Application Of Beam Theory Research Articles

Finite element cable-model for Remotely Operated Vehicles (ROVs) by application of beam theory

Increasing autonomy, efficiency and safety for Remotely Operated Vehicles (ROVs) is crucial for future subsea operations and requires accurate models for optimal control, operations and design. This involves precise modeling of the cable in conjunction with the ROV response. This paper presents a novel three-dimensional cable model for Remotely Operated Vehicles using Euler-Bernoulli beam theory. The presented model is implemented in Matlab and takes into account the most important effects related to the response of underwater cables and ROVs. Following beam theory bending stiffness is also included, making the model applicable for low tension scenarios. The presented model is modified to allow for compression of the cable. The resulting non-linear equations are discretized spatially by the Galerkin finite element method and solved temporally by the Newmark-β time integration scheme.The model is verified experimentally in ocean tank experiments on a real ROV system. A numerical example is presented and the results are compared to previous published results. Lastly, a sensitivity analysis for the hydrodynamic parameters is presented.

Investigation of the plane stress state of a multilayer structure under heat variations

Now that composite materials are used in various fields of technology, their resistance to heat variations, which cause additional stresses because of noncoinciding layer thermal expansion coefficients, becomes increasingly topical. Apparently, the first study in this field was performed in [1], where the stress state in beam-like thermostats was determined. In [2], it was shown that delamination moments arise at the ends of two-layer beams, and the possibility of their influence on the process of delamination of two-layer composites was considered. In [3], in a similar setting, delamination stresses in multilayer structures were considered. In [4–7], the stresses at the edges of two-layer beams were calculated. We note that in all these papers the main assumptions of beam theory were used, which were confirmed experimentally for the analysis of beams. When studying the stress state near the ends of multilayer structures, the applicability of beam theory is doubtful, because the plane cross-section hypothesis, usually acceptable for beams, is justified only for the main part of the beam but not for areas near its ends, where the delamination process usually begins. The paper [8] essentially deals with a problem for a rectangle whose short sides are free from external loads and whose long sides are free from normal pressures; some longitudinal displacements imitating the temperature strains from the neighboring rectangles are given on the long sides. In [9, 10], the same problem was solved with the use of different mathematical representations of the Airy function, but the obtained numerical results practically coincide. In the present paper, we consider a system consisting of infinitely many alternating isotropic elastic layers with repeated elastic and thermal characteristics; these layers are represented as rectangles connected along the long sides.

A mode II crack problem with sliding contact in an orthotropic strip

The problem of a centrally cracked, linear elastic orthotropic strip loaded in bending by three point forces is analyzed and discussed. Coulomb friction is assumed between the crack faces to study the influence of the friction coefficient on the strain energy release rate. Under certain simplifying assumptions the problem is reduced to the solution of a singular integral equation which is evaluated numerically. The results are compared with the solution of the same problem obtained using the beam theory; limits of the application of beam theory for the reduction of experimental data are discussed.

Investigation of Effective Bending and Shear Stiffness of Thin-Walled Girders Related to Ship Hull Vibration Analysis

Application of beam theory in flexural vibration analysis of thin-walled girders is extended for the high-frequency domain by introducing the concept of effective values of beam parameters, that is, cross-sectional moment of inertia, shear area, mass, and mass moment of inertia. Formulation of these parameters is based on equivalence of deformation energy and inertia work, respectively, for a considered structure and its beam model, resulting in the same values of their natural frequencies. For illustration, the natural vertical vibration of a simply supported pontoon has been considered, where it was possible to obtain the analytical solution due to sinusoidal mode shapes. The effective values of cross-sectional moment of inertia and shear area show significant variation in frequency domain. Transfer of effective values of beam parameters, determined for simply supported structure, in the case of other boundary conditions is suggested, based on equal mode wavelengths, and checked for the free pontoon. The results show very low discrepancies compared with a three-dimensional finite-element model solution, so this procedure may be applied generally, as well as to the problem of ship hull vibration. In conclusion, the possibility of calculating the values of effective parameters for multicell ship cross sections, utilizing the theory of folded structure and the finite-element method, is pointed out.

Analysis and Performance of Fiber Composites

Analysis and Performance of Fiber Composites

Static Stresses on Wide-Bladed Propellers

Static stresses were obtained in laboratory experiments for a destroyer propeller having aerofoil blade sections and a supercavitating propeller having wedge-shaped blade sections, using specially constructed pressure chambers which allowed the blade faces to be loaded under air pressure. A new method of application of beam theory is presented which closely predicts the magnitude and distribution of radial stresses on the destroyer propeller blade. For the supercavitating propeller, neither the proposed beam theory method nor a particular computerized shell analysis can be considered entirely satisfactory for prediction of blade stresses.