THE GEOMETRIC NONLINEARITY ANALYSIS OF HIGH ACCURACY TAPERED BEAM ELEMENT BASED ON THE STATIC CONDENSATION

On the basic assumptions of the Euler-Bernoulli beam, a new method based on the static condensation to obtain the stiffness matrix of tapered beam element is proposed, whose sections are continuously changing along its axial direction, and then, by use of the moving coordinate method, the analysis of large displacement, large rotation but small strain tapered beam structures is proposed. Firstly, according to the interpolation theory and the nonlinear finite element theory, the tangent stiffness matrix of the tapered beam element with 3-node is deduced. Then, the degrees of freedom of the middle node are eliminated by the static condensation method, and a new tapered 2-node beam element is given. Combined with the moving coordinate method, the following coordinate with simple supported is established, and the large displacement total equilibrium equation is obtained. Finally, a numerical example shows that the proposed tapered beam element has high efficiency, and it can be used for nonlinear analysis of structures with tapered beam.