Micropolar modeling approach for periodic sandwich beams

A micropolar Timoshenko beam formulation is developed and used to model web-core sandwich beams. The beam theory is derived by a vector approach and the general solution to the governing sixth-order equations is given. A nodally-exact micropolar Timoshenko beam finite element is derived using the solution. Bending and shear stiffness coefficients for a web-core sandwich beam are determined through unit cell analysis, where the split of the shear forces into symmetric and antisymmetric parts plays a pivotal role. Static bending of web-core beams is studied using the micropolar model as well as modified couple-stress and classical Timoshenko beam models. The micropolar 1-D results are in best agreement with 2-D web-core beam frame results. This is because the micropolar beam allows antisymmetric shear deformation to emerge at locations where the 2-D web-core deformations cannot be reduced to 1-D by considering only symmetric shear behavior.