2089
Technical Committee 207 /
Comité technique 207
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
3 APPLICATION
1.2
Numerical model
The presented topology optimization algorithm is applied to a
vertically loaded strip footing foundation. The topology
underneath the foundation is to be optimized. The inital width
of the foundation is 2 m and the height is 1 m. The load-
settlement behavior is simulated in a 2D finite-element analysis.
The discretization of the model is shown in Figure 5.
The foundation is vertically loaded with 500 kN. The soil
and the improved material underneath the strip foundation is
modeled using the hypoplastic constitutive model after von
Wolffersdorff (1996) with the extension of intergranular strain
after Niemunis and Herle (1997). Detailed information can be
found in Pucker and Grabe (2011).
1.3
Optimization
Three optimizations are performed at different material
volumes. The material volume is 2%, 5% and 10% of the design
domain. The design domain is 20 m of width and 14 m of
height, see Figure 5.
1.4
Results
In Figure 7 the optimized topologies with 2%, 5% and 10%
material volume are illustrated. Regarding the 2% material
volume, mainly the aera at the foundation edges are compacted.
Since the foundation can be considered to be rigid, the
optimization results can be explained with the theory of a rigid
foundation on an elastic half-space, according to which high
stresses will occur at the edges of the foundation. The
optimization algorithm compacts the material mainly in these
areas.
Figure 6 shows the displacement of the soil underneath the
foundation with the unoptimized (Figure 6 a) und the optimized
(Figure 6 b) structure with a volume of 5%. The settlements can
be reduced up to 50%.
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Figure 4: Change-over of the Young's modulus
E
of two different
materials depending on different values of the penalty term
p
Figure 5. Discretization of the FE-model of a strip foundation with a
width of 2 m and a height of 1 m, vertically loaded with 500 kN at the
loading point P
Figure 6. Vertical displacement before (left) and after (right)
the topology optimization with 5% material volume
