Overview of Displacement and Rotation

This section describes the theory of displacements and rotation.

See Also
Combined Terms

Parameter Name

Formula

DISP_X, DISP_Y, DISP_Z

ui

ROT_X, ROT_Y, ROT_Z

θi

DISP_X_ABS, DISP_Y_ABS, DISP_Z_ABS

ui2

DISP_ABS

ux2+uy2+uz2

Analysis Types: Static Linear or Nonlinear Analysis

Ku=F

where K might be linear or nonlinear.

For displacements and rotations, the following table shows the allowed combinations between the strategy and the items OBJ_FUNC and CONSTRAINT with C for controller and S for sensitivity based optimization. Tosca sensitivities support nonlinear contact, but material and large displacement theory are only supported by Tosca sensitivities for Topology optimization. Sizing, Shape and Bead optimization only allow linear material and small displacement theory.

TOPO

SHAPE

BEAD

SIZING

OBJ_FUNC

S

S

S

S

CONSTRAINT

S

S

S

S

Displacements and rotations are the primary variables in the FEM solution. They are also very often the main interest of the FEM-analyst, for example, the maximal displacement. Displacements and rotations should be defined using a nodal id, although node groups might also be referenced. Large node groups can lead to major performance issues, see Group Operations for Design Responses.

Displacements and rotations can also be referenced in a local coordinate system.

Important:
  1. It is always strongly recommended that the user defines design elements attached to nodes used in displacement definitions or reaction definitions (DRESP) as frozen elements. This stabilizes the optimization iterations and often leads to a significant lower number of optimization iterations.
  2. When using solver sensitivities, all types of nonlinear analysis are supported. See Remarks for Sensitivity-Based Optimizations