonal and square cells of commercial sandwich cores are special cases.

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A new theory of sandwich beams/one-dimensional plates is presented with finite rotations and shear allowed in each layer. The layers, variable in number from one to three, need not have the same thickness and the same length, thus allowing for ply drop-off. Restricting to planar deformation, the cross section has a motion identical to that of a multibody system that consists of rigid links connected by hinges. Large deformation and large overall motion are accommodated, with the beam dynamics referred directly to an inertial frame. An important approximated theory is developed from the general nonlinear equations. The classical linear theory is recovered by consistent linearization.

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We formulate a theory of geometrically‐exact multilayer beams and one‐dimensional plates that account for the through‐the‐thickness deformation in each layer, in addition to shear deformation. The complete set of nonlinear equations of motion together with the appropriate boundary conditions are derived, and a linear constitutive law is postulated for the model. The number of layers is arbitrary and unlimited, with a reference layer arbitrarily chosen among the layers. The length and the thickness of each layer are also variable, making the modeling of multilayer structures with ply drop‐offs possible. The present theory reduces exactly to the case of multilayer structures without through‐the‐thickness deformation, and to the case of single‐layer structures. The formulation allows the description of large deformation and large overall motion in multilayer structures.

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