ملخص: This paper presents a four-node Timoshenko beam finite element with variable degrees of freedom. Both the element transverse displacement and the rotation of the beam cross-section are described by a cubic polynomial plus a variable number of trigonometric sine terms. The polynomial terms are used to describe the transverse displacements and the rotations of the beam cross-section at the element's four nodes and the sine terms are used to provide additional freedom to the interior of the element. The four nodal transverse displacements and rotations of the beam cross-section and the amplitudes of the trigonometric sine terms are used as generalized co-ordinates. Inter-element compatibility is achieved by matching the generalized co-ordinates at the element end nodes. Numerical results of frequency calculations are given for simply supported and cantilever beams with two different slenderness ratios. Comparisons are made with exact Timoshenko beam solutions and with finite element solutions for the degenerate case with no trigonometic terms to represent a polynomial finite element. Comparisons show that using one or two variable order Timoshenko beam elements with a few trigonometric terms yields a better accuracy with fewer system degrees of freedom than using many polynomial Timoshenko beam finite elements.

لغة: إنجليزية