Exact Expression of Element Stiffness Matrix for a Tapered Beam and its Application in Stability Analysis
The exact stiffness matrix of a tapered Bernoulli-Euler beam is proposed, whose profile is assumed linear variation. Classical finite element method to get stiffness matrix through interpolation theory and the principle of virtual displacement is abandoned. Starting from the governing differential equation with second-order effect, the exact stiffness matrix of tapered beam can be obtained. In the formulation of finite element method, the stiffness matrix derived has the same accuracy with the solution of exact differential equation method. As is demonstrated in the numerical examples, the presented method can yield, in a very efficient way, accurate results for single tapered beam or structures consisting of tapered elements.
L. X. Meng et al., "Exact Expression of Element Stiffness Matrix for a Tapered Beam and its Application in Stability Analysis", Advanced Materials Research, Vols. 255-260, pp. 1968-1973, 2011