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Notes: Summary Failure of earth structures or laboratory specimens of soils is often characterized by the existence of bands or surfaces at which strain localizes. Numerical simulation of shear band development has attracted the attention of many research groups during past years. Here it is proposed that adaptive remeshing techniques can be applied to better simulate strain localization problems in geotechnique. The algorithm has been previously applied to compressible fluid dynamics problems to capture discontinuities such as shocks. A new refinement functional has been introduced to improve quality of produced meshes. Finally, the algorithm is applied to solve inception and development of shear bands on both homogeneous stress fields and non-homogeneous stress fields.

Notes: Abstract An adaptive remeshing procedure for solving Navier-Stokes incompressible fluid flow problems is presented in this paper. This procedure has been implemented using the error estimator developed by Zienkiewicz and Zhu (1987, 1989) and a semi-implicit time-marching scheme for Navier-Stokes flow problems (Zienkiewicz et al. 1990). Numerical examples are presented, showing that the error estimation and adaptive procedure are capable of monitoring the flow field, updating the mesh when necessary, and providing nearly optimal meshes throughout the calculation, thus making the solution reliable and the computation economical and efficient.

Notes: The severe restrictions of the Babuška-Brezzi stability criteria permit only a limited number of interpolations for velocities (displacements) and pressure to be used for incompressible behaviour. These restrictions preclude the use of many useful elements. We show in this paper how such difficulties can be side-stepped by seeking the steady state solution through the use of various time marching schemes. This permits a simple iterative approach to incompressible (or nearly incompressible) problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow, etc.

Notes: A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.

Notes: Computational Mechanics or Computational Applied Science is today the base on which most of the achievements of engineering and physics are built. Its concern is the solution of complex mathematical theories in numerical terms, without which the translation of these into practical artifacts would be impossible. Indeed, by providing such quantitative measures it enhances the understanding of the physical phenomena and stimulates further development of theory and physical experiment.Most of the theory underlying physical phenomena is cast in terms of, often involved, differential equations for which closed forms of solution are seldom possible. Numerical approximation or discretization processes are necessary for quantitative solution. Here the first steps were taken at the start of this century by the pioneering work of Richardson introducing finite difference approximations. The invention of relaxation methods by Southwell during the Second World War allowed many practical solutions to be achieved. However, it was the advent of the electronic digital computer that marked the turning point in Computational Mechanics. The dramatic escalation of the power of these machines, which still continues today, allowed the development of the field of Computational Mechanics as we know it.It is through this computer power that such methods of approximations as finite elements, finite differences, boundary solutions and spectral processes became a practical reality, though each was anticipated in the pre computer area. It is not surprising therefore, that the mathematical foundations and the full development of such methods have been accomplished only relatively recently.Today we see the field of activity subdivided between those specializing in the development of the various computational approximation processes and those seeking optimal numerical solutions for their particular field of application. It is the objective of this Congress and indeed of the International Association of Computational Mechanics to provide a forum at which an interdisciplinary exchange of information can take place between the various sections and disciplines of the whole field. Indeed, this is the way progress can best be achieved. Recent history indicates that substantial advances are as frequently made due to a method seeking a new application as through a problem requiring a solution.In recent history we have seen on occasion a liaison of a particular computational approximation method to a field of application occurring through historical accident. Here the intimate association of the finite method and the field of SOLID MECHANICS (CSM or Computational Solid Mechanics) and that of the finite differences with FLUID DYNAMICS (CDF or Computational Fluid Dynamics) can be observed as classical examples. Today the advent of new application fields and a better understanding of the approximation theory are helping to break down the barriers and ensure a more rational matching of objectives and methods. We shall illustrate the lecture with examples of such recent progress and state some possibilities as yet unexplored. Indeed, we are sure that the Congress will achieve in much more detail the same aims.This presentation stresses the essential unity of the subject and discusses some areas where progress and research are currently active. Two of such, adaptive error controlled analysis and treatment of hyperbolic (fluid) problems, are singled out due to their wide applications.

Notes: This note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases. It is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided. The algorithm permits the use of equal interpolation for all variables by avoiding the need for the Babuska-Brezzi constraints in regions where the flow is nearly incompressible.The success of the algorithm, which here is written for the non-conservative equation form, is demonstrated on several examples ranging from (nearly) incompressible through transonic regions to supersonic flows. Up to mild shocks such as those occurring in the examples presented in this paper, no 'artificial' viscosity is added at any stage.The algorithm extends some concepts introduced in an earlier paper.

Notes: A modification has been introduced to the new superconvergent patch derivative recovery technique recently developed (Zienkiewicz and Zhu, 1991). By use of a locally normalized co-ordinate system, the application of this technique can now be applied to higher-order finite-element shape functions. Numerical studies are carried out for up to 6th-order elements in one dimension and for up to quartic elements in two dimensions, and superconvergent results are obtained for all examples tested.

Notes: An adaptive refinement procedure using a new automatic quadrilateral element mesh generator is presented. The performance of the adaptive procedure in achieving a given accuracy with different mesh refinement strategies is compared. It is found that when using bilinear or biquadratic quadrilateral elements refinement strategies of both mesh enrichment and mesh regeneration can lead to a prescribed accuracy being achieved by the Zienkiewicz-Zhu adaptive procedure1 with the optimal rate of convergence. However, fewer mesh refinement steps are needed if the strategy of mesh regeneration is employed with the newly developed automatic quadrilateral element mesh generator2.