Helicoseir as Shape of a Rotating String (I): 2D Theory and Simulation Using ANCF

A physically simple but mathematically cumbersome problem of rotating heavy string with one fixed top point was studied. A nonlinear equation of its two-dimensional shapes of relative equilibrium was obtained and solved numerically. A linear case of small displacements was analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of a bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions were studied with the help of a simulation using the absolute nodal coordinate formulation (ANCF); the equilibriums were found to be instable. The reason for instability is explained using a variational principle. The outlines for further full three-dimensional analysis are briefly proposed in this paper, and the full derivation will be explained in the next paper.     

Restricted proteolysis of legumin of broad beans: Effect on thermodynamic properties of aqueous solutions and interaction with ficoll

Thermodynamic properties of aqueous solutions of both native and modified legumin of broad beans (Vicia faba L.) have been examined. A restricted trypsin-induced proteolysis was used to modify protein structure. Evaluation of protein affinity to ficoll in aqueous solutions showed that modified protein possessed higher hydrophilicity. Thermodynamic properties of diluted solutions were used to predict the phase behaviour in concentrated systems containing protein and ficoll. At specific concentrations of native legumin, the system can separate in two phases, whereas in the case of modified protein the single-phase behaviour of the system was predicted for any concentrations of both components. The experimental data obtained in concentrated systems confirmed predictions of thermodynamic analysis of diluted solutions.     

Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation

We propose a way to generate new finite elements in the absolute nodalcoordinate formulation (ANCF) and use a generalization of displacementfields and degrees of freedom (d.o.f.) of ordinary finite elements usedin structural mechanics. Application of this approach to 16- and12-d.o.f. rectangle plate elements as well as to 9-d.o.f. triangleelement gives, accordingly, 48-, 36- and 27-d.o.f. ANCF plate elements.We perform a thorough study of a 48-d.o.f. Hermitian element. Its shapefunction set is a Cartesian product of sets of one-dimensional shapefunctions for beam elements. Arguments of the shape functions aredecoupled, that is why an explicit calculation of terms of equations ofmotion leads to single integration only. We develop several models ofelastic forces of different complexity with their Jacobian matrices.Convergence and accuracy of the finite element is demonstrated ingeometrically nonlinear static and dynamic test problems, as well as inlinear analysis of natural frequencies.     

Restricted enzymatic hydrolysis of legumin of broad beans (Vicia faba L.) by trypsin in concentrated solutions. Control of hydrolysis process at the expense of change of enzyme-substrate ratio

Kinetics and mechanism of proteolysis of broad bean (Vicia faba L.) legumin by trypsin in concentrated solutions at different enzyme-substrate ratios (E/S = 1/40, 1/100, 1/200, 1/1000) were studied. By the method of HPLC it was established that during proteolysis process (E/S = 1/40) take place both protein content decrease in hydrolysate and change of its molecular mass (from 360 to 280 kD), which evidences for the mixed type of proteolysis, including cooperative and non-cooperative mechanisms. Decrease of E/S from 1/40 up to 1/100–1/1000 leads not only to unproportional drop in proteolysis rate, but also to decrease of the relative contribution of cooperative proteolysis which is, possibly, connected with presence in protein molecule of at least two groups of attack sites, differentiating by their affinity with enzyme. Change of enzyme-substrate ratio is accompanied also by change of subunit composition of product of non-cooperative proteolysis (‘modified protein’) and also of temperature and enthalpy of its denaturation.     

Three- and four-noded planar elements using absolute nodal coordinate formulation

This paper investigates two new types of planar finite elements containing three and four nodes. These elements are the reduced forms of the spatial plate elements employing the absolute nodal coordinate approach. Elements of the first type use translations of nodes and global slopes as nodal coordinates and have 18 and 24 degrees of freedom. The slopes facilitate the prevention of the shear locking effect in bending problems. Furthermore, the slopes accurately describe the deformed shape of the elements. Triangular and quadrilateral elements of the second type use translational degrees of freedom only and, therefore, can be utilized successfully in problems without bending. These simple elements with 6 and 8 degrees of freedom are identical to the elements used in conventional formulation of the finite element method from the kinematical point of view. Similarly to the famous problem called “flying spaghetti” which is used often as a benchmark for beam elements, a kind of “flying lasagna” is simulated for the planar elements. Numerical results of simulations are presented.     

Large Deflection Analysis of a Thin Plate: Computer Simulations and Experiments

Many previous studies have conducted computer-aided simulations ofelastic bodies undergoing large deflections and deformations, but therehave not been many attempts to validate their numerical results. Thesubject of this paper is a thin clamped plate undergone large vibrationdue to attached end-point weight. The main aim of this paper is to showthe validity of the absolute nodal coordinate formulation (ANCF) bycomparing to the real experiments. Large oscillations of thin plates arestudied in the paper with taking into account effects of an attachedend-point weight and aerodynamic damping forces. The physicalexperiments are carried out using a high-speed camera and dataacquisition system. For numerical modeling of the plate, the absolutenodal coordinate formulation is used.     

Matching of physical experiments and multibody dynamic simulation for large deformation problems

Many papers have studied computer simulations of elastic bodies undergoing large deflections and large deformations. But there have not been many attempts to check the validity of the numerical formulations because the simulation results could not be matched without correct input data such as material properties and damping effects. In this paper, these values are obtained from real experiment with a high-speed camera and a data acquisition system. The simulation results with the absolute nodal coordinate formulation (ANCF) are compared with the results of real experiments. Two examples, a thin cantilever beam and a thin plate, are studied to verify whether the simulation results are well matched to experimental results.     

Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF

This paper is the second one devoted to studying the dynamical behavior of a rotating uniform string with one fixed top point. Two-dimensional shapes of relative equilibrium for a string were analyzed in our paper [3] both analytically and numerically and found to be instable. This fact disagrees with the experimental appearance of this so-called helicoseir problem because one can easily demonstrate that its stable motion is possible. In this paper, spatial nonlinear equations of motion are derived and shown that a 2D equilibrium equation is one of their partial cases. The equations are, however, very complicated that is why we decided at first to analyze the motion numerically by a finite element approach called the absolute nodal coordinate formulation (ANCF). We developed a new 12-dof element of a thin string based on the Euler-Bernoulli theory. The simulation shows that the undamped spatial motion of the helicoseir is stable and looks like self-excited oscillations near the flat instable configurations that were obtained previously. This stability is destroyed when external damping is added to the system. Some examples of bifurcation instability fore spatial motion are presented; they satisfy the bifurcation diagram obtained in the previous work. Unfortunately, numerical simulation cannot give answers to some interesting questions, e.g. dependence of parameters of the self-excited oscillations on the angular velocity of rotation. Thus, further analytical research of this problem is desirable.