The paper presents a classification of mathematical formulations commonly encountered in connection with solution of non-linear finite element problems. The principal methods for numerical solution of the non-linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap-through and snap-back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non-linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several examples.A crucial factor in the development of finite element computer programs for non-linear analysis is the proper selection of solution algorithms. Non-linear problems, in general, require the solution of a set of non-linear algebraic equations, which, in itself, is a formidable task. In addifion, the non-hear prob\ems encountered in structural mechanics may be path-dependent (e.g. plasticity, non-conservative loading) or they may possess multiple solutions (e.g. snap-through buckling). Thus, the quest for reliable solutions to non-linear structural problems is indeed very demanding.Solution procedures for non-linear problems have been discussed by several authors.'-' As opposed to linear problems, it is extremely difficult, if not impossible, to develop one single method of general validity that can be used in a routine manner. Several of the existing solution procedures are either limited to certain classes of non-linear problems, or certain requirements must be satisfied in order to ensure convergence to the correct solution. Very often, the particular problem at hand will require special consideration and it may be necessary to modify the available solution algorithms. For these reasons, it is believed that a computer program for non-linear analysis should possess several alternative algorithms for the solution of the non-linear system. These procedures should also allow for the possibility of an extensive control over the solution process by parameters that are input to the program. Such a scheme would lead to increased flexibility, and the experienced user has the possibility of obtaining improved reliability and efficiency for the solution of a particular problem.t Associate Professor. f dr. ing. 5 Lecturer, dr. ing.
Vortex induced vibration (VIV) of free spanning pipelines in current is considered. In standard VIV estimation, one mode of oscillation is considered only. Increasing the length of the span, several modal shapes may be excited. Further, due to the sag effect of a long free span, the dynamic properties in vertical and horizontal direction of the span are different. This causes a much more complex VIV response pattern for long free spans than for short spans. The observed VIV response of long free spans during model testing is discussed. Hypotheses that may explain the observed behaviour are presented. Also a format of new design principles for long free spans is outlined.
The paper presents new approaches for nonlinear system analysis of trusswork platforms. The main idea behind the technique is.to minimize the cost of the nonlinear analysis by reducing the number of parameters and the size of element model.
A brief description is given on the theoretical basis of the computer program including the formulation of incremental stiffness with modifications for plastic hinges. Special emphasis is given to the choice of adequate interpolation functions and to the evaluation of nonlinear element characteristics.The solution strategy follows the conventional incrementation procedure with special algorithms for handling stability problems and load reversal. The numerical procedure is demonstrated on buckling analysis of simple columns and_ frames.Comparison with experiments and alternative numerical computations proves the accuracy and efficiency of the procedure. Practical design examples are given on progressive collapse analysis of a jacket structure, a deep water tripod typer of platform and a module support frame.
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