Abstract:
Started from the governing differential equation with second-order effect, the stiffness and stability of a tapered Bernoulli-Euler beam with elastic constraints are analyzed, whose profile is assumed linear variation. Then the exact expression of deflection and critical load of elastic tapered beam with composite loads are proposed; while the deflection coefficients caused by axial force are derived. In extreme situations, the proposed stiffness formulas can degenerate into the stiffness of tapered cantilever and uniform cantilever, respectively. Comparison with the results of ANSYS in the numerical examples indicates that the proposed method can lead to accurate results for stiffness and stability analysis of a tapered Bernoulli-Euler beam with elastic constraints.