Evaluation of two finite element formulations for a rapid 3D stress analysis of sandwich structures

Abstract

For efficiently simulating the impact behavior of sandwich structures made from composite face sheets and a lightweight core a rapid and accurate 3D stress analysis is essential. For that reason, a three-layered finite element formulation based on plane stress assumptions was recently developed by Kärger et al. [Kärger, WA, Rolfes R, Rohwer K. A three-layered sandwich element with improved transverse shear stiffness and stress based on FSDT. Comput Struct, submitted for publication]. It has turned out, however, that under concentrated out-of-plane loads this element formulation lacks appropriate accuracy of stress results. Therefore, an improved finite element formulation is developed, which accounts for the full 3D stress state. In a post-processing routine, the transverse stresses are improved by using the Extended 2D Method, which was developed by Rolfes and Rohwer [Rolfes R, Rohwer K. Improved transverse shear stresses in composite finite elements based on first order shear deformation theory. Int J Numer Meth Eng 1997;40:51–60] and extended to a three-layered sandwich structure by Kärger et al. Both the finite element formulation by Kärger et al. and the new formulation presented in the present article use pure displacement approaches and require only C 0-continuity conditions, which simplifies integration into existing FE codes and allows combined application with other finite elements. Two examples demonstrate the accuracy and applicability of the two elements.