Solution Of Structural Strength
By Free Hexagon Method
Author(s)
P. Procházka & V. Dolezel
Abstract
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.
Keywords
Related Book
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