Biomedical Engineering Reference
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Fig. 7.44 Plane strain model
with the initial support
configuration (t 0 = 35 mm)
prior support shape
optimization
two-dimensional 3-node linear plane strain elements are used to model foam
material, bone structures are assumed as rigid and are modelled with 3-node
triangular facet elements. Assigned fat and muscle tissue material parameters are
as derived in Sect. 5.2 .
To avoid high element distortion of the support mesh due to uncontrolled
displacement of the top layer nodes in the optimization process, restrictions were
introduced limiting the mesh gradients in the vertical direction. Thus, a smooth
''connecting line'' linking the design nodes is obtained. These restrictions limit the
difference
in
vertical
displacement
of
two
neighbouring
nodes
to
a
certain
magnitude, P. In the case of vertical smoothing one obtains
x 2 ; k þ 1 x 2 ; k P
for
k ¼ 1 ; 2 ; ... ; N 1
ð 7 : 1 Þ
where x 2 ; k is the vertical displacement coordinate of the k-th node, N is the number
of top layer nodes and P is the maximum allowable vertical distance between two
neighbouring nodes.
The design space sets limits for node displacements in both the negative and
positive vertical directions: (1) top layer nodes are restricted from intersecting with
the buttock model mesh preventing initial penetration and contact interaction
difficulties leading to convergence problems, (2) top layer nodes are prevented from
reducing to zero volume by incorporating limits for the minimum element side
length. For simplicity, features to rearrange the coordinates of the internal nodes of
the support mesh, to retain equal mean element side lengths, have been neglected.
7.2.3.2 Optimized Support Shapes
The modified cushion support geometry obtained from the optimization process
using the plane strain model (symmetric half model) in the transversal body plane
is depicted in Fig. 7.45 a. In the same manner, shape optimization was additionally
performed employing a plane strain model representing the sagital body plane with
the plane intersecting the ischial tuberosity. Modified cushion geometry obtained
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