Solution Of Structural Strength By Free Hexagon Method
Free (open access)
P. Procházka & V. Dolezel
Numerical methods seem to be the cheapest tool for assessing different types of structures. If the theory of damage is to be involved in the formulation of the problem to be solved, special treatment is required. The methods, which are extensively used, start with realization of the trial body by a continuum. We can name the \“Cohesive zone method,” which deals with Barenblatt's theory, for example. In our problem such methods are on the one hand difficult to apply and on the other hand exhibit unreal behavior, according to a couple of test examples. This is why test experiments have been carried out to gain knowledge about a reasonable approach for solving the problem. The free hexagon method seems to be very promising. First, the method will be briefly described and basic formulas will be derived and then some applications to structural strength below foundations will be presented. In comparison with some previous works of the authors of this paper, the method presented here involves time-dependent problem with Newtonian forces, which are caused by contact forces of moving particles. It simplifies the body of the earth (soil) to a set of hexagons, which are, or are not, in mutual contact. The material properties of the hexagons are determined from the state of stresses. In this paper we adjust the idea of PFC (particle flow code), which starts with balls instead of hexagons and dynamical equilibrium, while in our case the static equilibrium is considered. The hexagons represent a typical shape of grains the earth consists of. The model proposed in this paper may, in contrary to modern numerical methods (FEM, BEM, etc.), enable one to disconnect the medium described by the balls, when needed (e.g. providing certain requirement on tensile strength). The most natural contact conditions—Mohr-Coulomb hypotheses—may be simply introduced and, after imposing all such contact conditions.