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

This is the first of three companion papers that examine the elastic buckling andcollapse of laser-welded sandwich panels with an adhesively bonded core and uni-directionalvertical webs. In compression parallel to the webs the face sheet in between two webs can betreated as a long rectangular plate supported at the sides and resting on a continuous elasticfoundation. Using a generalized form of the Kirchoff equation, the plate buckling load isevaluated for a Winkler and Pasternak foundation, and for a foundation model where thecore is characterized by an elastic half-space. Although the elastic half-space model is mostsophisticated in the way that the decay of transverse stress through the core is described, itrequires that the buckling load is calculated iteratively and is therefore not suitable for engineeringapplications. In contrast, the Pasternak foundation model is able to demonstrate the effectof different boundary conditions at the laser weld and different core properties by the variationof 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 thefoundation moduli, it is possible to distinguish between symmetrical and anti-symmetricalbuckling 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 laserweld, while for high modulus materials anti-symmetrical wrinkling dominates. To improvethe accuracy of the solution for non-standard configurations, the foundation moduli arecalibrated using the elastic half-space model and finite element results as a reference. It isfound that, by using a smaller Winkler foundation modulus, the accuracy and consistency ofthe Pasternak model are improved considerably. However, the results also show that, for currentsandwich configurations, the proportional limit of the face plate material is usually reachedwell before elastic buckling occurs. All experimental work is therefore delegated to the thirdpaper, which deals with extension of the Pasternak foundation model into the elasto-plasticregime and non-linear finite element modelling.QC 20111220