Large deformation analysis of sandwich beams using compound $$C^1$$ continuous finite element approximation

Abstract A novel computational framework for the geometrically nonlinear elastic response of sandwich rods, plates and shells is proposed and investigated in the context of statics of a straight sandwich beam. Particular attention is paid to the local effects associated with thickness deformation. Modeling the face sheets as geometrically exact 1D rods with bending and tension/compression, and the soft core as a 2D continuum at plane stress, is efficient with the $$C^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> continuous approximation of displacements using the corresponding bonding conditions. The benchmark problems include bending of the sandwich beam under distributed loading and under the action of a concentrated force, buckling under compression, and local wrinkling analysis at force bending. The mesh convergence of the numerical model is established, and the solutions are validated for a wide range of core stiffness against other reference results obtained with commercial finite element software as well as against analytical results available in the literature.