INSTABILITY OF TAPERED THIN-WALLED-BEAMS OF GENERIC SECTION

Buckling loads and natural frequencies and the corresponding modal sha pes and: forms for thin-walled tapered beams of open sections are exam ined 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 rigorou s expression for strains based on membrane theory of shells is conside red. The flexural stiffness matrix, geometric stiffness matrix, and co nsistent mass matrices are derived in a companion paper. The convergen ce and accuracy of the method is tested based on other numerical resul ts. Using the present theory, one is able to investigate various torsi onal and flexural static and dynamic instability problems. Examples ar e presented and comparisons are made with the existing solutions.