Buckling of long clamped anisotropic plates under compression

The most efficient structures transmit forces by uniform compression and uniform tension. Examples include three-dimensional space frames and membrane structures. If the compression loaded part of the structure is slender with respect to one or two of its spatial dimensions then buckling phenomena arise. The development of buckling expressions during the 20th Century owes much to the concurrent industrial development of steel ships, submarines, bridges and of course, aircraft and spacecraft; all of which are thin-walled structures. Manufactured composites were first used in primary structures of aircraft during the 1930s when plywood was introduced as a means for using low quality wood in a relatively high quality manufactured form. Buckling formulae for orthotropic plates derived by Huber in the early 1920s in connection with reinforced concrete, came to the attention of aeronautical engineers who adapted and advanced the formulae to model buckling of plywood skin and spar web structures. In commonly used composite laminates constructed from unidirectional pre-preg material with angle-ply layers, it is in general, impossible to eliminate all coupling responses such that flexural/twist or flexural anisotropy is present. The buckling formulae in current design manuals neglect such effects which is unconservative for compression buckling and either conservative or unconservative for shear depending on the direction of loading. Up until recently there have been no closed form solutions to assess this effect, and so aid the designer. The current work extends that done previously to the case of plates with long edges clamped. The models will be compared with detailed finite element analysis and conclusions drawn for design purposes. Practical examples of which include composite plates containing angle-ply layers and stiffened plates in which the reinforcing members are positioned obliquely to the plate. The design of lightweight structures, if pushed to its limit, may be ultimately driven by buckling. It is known that flexural anisotropy reduces buckling loads for rectangular plates under compression loading. Recently, closed-form solutions were developed to quantify such effects. The current work extends that done previously to the case of plates with long edges clamped. The models will be compared with detailed finite element analysis and conclusions drawn for design purposes. The work is particularly relevant for rapid analysis of new generation all-composite passenger aircraft.