Abstract
The principle of virtual force and concept of force interpolation is employed to develop a systematic method for deriving the shape functions for the tapered three-dimensional frame element with flexible end connections. These shape functions can be used to calculate the stiffness, geometric stiffness and consistent mass matrices of the tapered frame element with flexible connections. The formulation adopts the Euler–Bernoulli hypothesis and linear elastic material behaviour, with local buckling effects being ignored. The formulation is verified by some numerical examples on the buckling load and dynamic frequency analysis of tapered beams with rigid and flexible connections. It is shown that the systematic method developed in the paper is mostly superior in its efficiency compared with elements based on Hermitian interpolation functions.
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