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Critical linear buckling load calculation is one of the possible ways to check structural stability. Structural analysis programs usually model beams and columns with just one element, but this is not enough to obtain an accurate value of the critical buckling load when the buckling mode is associated with an effective length that is less than twice the element length. This paper presents a method for the accurate calculation of the buckling load of frames modeled with only one finite element per structural element. For this purpose, a local correction is applied to some elements a few times until convergence is achieved. The validity of the presented method is confirmed by several examples ranging from simple canonical cases to large structures.

This study deals with the comparison of stresses and displacements of a circular ring obtained by two numerical formulations, namely the stiffness method and the hybrid method, applied to isoparametric quadrilateral elements. After explaining the formulation of the hybrid method in finite elements, an orthogonalization method proposed previously for hybrid elements is applied. Then, the computational cost per element of the stiffness method and of the hybrid method with and without orthogonalization has been evaluated for the first time. A circular ring loaded by two opposing forces is analyzed in order to compare the solution obtained by the hybrid method and the stiffness method with experimental and analytical results. The agreement between analytical and experimental results with those numerical is better in the case of the hybrid method than in the case of the stiffness method. It is observed that the element ratio needed to obtain a given relative error is one magnitude order greater in the stiffness method than in the case of the hybrid method.