Stiffness matrix sensitivity approach for efficient computations of slender structure large deformations

Slender structures are widely encountered in engineering applications and often exhibit strongly nonlinear responses when subjected to large deformations involving bending, torsion, axial stretching and shear effects. Accurate numerical modelling of such behaviour typically requires fully nonlinear finite element formulations, which may lead to high computational cost when applied to complex structural systems. This paper proposes a simple stiffness matrix sensitivity approach to identify the most influential nonlinear contributions within the beam element formulation. By analysing the sensitivity of individual nonlinear stiffness matrix terms, the method enables the systematic identification of dominant nonlinear components and the construction of reduced yet physically consistent beam models tailored to specific loading scenarios. The proposed framework is applied to several representative problems involving large deformations of slender structures, demonstrating that only a subset of nonlinear stiffness contributions may be required to accurately capture the dominant structural response. This provides a systematic strategy for selecting relevant nonlinear terms for different classes of slender-structure problems while maintaining modelling accuracy. • A nonlinear beam methodology was using a custom FE formulation to capture nonlinear couplings. • We explain how nonlinear stiffness terms are developed using a sensitivity methodology. • Our FE model was validated against ABAQUS results, especially through torsional buckling comparisons. • Key nonlinear terms were identified for various loading scenarios for computationally efficient models. • The methodology offers significant computational time savings for slender structures.