Łukasz Drąg

Modelling of Ropes with Consideration of Large Deformations and Friction by Means of the Rigid Finite Element Method

This paper presents a model of a rope, which is an example of a slender system. The method used for modelling is the modified rigid finite element method, which enables us to consider not only bending flexibility but also longitudinal flexibility. A new approach presented in the paper is validated by comparison of our own results with an analytical solution for a catenary line. For this problem the influence of both the number of elements into which the link is discretised and various values of stiffness coefficient is analysed. Numerical simulations of the dynamics of a rope of an offshore crane lifting a load from a vessel are presented.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z′Y′X′. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Application of the Rigid Finite Element Method to Static Analysis of Lattice-Boom Cranes

Abstract In the paper a nonlinear model of a lattice-boom crane with lifting capacity up to 700mT for static analysis is presented. The rigid finite element method is used for discretisation of the lattice-boom and the mast. Flexibility of rope systems for vertical movement and for lifting a load is also taken into account. The computer programme developed enables forces and stress as well as displacements of the boom to be calculated. The model is validated by comparison of the authors’ own results with those obtained using professional ROBOT software. Good compatibility of results has been obtained.

Artificial Neural Network for Stabilization of the Flexible Rope Submerged in Sea Water

The paper presents an application of artificial neural network to control the position of the end of the rope. The proposed model allows stabilization of payload at a given depth despite the sea waves and the sea currents. The flexible rope is discretized by means of the one of the modifications of rigid finite element method. For each element of a rope submerged in water, the hydrodynamics forces are taken into account. The MLP and the RBF types of ANN network are considered. Selection of ANN network architecture and calculation of neurons weights has been made in own software. The influence of the sea environment, vessel velocity and lumped mass at the end of the rope on the displacement of the end of the rope is discussed.

Numerical Effectiveness of Different Formulations of the Rigid Finite Element Method

Abstract The paper presents an application of different formulations of the rigid finite element method (RFEM) to dynamic analysis of flexible beams. We discuss numerical effectiveness of the classical RFEM and an alternative approach in which continuity of displacements is preserved by means of constraint equations. The analysis is carried out for a benchmark problem of the spin-up motion in planar and spatial cases. Torsion is omitted for numerical simulations and two cases of the new approach are considered. The results obtained by means of these methods are compared with the results obtained using a nonlinear two-node superelement