Abstract

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation.

Abstract

The objective of this paper is twofold. First, a stabilized finite element method for the incompressible Navier-Stokes is presented, and several numerical experiments are conducted to check its performance. This method is able to deal with all the instabilities that the standard Galerkin method presents, namely, the pressure instability, the instability arising in convection dominated situations and also the less popular instabilities found when the Navier-Stokes equations have a dominant Coriolis force, or there is a dominant absorption term arising from the small permeability of the medium where the flow takes place.

The second objective is to describe a nodal-based implementation of the finite element formulation introduced. This implementation is based on an a priori calculation of the integrals appearing in the formulation and then the construction of the matrix approximations, this matrix and this vector can be constructed directly for each nodal point, without the need to loop over element and thus making the calculations much faster. In order to be able to do this, all the variables have to be defined at the nodes of the finite element mesh, not on the elements. This is also so for the stabilization parameters of the formulation. However, doing this given rise to questions regarding the consistency and the conservation properties of the final scheme that are addressed in this paper.

Abstract

Unsuitable soil materials along the alignment of road projects have a significant influence on planning, design, construction, and maintenance. Expansive soils are susceptible to considerable volume changes due to seasonal variations and moisture content. Most soils found in Jimma and Ambo Zones composed of plastic clay soil, causing severe damage at the intermittent of pavement sections. This research study conducted laboratory investigation considering combinations of materials blended to stabilize the expansive soil for subgrade construction. An experimental type of study performed started by collecting specimens. Two clayey soil specimens considered to test the free swell index obtained from a depth of 1.5m to remove the organic impurities. Results indicated the chemical analysis of pumice contained 82.68%, while its physical properties of the test of fineness specific surface and residue on 45 microns showed 3770 cm2/gm and 30%, respectively. As the lime content increased, the CBR strength also increased. But, if the percent content of lime decreased with an increasing pumice content, the CBR value did not show any significant increase. Both the chemical and physical properties satisfied the requirements according to ASTM C-618. Hence, this experiment obtained 7% lime + 3% pumice as an optimum mix ratio to stabilize expansive soils.