The general theory of elastic stability has for some time been written in an algorithmic form suitable for computer analysis, although until now the process has never been directly implemented. The nonlinear problem is reduced by the perturbation method to a series of linear problems, each of which is readily solvable. The analytical procedure for a structural buckling problem, an axially-loaded thin cylinder for example, follows a series of readily definable steps, which quickly become too difficult to cope with by hand but are quite simple to express logically. The steps include derivation of in-plane u and v displacements from an assumed out-of-plane w displacement; determination of strains from strain-displacement relations giving the membrane and bending strain energy and the work done by the load; removal o f the initial pre-buckling deformation from consideration; and manipulation of the resulting potential energy function according to the general theory to give the post-buckling results of interest. An entirely parallel manipulation is also achieved for nonlinear laterally-loaded problems, illustrated by a point load on a cylindrical shell.

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