ABSTRACT of the Doctoral Thesis
The aim of this work is to present a general analytical approach to the local instability failure mode of sandwich plates commonly referred to as wrinkling. The wrinkling problem is assumed to be a localized phenomenon and interaction with global buckling is not considered. Due to this assumption and the generality of the approach, it can also be used for automatic post processing of FE sandwich shell results. In this case, safety factors against wrinkling can be calculated on the basis of the FE stress results at integration point level of appropriate finite sandwich shell elements. This has not been generally possible up to now due to the lack of generality of the corresponding wrinkling models in terms of sandwich configuration and loading.
The new approach is much more general than existing ones focusing on wrinkling, since it takes into account unsymmetric sandwiches, arbitrary loading and orthotropic constituent materials. The Rayleigh Ritz method is employed, leading to a numerically efficient calculation scheme although the complexity of the problem is considerable and numerical optimization has to be used.
Within this study three different types of finite element verification models are formulated, including periodic unit-cell models. The advantages and drawbacks of the periodic unit-cell formulation as compared to classical models are evaluated. The FE verification models and the new analytical model generally show very good agreement. The deformation field which has been chosen for the Ritz ansatz was also verified by these FE calculations. Experimental verification is under progress, but not included in this work.
Apart from the analytical approach itself numerous results are presented which show the shortcomings of the commonly used wrinkling calculations and the resulting errors. It is demonstrated that even in the simplest case of a symmetric sandwich beam under compression, the commonly used wrinkling calculation schemes may lead to qualitatively and quantitatively wrong results. It is shown, that the type of core material used within the sandwich has a major influence on the applicability of the classical design formulas and on the decision whether the sandwich is sufficiently thick for precluding face layer interaction. This is due to the fact that the in-plane core stiffness plays an important role concerning wrinkling. This new finding is of major importance to all existing wrinkling approaches because the influence of the in-plane core stiffness has generally been ignored in sandwich analysis up to now. The new approach presented in this work uses, in contrary to almost all other approaches, a core material description which is taking the in-plane core stiffness into account. Therefore it is applicable for all commonly used core materials.
Furthermore, results for pure bending of sandwich beams are presented which show, for the first time, the influence of the face layer which is under tension on the critical wrinkling load. The calculations show a significant influence for rather thin sandwiches.
Unsymmetric or orthotropic sandwich plates under general loading conditions, which are beyond the scope of the other currently used wrinkling models, have also been studied. The corresponding effects are evaluated using different example problems starting with rather simple cases and successively moving to more complex configurations. The corresponding results give valuable insight into the wrinkling behavior of these sandwich constructions.