A novel strategy to construct exact structural-property matrices for nonprismatic Timoshenko’s frame elements.

Abstract

Assuming Timoshenko’s beam hypothesis, this paper proposes a unified strategy to derive exact finiteelement (FE) matrices for framed structures having elements with variable rigidity. Its basic idea is to apply the principle of virtual forces (PVF), at the element level, to obtain a flexibility-based set of equations from which structural-property and nodal-load coefficients can be directly evaluated. The variable physical-geometric characteristics along the frame elements are approximated by polynomials of different orders. For evaluating structural-property coefficients that depend on the deformation of the structure, as e.g. the geometric stiffness coefficients, one employs Timoshenko’s consistent shape functions. A novel process for building them under the most general cases of rigidity variation is presented in this paper. In this study, we particularly apply the technique to effect second-order analyses of 2D frames with nonprismatic elements.