EXACT ELEMENTAL STIFFNESS MATRIX OF A TAPERED BEAM CONSIDERING SECOND-ORDER EFFECTS

The exact stiffness matrix of the tapered Bernoulli-Euler beam is proposed, whose profile is assumed to be varying linearly, and it can be incorporated into stability analysis with high accuracy. The Bernoulli-Euler theory of bending is used to describe the motion of the beam. Classical finite element method to obtain stiffness matrix is replaced by interpolation method and the principle of virtual work. Solving the governing differential equation of motion with second-order effects, the force- displacement relation is obtained. In the formulation of finite element method, the derived stiffness matrix has the same accuracy with the solution of exact differential equations. The results are compared with some classical ones and ANSYS’s. It shows that the proposed exact stiffness matrix offers an accurate and effective tool for stability analysis of tapered beam structures, and obtains the exact Euler critical force.