A simple method for the calculation of postcritical branches

Abstract

The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path‐following methods such as arc‐length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch‐switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.