A new approach to stability analysis of frame structures using Trefftz-type elements

This paper presents some new developments in structural stability analysis. A novel Trefftz-type finite element and efficient algorithms are proposed for calculating numerically exact solutions for frame structures. New shape functions are constructed by using general solutions of the homogeneous governing equation and an exact Trefftz element is formulated. An iterative algorithm based on conventional eigenvalue extraction method is then proposed, with which very accurate solutions can be obtained efficiently by using coarse finite element meshes. Further, an efficient method based on the new element matrices and Rayleigh's quotient is developed for a posteriori error estimation and solution improvement. Numerical examples are presented to demonstrate the effectiveness of the proposed element and algorithms. Finally, concluding remarks are made including those on the further extension of the approach.

► A Trefftz element is formulated for stability analysis of frame structures.
► An iterative algorithm is proposed for calculating numerically exact solutions based on conventional eigenvalue extraction method.
► An efficient method is developed for a posteriori error estimation and solution improvement.
► The proposed element and algorithms are easy to be implemented in general-purposed finite element software packages.