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This paper presents a new finite element formulation of the upper bound theorem. The formulation uses a six-noded linear strain triangular element. Each node has two unknown velocities and each corner of a triangle is associated with a specified number of unknown plastic multiplier rates. The major advantage of using a linear strain element, rather than a constant strain element, is that the velocity field can be modelled more accurately. In addition, the incompressibility condition can be easily satisfied without resorting to special arrangements of elements in the mesh. The formulation permits kinematically admissible velocity discontinuities at specified locations within the finite element mesh. To ensure that finite element formulation of the upper bound theorem leads to a linear programming problem, the yield criterion is expressed as a linear function of the stresses. The linearized yield surface is defined to circumscribe the parent yield surface so that the solution obtained is a rigorous upper bound. During the solution phase, an active set algorithm is used to solve the resulting linear programming problem. Several numerical examples are given to illustrate the capability of the new procedure for computing rigorous upper bounds. The efficiency and accuracy of the quadratic formulation is compared with that of the 3-noded constant strain formulation in detail.

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Abstract. A computer model for the infiltration at the soil surface is described. The model has been developed for computation of seasonal suction changes in the soil profile. It simulates time dependence of the vector of sources and sinks for the finite element solution of Richard's equation. Lumped meteorological and soil parameters are used. Meteorological input to the model consists of the records for rainfall, pan evaporation, air temperature, and air humidity. As an example of an application of the model, the daily magnitudes of infiltration/evapotranspiration at the soil surface at Maryville, New South Wales, Australia, in March and April 1993 were obtained, and the resulting suction profile was calculated numerically. This example shows that the model adequately reflects major meteorological changes. The resulting suction profile correlates well with the experimental data, better than profiles resulting from the models, which assume periodic or sudden changes in surface suction.

This report presents a simplified large‐deflexion theory for thin flat plates subjected to normal loading. The theory is applicable to plates in which the loading is resisted primarily by the flexural rigidity of the plate. The middle surface of the plate is assumed to be inextensional so that the mode of deformation is a developable surface. There is good agreement with experiment.