A new shape function for tapered three-dimensional beams with flexible connections

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.

► Derivation of shape functions for tapered beams using force-interpolation concept.
► Deriving shape function of tapered 3D beams with flexible end connections.
► Systematic derivation of consistent mass and geometric stiffness matrix for beams.
► Sensitivity of numerical results with respect to taper type and severity.