Overview
The objective function is the function, which value can be maximized
or minimized during the optimization. This function depends on the
results of the FE analysis combined into design responses (DRESP
).
Tosca Structure.shape
works with a CONTROLLER
-based algorithm that homogenizes the
stresses with respect to a reference value. For simple optimizations this reference value
can be ignored - Tosca Structure.shape
will automatically generate a reference value that will be adequate for most cases.
Reference Stress
You might want to define a reference value yourself. In this case, you need to understand how
Tosca Structure.shape works.
The CONTROLLER
-based algorithm is driven by following redesign rule:
- Design nodes with stress above the reference value are moved outwards (growth).
- Design nodes with stress below the reference value are moved inwards (shrinkage).
This produces components with homogenized stress in the design area.
So, if you choose a high reference value most design nodes will shrink to achieve this value. A
low reference value has the opposite effect. With some practice, a good choice of reference
value can be estimated giving the designer an optimal control over the shape
optimization.
You can also choose the reference value to be a variable (for example, dependent on a design response).
This has a special use for the design of relief notches where the reference value is chosen
outside the design nodes area. This causes the design nodes to shrink until they have the
same stress value as the reference value. This technique can only be done if the design area
is relatively close to the area where the reference value is. Otherwise, you will not get
the stress dampening effect of a relief notch.
Note:
-
A reference value is NOT the same as a CONSTRAINT. For most real structures,
the maximum stress of a converged shape optimization will be some percent
larger than the given or the automatically calculated reference stress.
-
Some structures and/or loading situations are not well suited for
the CONTROLLER-based algorithm. You must have the correlation between
growth in design nodes also minimizes the stresses.
-
One example is a cantilever beam with a prescribed
displacement at its free end. Due to the high stresses at the supports, the beam
becomes thicker. Because of the prescribed displacement, the stresses are higher in
the next iteration. The homogenization works, but the stresses increase because the
beam stiffness increases as well.
-
Another example is shape design in contact area: In
this case, we know that the design rule must be the opposite the normal design rule
because growth will cause even greater contact stresses. This can be turned around by
using the optimization setting SCALE and set it to a negative value. Now, the shape
optimization will shrink by high contact stresses and thus homogenize these to achieve
a homogeneous contact.
Objective Function Terms
Tosca Structure.shape
allows optimization on different stress hypotheses, strain formulations, and damage results. The most used equivalent stress is von Mises (SIG_MISES
).
Solver-specific results |
Description |
ABQ_ND_PEEQ ** |
Abaqus PEEQ nodal value |
Damage results |
Description |
DAMAGE DAMAGE_LC |
Damage value from durability analysis
Damage value from durability analysis with
load case information (must use ONF 601) |
Eigenfrequency results |
Description |
DYN_FREQ
DYN_FREQ_KREISSEL |
Eigenfrequency from modal analysis. |
Stress hypotheses |
Description |
SIG_1
SIG_2
SIG_3 |
Maximum principal stress
2nd. principal stress
Minimum principal stress |
SIG_11
SIG_22
SIG_33
SIG_12
SIG_23
SIG_13 |
Components of stress tensor |
SIG_ABS_123 |
Maximum of the absolute value of the principal stresses |
SIG_ABS_3 |
Absolute value of the minimum principal stress |
SIG_BELTRAMI
SIG_DRUCKER_PRAGER
SIG_KUHN
SIG_MARIOTTE
SIG_MISES
SIG_SANDEL
SIG_SAUTER
SIG_TRESCA
SIG_CONTACT_PRESSURE* |
Beltrami stress hypothesis
Drucker-Prager stress hypothesis
Kuhn stress hypothesis
Mariotte stress hypothesis
von Mises stress hypothesis
Sandel stress hypothesis
Sauter stress hypothesis
Tresca stress hypothesis
Contact stress pressure |
SIG_CONTACT_SHEAR *
SIG_CONTACT_SHEAR_X *
SIG_CONTACT_SHEAR_Y *
SIG_CONTACT_TOTAL * |
Total shear contact stress
Shear X Contact stress
Shear Y Contact stress
Total Contact stress |
Strain formulations |
Description |
STRAIN_ELASTIC*
STRAIN_PLASTIC*
STRAIN_TOTAL*
STRAIN_ENERGY
STRAIN_ENERGY_DENS |
Elastic Strain
Plastic Strain
Total Strain (elastic + plastic)
Strain energy
Strain energy density |
Analysis-independent results |
Description |
VOLUME
WEIGHT |
Volume design response
Weight design response |
* The marked design responses are supported only by the Abaqus
and ANSYS® interface and only for nonlinear analysis.
** ABQ_ND_PEEQ is the scalar value that Abaqus
calculates as PEEQ, which is NOT the same as STRAIN_PLASTIC. ABQ_ND_PEEQ is only available in Abaqus. |