Papers by Keyword: Tapered Beam

Abstract: The dynamic response of non-uniform Timoshenko beams made of axially functionally graded materials subjected to multiple moving point loads is studied by using the finite element method. The material properties are assumed to vary continuously in the axial direction according to a power law. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials obtained from the governing differential equations of a homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving loads. The effects of the distance between the moving loads, material non-homogeneity, section profile as well as aspect ratio on the dynamic response of the beams are investigated in detail and highlighted.

Abstract: Different continuous variations in the inertia are considered in achieving cantilever tapered beams to match functional design and resistance requirements. In this investigation, the expressions of linear and cubic variations in the inertia are associated to a linear mass distribution. An exact solution of the fourth order differential equation, with none constant coefficients governing the studied tapered beam element equilibrium, is obtained for each case. These displacements functions are normalized and introduced in the well known Rayleigh quotient formula for calculating the fundamental natural frequency. The accuracy of the approach over the use of the above approximation has been validated by beam references results, produced quite interesting results in numerical comparisons. Also, two curves corresponding to fixed-free and free-fixed boundary conditions, for a graphical evaluation of the natural frequency are given. They consider various degrees of taper corresponding to the two inertia variations.

Abstract: The purpose of this paper is to investigate the elastic local buckling strength and the behavior of tapered H-shaped beams under stress condition of cantilever beam. The analyses were conducted by separating H-shaped beam into two plate elements (web and flanges). From the results of analyses, authors evaluate elastic local buckling strength of each plate element, and clarify the several effects of tapered shape by comparing buckling strength and the behavior of tapered H-shaped beam with uniform H-shaped beam. In addition, authors examine coupled buckling of the two plate elements and confirm that the evaluations can be appropriate in case of coupled buckling.

Abstract: Starting from second-order effect, the governing differential equation of a tapered beam considering effects of axial force and shear deformation is established, the exact element stiffness matrix of a tapered beam with effects of shear deformation is proposed, and whose inertia moment is quadratic along the longitudinal axis. When the effect of shear deformation is ignored, the proposed stiffness matrix will degenerate into the Bernoulli-Euler ones. By using of the presented stiffness matrix, the stability and nonlinear of structures which contain tapered elements can be analyzed. Finally, the stability of some typical structures are analyzed in the numerical examples, the results prove that when the slenderness ratio is small, the effect of shear deformation can’t be neglected; As increasing, the results of beam considering shear-deflection are close to Bernoulli-Euler ones’.

Abstract: 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.