Further results for modal characteristics of rotating tapered Timoshenko beams

The in-plane and out-of plane modes of free vibration of a tapered Timoshenko beam mounted on the periphery of a rotating rigid hub are investigated. The finite element method is used to discretize the beam. This formulation permits unequal breadth and depth taper ratios as well as unequal element lengths. THe effects of shear deformation, rotary inertia, hub radius, setting angle, and spinning rotation are considered. The generalized eigenvalue problem is defined using explicit expressions for the mass and stiffness matrices and numerical solutions are generated for a wide range of parameter variations. Explicit expressions of Southwell coefficients are presented for the first time for the case of rotating uniform and tapered Timoshenko beams. Comparisons are made wherever possible with exact solutions and other numerical results available in the literature. Extended results are obtained to serve as a benchmark solution for other numerical techniques and specialized application

Effect of Tapering on Natural Frequencies of Rotating Beams

The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement

Shape functions of three-dimensional Timoshenko beam element

Beams represent fundamental structural components in many engineering applications, and shape functions are essential for the finite element discretization of such structures. Premeniecki (1) derived explicit expressions for the shape functions of two-dimensional Timoshenko and three-dimensional Euler-Bernoulli (EB) beam elements. Note that for the three-dimensional EB element presented in reference (1), a change of sign is required in those entries of the third column of the shape function matrix which correspond to the twist terms. Since that pioneering work, there does not appear to have been any attempt to extend these results to a three-dimensional Timoshenko beam element, and it is the purpose of this note to fill this gap in the literature

Simulation of Balloon-Expandable Coronary Stent Apposition with Plastic Beam Elements

International audienceThe treatment of the coronary artery disease by balloon-expandable stent apposition is a fully endovascular procedure. As a consequence, limited imaging data is available to cardiologists, who could benefit from additional per-operative information. This study aims at providing a relevant prediction tool for stent apposition, in the form of a mechanically precise simulation, fast enough to be compatible with clinical routine. Our method consists in a finite element discretisation of the stent using 1D connected beam elements, with nonlinear plastic behaviour. The artery wall is modelled as a surface mesh interacting with the stent. As a proof of concept, the simulation is compared to micro-CT scans, which were acquired during the apposition of a stent in a silicone coronary phantom. Our results show that the simulation is able to accurately reproduce the stent final geometry, in a computational time greatly lower than for classic 3D finite element codes. Although this first validation step is preliminary, our work is to be extended towards more realistic scenarios, notably with the introduction of a personalised artery model and the corresponding in vivo validation