O. C. Zienkiewicz

Triangles and tetrahedra in explicit dynamic codes for solids

Explicit dynamic codes which are used currently for the study of plastic deformations in impact, or with some modification for metal forming, suffer two serious limitations. First, only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing. Second, even with the use of such elements, special devices such as reduced integration must be introduced to avoid locking and reduce costs. These necessitate complex hour glass control, mending-type procedures. The main difficulties are those due to the need of treatment of (almost) incompressible deformation modes. Recently, similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem, thus allowing an almost unrestricted choice of element interpolations.

Achievements and some unsolved problems of the finite element method

After outlining the early history of the finite element method the paper concentrates on to (1) some important achievements of the last decade and (2) presents an outline of some problems still requiring treatement. In the first part, the developments of the patch test for assessment of elements, new developments of adaptive refinement and the principles of the general CBS algorithm for fluid dynamics are presented. Copyright

Finite element methods in the analysis of reactor vessels

The application of the finite element method to linear and non-linear problems in pressure vessel technology is presented. New developments for dealing with components such as liners, prestressing cables and reinforcement are outlined and some improvements possible in thin shell situations are discussed. A general solution technique for non-linear analysis is presented and applied firstly to the problem of the plastic behaviour of steel pressure vessels. The failure of PCRVs by concrete cracking is then considered. Finally, the time-dependent phenomenon of creep is discussed. In all cases the theory is illustrated by practical examples.

New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems

A new class of unconditionally stable staggered implicit–implicit time-stepping algorithms for coupled soil-pore fluid dynamic problems is presented. The proposed schemes are stabilized with a pressure correction method and the staggered procedure introduced earlier by the second author is a simplified case of the new algorithms. The stabilized procedure is efficient in numerical time domain analysis of soil-pore fluid interaction occurring in earthquake and consolidation problems. Several examples of linear and non-linear problems demonstrate the stability and accuracy of the proposed numerical solution algorithms.