No abstract

The visco-plastic model is established as a realistic general description of soil behaviour as well as a computationally convenient fiction for solving any properly formulated plasticity problem. The Paper focuses attention on simple elastic-ideally plastic formulations in which both associated and non-associated forms of behaviour are assumed. In the non-associated form the usual bounding theorems are not applicable and it is of interest that in some cases collapse situations significantly different from those given by limit theorems are predicted. Also, some problems of strain-dependent plasticity are solved to demonstrate the flexibility of the viscoplastic algorithm. Le modèle viscoplastique constitue une description générale et réaliste du comportement du sol aussi bien qu'un modèle facilement calculable pour résoudre tout problème de plasticité convenablement formulé. L'étude concentre l'attention sur des schémas (ou modèles) où les deux types de comportement (élasticité simple et plasticité idéale) sont pris en compte simultanément ou séparément. Dans les schémas (ou modèles) où les deux types de comportement ne sent pas associés, les théorèmes limites ordinaires ne sont pas applicables et il est intéressant de noter que dans certains cas on prévoit des situations de rupture très différentes de celles données par les théorèmes limites. Il y a également quelques problèmes de déformation plastique qui sent résolus afin de démontrer la flexibilité de l'algorithme visco-plastique.

SUMMARYThe paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration.Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy.Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.

SUMMARYA robust, artiÿcial compressibility scheme has been developed for modelling laminar steady state and transient, incompressible ows over a wide range of Reynolds and Rayleigh numbers. Artiÿcial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations. A locally generalized preconditioner is introduced, designed to be robust and o er good convergence rates. Free artiÿcial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artiÿcial compressibility scheme. Memory e ciency is achieved through a multistage, pseudo-timeexplicit time-marching solution procedure. A node-centred dual-cell edge-based ÿnite volume discretization technique, suitable for unstructured grids, is used due to its computational e ciency and high-resolution spatial accuracy. In the interest of computational e ciency and ease of implementation, stabilization is achieved via a scalar-valued artiÿcial dissipation scheme. Temporal accuracy is facilitated by employing a second-order accurate, dual-time-stepping method. In this part of the paper the theory and implementation details are discussed. In Part II, the scheme will be applied to a number of example problems to solve ows over a wide range of Reynolds and Rayleigh numbers.