This study proposes a weight reduction design approach for urban transit carbody using a material selection method and size optimization. First, the material selection method, which uses specific stiffness and strength indices to predict the weight reduction rate, is set up when the materials of the under-frame and roof structure are substituted. The CFRP was chosen as the best weight reduction material in terms of the material selection method but was not appropriate for application to an urban transit carbody as a thin panel because of outof-plane deformation. Therefore, we applied CFRP-AL honeycomb sandwich composites to the under-frame and roof structures, and the size optimization method was subsequently applied to derive a lightweight composite hybrid carbody design. Finally, the proposed approach was applied to an urban transit carbody, i.e., a Korean electrical multiple units carbody made of aluminum extrusion profiles. The weight of the optimized composite hybrid carbody design was 29.0% lighter than that of the original K-EMU. The resulting composite hybrid carbody design satisfied the design guidelines of the Performance test standard for K-EMU according to the corresponding FE simulations.

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A variational formulation for a Timoshenko beam element is derived by the separation of the deformation mode into the bending deflection and shear deflection. Shear deflection is projected into bending deflection and the projection matrix is constructed by using the equilibrium equation and the relation of force and displacement. The exact stiffness matrix of the Timoshenko beam element can be obtained by the present method. Examples are solved in order to show the effectiveness of the beam element in comparison with other elements.

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