Geometrically nonlinear transient analysis of Timoshenko tapered beam-column element using a finite element formulation based on the exact shape functions.

In this paper, a numerical formulation was developed to generate the consistent mass matrix for Timoshenko tapered beam-column element for geometrically nonlinear transient analysis. The basis of the suggested solution is the exact shape functions and their derivatives, which describe the non-uniformity of the element properties. To illustrate the variations in section properties along the tapered element length, the section properties were presented as exponential functions with tapering indices. The model can simulate elements with various solid and hollow cross-sections. The suggested formulation is integrated into a Visual Basic program to perform the analysis, along with numerous examples to verify its precision and effectiveness. As a practical application of the proposed formulation, a structural system was proposed for offshore wind turbines with high elevations, and a geometrical nonlinear dynamic analysis was conducted. The results demonstrated the proposed model's ability to perform this type of complex calculation with minimal computational effort. [ABSTRACT FROM AUTHOR]