Finite element implementation of a new sandwich homogenization procedure

A new homogenization procedure for finite element (FE) analysis of sandwich shells was recently developed and presented by the authors. To the authorsʹ knowledge all present FE approaches to sandwich structures are incorporated into the FE formulation on the element formulation level. Unlike other formulations, the present approach works on the constitutive level. A homogenization of the sandwich shell is performed at each call of the corresponding constitutive subroutine. Thus, the sandwich nature of the problem is hidden from the main FE program. As a consequence, there is no need to develop a new shell element formulation, instead all available homogeneous shell elements in the utilized FE code can be used for the analysis of sandwich shells. This would provide versatility of the FE analysis and potentials to trade off between the level of accuracy and computational efficiency by using more accurate or simpler shell elements. Furthermore, the sandwich homogenization procedure (SHOP) can be easily coupled with a composite homogenization model to enable analysis of sandwich shells with composite faces. To validate the present approach and check its accuracy, efficiency and overall performance, it is implemented in a FE package and combined with existing first-order shear deformable shell elements for homogeneous materials. Results are obtained and herein presented for problems previously investigated experimentally and by different theoretical and numerical techniques. The presented results show good agreement with published results from far more complicated and computationally intensive analyses, which build confidence in the approach and motivate its future elaboration and development.