The use of conventional iterative techniques such as conjugate gradient methods has not been effective in the analysis of large deformation problems. In order to achieve convergence the standard practice requires the analyst to reduce the bulk modules by a factor of one hundred or so. In applications such as flex joints this cannot be tolerated. We are developing a pre-conditioner that will be inexpensive and effective so that the real material properties of an elastomer can be used.
This project is highly relevant to the primary goals of the OTRC- development of knowledge and training of engineers in the exploitation of deep water petroleum production. This program contributes to the development of realistic models to predict damage to structures subject to numbers of load cycles, and guides to effective design of joints and connections. The use of flex joints will certainly be critical in reducing the repeated bending moment applied to the risers/tendons – the design of effective composite structural systems.
The pre-conditioner that we have developed has been tested on two and three dimensional finite element models of rubber pads. Our scheme is effective in relieving the poor conditioning of the equilibrium equations due to near incompressibility. Large shape factors and or nonuniform meshes lead to poor conditioning of the shear response (independent of bulk stiffness). To be effective our iterative solver must work well in these cases. We are testing variations of our pre-conditioner that are designed to treat the shear as well as bulk induced ill-conditioning. We expect to implement our method and to demonstrate its practical use in bearing problems by the end of the summer.
There is an ongoing joint industry funded program on Fatigue Life of Laminated Elastomeric Bearings that is being carried out by Materials Engineering Research Laboratories of Hertford England. Dr. Becker works with the JIP. At The University of Texas Austin the CAM (Computational and Applied Mathematics) group, comprising engineering, mathematics and computer science faculty and students, have developed a variety of software tools that will be useful in implementing our proposed methods.
The results of this project will provide a sound starting point for the development of a production program. With the availability of the finite element solver that we will develop , along with some important development in material modeling, it will be practical to put together a code that will predict the initiation and growth of fatigue cracks in flex joints. The design of these components will be improved and rational monitoring of the components in the field will be possible.
Related Publications: Chang, J.H. and Becker, E.B., “Finite element calculation of energy release rate for 2-D Rubbery materials with non-conservative crack surface tractions,” International Journal for Numerical Methods in Engineering, Vol. 33, pp. 907-927, 1992.
Luneau, M.J. “Investigation of a Finite Element Method for Modeling Cracks in Elastomers,” M.S. Thesis, The University of Texas at Austin, December 1992
Marusek, R.E. and Becker, E.B. “A Finite Element Procedure for Axisymmetric Elastomeric Solids Under General Loading,” International Journal for Numerical Methods in Engineering, Vol. 36, pp.2031-2048, 1993.