Buckling of laser-welded sandwich panels. Part 1: Elastic buckling parallel to the webs

Abstract

This is the first of three companion papers that examine the elastic buckling and collapse of laser-welded sandwich panels with an adhesively bonded core and uni-directional vertical webs. In compression parallel to the webs, the face sheet in between two webs can be treated as a long rectangular plate supported at the sides and resting on a continuous elastic foundation. Using a generalized form of the Kirchoff equation, the plate buckling load is evaluated for a Winkler and Pasternak foundation, and for a foundation model where the core is characterized by an elastic half-space. Although the elastic half-space model is most sophisticated in the way that the decay of transverse stress through the core is described, it requires that the buckling load is calculated iteratively and is therefore not suitable for engineering applications. In contrast, the Pasternak foundation model is able to demonstrate the effect of different boundary conditions at the laser weld and different core properties by the variation of a simple clamping factor and two foundation moduli. By changing the clamping factor, the model can be used to describe plate buckling as well as wrinkling, and, by varying the foundation moduli, it is possible to distinguish between symmetrical and anti-symmetrical buckling modes. Evaluation of the buckling solution shows that, for low modulus core materials, the plate buckling strength is determined only by the boundary conditions at the laser weld, while for high modulus materials anti-symmetrical wrinkling dominates. To improve the accuracy of the solution for non-standard configurations, the foundation moduli are calibrated using the elastic half-space model and finite element results as a reference. It is found that, by using a smaller Winkler foundation modulus, the accuracy and consistency of the Pasternak model are improved considerably. However, the results also show that, for current sandwich configurations, the proportional limit of the face plate material is usually reached well before elastic buckling occurs. All experimental work is therefore delegated to the third paper, which deals with extension of the Pasternak foundation model into the elasto-plastic regime and non-linear finite element modelling.