Paweł Fritzkowski

Application of the rigid finite element method to modelling ropes

Two-dimensional motion of a rope fixed at one end is considered. The Rigid Finite Element Method (RFEM) is reviewed and applied to obtain a model of the rope, including its elastic and dissipative properties. Equations of motion are derived without the small displacement assumption, using the Lagrange equations. The resulting model is compared to another one, being derived within the framework of standard analytical mechanics methods and the Lagrange formalism. Advantages of the RFE approach are discussed from a computational point of view. The presented, alternative model can be a basis for e cient numerical simulations, which seem to be useful in further, comparative studies of the rope dynamics.

NON-LINEAR DYNAMICS OF A HANGING ROPE

Two-dimensional motion of a hanging rope is considered. A multibody system with elastic-dissipative joints is used for modelling of the rope. The mathematical model based on the Lagrange formalism is presented. Results of some numerical simulations are shown for the mechanical system with kinematic excitation. Basic tools are used to qualify dynamics of the rope: the maximum Lyapunov exponent (MLE) is estimated numerically by the two-particle method, frequency spectra are generated via the Fast Fourier Transform (FFT) and bifurcation diagrams are produced. Influence of the excitation amplitude and frequency as well as damping on behaviour of the system is analyzed. The work can be treated as the first step in more advanced analysis of regular and chaotic motion of the complex system.

Kinematics of a vertical axis wind turbine with a variable pitch angle

A computational model for the kinematics of a vertical axis wind turbine (VAWT) is presented. A H-type rotor turbine with a controlled pitch angle is considered. The aim of this solution is to improve the VAWT productivity. The discussed method is related to a narrow computational branch based on the Blade Element Momentum theory (BEM theory). The paper can be regarded as a theoretical basis and an introduction to further studies with the application of BEM. The obtained torque values show the main advantage of using the variable pitch angle.A computational model for the kinematics of a vertical axis wind turbine (VAWT) is presented. A H-type rotor turbine with a controlled pitch angle is considered. The aim of this solution is to improve the VAWT productivity. The discussed method is related to a narrow computational branch based on the Blade Element Momentum theory (BEM theory). The paper can be regarded as a theoretical basis and an introduction to further studies with the application of BEM. The obtained torque values show the main advantage of using the variable pitch angle.

Flow of subretinal liquid through the retinal hole after surgery – mechanical model and FEM simulations

The objective of this study is to analyze subretinal liquid dynamics by means of numerical simulations in patients with retinal detachment after insertion of intussusception. The main parameter being analyzed is the outflow velocity of subretinal fluid through the hole in the retina. All calculations were performed using FEM and the results were evaluated in relation to the velocity of outflow when considering parameters such as; i) speed of eyeball movement, ii) shift of intussusception in relation to the center of the hole in the retina, iii) viscosity of the subretinal fluid. Results obtained suggest an optimal speed of eyeball movement for patients to achieve maximal speed of outflow of subretinal fluid. This is a significant factor in achieving improved clinical outcomes for patients.