Biomedical Engineering Reference
In-Depth Information
18.5 The m-file
demo_bend
in the directory
twode
analyses the pure bending
of a single element (for quadrilaterals) or two elements (for triangles). The
analysis is based on plane stress theory. The geometry is a simple square
domain of dimensions 1
1. Along the left edge the displacements in the
x
-direction are set to zero, while at the lower left corner the displacement in
the
y
-direction is set to zero to prevent rigid body motions. The two nodes
at the right edge are loaded with a force
F
of opposite sign, to represent
a pure bending moment. Investigate the stress field for various elements:
linear triangle, bi-linear quadrilateral, and their quadratic equivalents.
Explain the observed differences. To make these choices use
itype
and
norder
:
itype = 1 : quadrilateral element
itype = 20 : triangular element
norder = 1 :(bi-)linear element
norder = 2 :(bi-)quadratic element
×
18.6
In a shearing test a rectangular piece of material is clamped between a
top and bottom plate, as schematically represented in the figure. This
experiment is generally set-up to represent the so-called 'simple-shear'
configuration. In the simple-shear configuration the strain tensor is given as
ε
=
ε
xy
e
x
e
y
+
ε
xy
e
y
e
x
using the symmetry of the strain tensor. As a consequence, the stress-strain
relation according to Hooke's law reduces to
σ
xy
=
2
G
ε
xy
.
Hence, measuring the clamp forces and the shear displacement provides
h
a direct means to identify the shear modulus
G
. However, the 'simple-
shear' state is difficult to realize experimentally, since the configuration
of the figure does
not
exactly represent the simple-shear case. This may be
analysed using the m-file
demo_shear
.
(a) Analyse the shear and the simple-shear case using this m-file. What
is the difference in boundary conditions for these two cases?
