Combined Responses in Sensitivity-Based Optimization

Displacements

1. For TYPE=DISP_ABS with VAR_OPER=SUB both VAR_A and VAR_B are TYPE=DISP_ABS. For this case the displacement of DRESP is calculated as following:

   $\text{DRESP=}\Delta u=l_{\text{def}}-l_{\text{ini}}$ with $l_{\text{def}}=\sqrt{{(\Delta x_{\text{pos}}+\Delta u_x)}^2+{(\Delta y_{\text{pos}}+\Delta u_y)}^2+{(\Delta z_{\text{pos}}+\Delta u_z)}^2}$ as deformed length and $l_{\text{ini}}=\sqrt{{(\Delta x_{\text{pos}})}^2+{(\Delta y_{\text{pos}})}^2+{(\Delta z_{\text{pos}})}^2}$ as initial length. Thereby $\Delta n_{\text{pos}}=\Delta n_{\text{pos}1}-\Delta n_{\text{pos}2}$, for n = x,y,z and $\Delta u_n=\Delta u_{n1}-\Delta u_{n2}$, for n = x,y,z, where pos1 and pos2 are the coordinates of the nodes and u the displacements. The DRESP can also be negative and gives the stretch between two nodes (i.e. the difference between the two notes in deformed and undeformed configuration).

2. GROUP_OPER is default GROUP_OPER = MAX.
3. A node group (ND_GROUP) has to be applied in the DRESP when more than one node is required.
4. Maximal 5000 DRESPs can be defined. Therefore, the maximal number of nodes for GROUP_OPER = MAX is 5000 or less as in this case one design response is created for each group member.
5. If possible, define design responses for displacements for single nodes (allows better control). Often 1 representative node is sufficient for the task.
6. The maximal number of nodes for GROUP_OPER = SUM us unlimited.
7. Design responses combined using VAR_OPER should refer to the same group.

Reaction Forces

Internal Forces

Modal Eigenfrequencies

Note that with the operator KSO the Kreisselmaier-Steinhauser formulation can be constructed from single eigenfrequency DRESPs in context of sensitivity-based topology and sizing optimization. It is given by $-\frac{1}{k}ln\left(\sum _j{e}^{-k{f}_j}\right)$ .

Frequency Spectrum Responses