Marek Szczotka

Rigid Finite Element Method in Analysis of Dynamics of Offshore Structures

This book describes new methods developed for modelling dynamics of machines commonly used in the offshore industry. These methods are based both on the rigid finite element method, used for the description of link deformations, and on homogeneous transformations and joint coordinates, which is applied to the modelling of multibody system dynamics. In this monograph, the bases of the rigid finite element method and homogeneous transformations are introduced. Selected models for modelling dynamics of offshore devices are then verified both by using commercial software, based on the finite element method, as well as by using additional methods. Examples of mathematical models of offshore machines, such as a gantry crane for Blowout-Preventer (BOP) valve block transportation, a pedestal crane with shock absorber, and pipe laying machinery are presented. Selected problems of control in offshore machinery as well as dynamic optimization in device control are also discussed. Additionally, numerical simulations of pipe-laying operations taking active reel drive into account are shown.

The Rigid Finite Element Method

Actual kinematic chains commonly contain links whose flexibility greatly exceeds that of other links. It may then be necessary to take that flexibility into account. Booms of cranes and certain links of manipulators count among those. A large number of approaches in analysis of multibody systems can be found in literature with with one and more flexible links [Zienkiewicz O. C., 1972], [Wittbrodt E., 1983], [Wojciech S., 1984], [Huston R. L., Wanga Y., 1994], [Arteaga M. A., 1998], [Zienkiewicz O. C., Taylor R. L., 2000], [Berzeri M., et al., 2001], [Adamiec-Wojcik I., 2003], [Wittbrodt E., et al., 2006]. Chapter 9 introduces models of offshore cranes (a column one and an A-frame) which enable taking into account the flexibility of the supporting structure.

Numerical Effectiveness of Models and Methods of Integration of the Equations of Motion of a Car

The paper presents models of car dynamics with varying complexity. Joint coordinates and homogenous transformations are used to model the motion of a car. Having formulated the models of the car, we discuss the influence of the complexity of the model on numerical efficiency of integrating the equations describing car dynamics. Methods with both constant and adaptive step size have been applied. The results of numerical calculations are presented and conclusions are formulated.

THE INFLUENCE OF FLEXIBILITY OF THE SUPPORT ON DYNAMIC BEHAVIOR OF A CRANE

The problem of control of the motion of a crane is considered in the paper. The mathematical model of the system is formulated using joint coordinates and homogenous transformations. The dynamic optimization method is applied in order to find drive functions realizing the desired trajectory and stabilizing the final position of the load at the end of motion in spite of the flexibility of the support. The results of numerical calculations and possible applications of models developed using artificial neural networks are also presented.

Modelling of Joining Elements: Constraint Equations

Individual links of a kinematic chain are often interconnected by elastic or damping (or both) elements. Among these are mainly: springs, dampers, absorbers, actuators. Components expressing the potential energy accumulated in such elements and its dissipation need to be introduced to the system’s equations of motion. The present chapter discusses a method of modelling spring-damping elements treated as massless objects. Constraint equations occurring when kinematic subchains are joined in certain systems are also presented.

Equations of Motion of Systems with Rigid Links

In the current chapter the main steps of determining the components of the equation of motion for open kinematic chains consisting of rigid links are presented [Wittbrodt E., et al., 2006]. The method is based on the Lagrange equations of the second order, homogeneous transformations and joint coordinates.

Nonlinear Models of Materials

In numerous technical applications the supporting structure of a device is assumed to be subjected to stresses within the limits of proportionality, i.e. where the Hooke’s law is applicable. It is also the case with offshore cranes. In the installation process of underwater pipelines with the reel method, however, the pipes are commonly deformed plastically when they are wound onto the reel. Furthermore, material exposed to prolonged deformation may show a tendency to creep. Hence, the present chapter which briefly introduces these models of construction materials: elasto-plastic and visco-elastic.

Overview of Selected Problems in Offshore Technology

Extraction of undersea natural resources, particularly oil and gas, has expedited the progress in offshore technology for a few decades, including the construction of platforms as well as the development of new extraction techniques and methods of laying underwater pipelines. Various types of cranes are an important aid in the construction of extraction infrastructure as well as its operation and servicing. The current chapter describes some most important elements of the infrastructure necessary for extracting oil and gas and methods of installation of offshore pipelines. Specific conditions pertaining to offshore cranes’ operation and their basic typology are presented.

Applications of Models of Offshore Structures

Each offshore structure is unique in the sense that it is built only after a customer with a specific need actually places an order. Design companies and manufacturers of engineering systems of this type are often small and medium enterprises, which cannot afford purchasing costly computer software packages for numerical computation involved in dynamics of mechanical systems. Therefore, they often employ custom, in-house dynamic models of the structures designed. In the present chapter, dynamic models of the following are presented: a gantry suited for relocating sets of BOP valves on an extraction platform, a column crane and a device for laying pipes on the seabed. The formulation of models thereof leverages the methods described in earlier chapters.

Selected Applications Related to Control of Offshore Structures

Dynamic analyses of mechanical systems are often considered together with problems related to their control. With traditional ways of operating machines it the operator who decides what the working motions are. In contemporary machines, it is becoming commonplace to support the process of control. Control systems based on microprocessor technology (programmable drivers, onboard computers) are supposed to facilitate human work or even replace it. They enable realization of various strategies unachievable with manual control. Automated control is used also in offshore structures, including cranes. The criteria of control strategies may be different, for example: