Instability of Tapered Thin‐Walled Beams of Generic Section

Buckling loads and natural frequencies and the corresponding modal shapes and forms for thin‐walled tapered beams of open sections are examined using the finite‐element method. A tapered thin‐walled bar finite element with seven degrees of freedom at each node is adopted. In the virtual work formulation, the updated Lagrangian approach is adopted in which the effect of geometric nonlinearity is considered. A rigorous expression for strains based on membrane theory of shells is considered. The flexural stiffness matrix, geometric stiffness matrix, and consistent mass matrices are derived in a companion paper. The convergence and accuracy of the method is tested based on other numerical results. Using the present theory, one is able to investigate various torsional and flexural static and dynamic instability problems. Examples are presented and comparisons are made with the existing solutions.