Center of Gravity

The center of gravity for the three directions is defined by CENTER_GRAVITY_X, CENTER_GRAVITY_Y and CENTER_GRAVITY_Z, respectively.

This page discusses:

Parameter Name

Formula

CENTER_GRAVITY_X

 xG=∫ρxdV∫ρdV

CENTER_GRAVITY_Y

 xG=∫ρydV∫ρdV

CENTER_GRAVITY_Z

 xG=∫ρzdV∫ρdV

Analysis-Independent Design Response

For the center of gravity, 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.

TOPO

SHAPE

BEAD

SIZING

OBJ_FUNC

S

S

S

S

CONSTRAINT

S

S

S

S

The center of gravity for the three directions is defined by CENTER_GRAVITY_X, CENTER_GRAVITY_Y and CENTER_GRAVITY_Z, respectively. The center of gravity and the moments of inertia can be defined as a DRESP (design response) and as a VARIABLE in the sensitivity-based topology, bead, and sizing optimization. For controller-based optimization, the center of gravity and the moments of inertia can only be defined as a VARIABLE which means that the values can only be used for output or control purposes.

Both the center of gravity and the moments of inertia can be defined as a design response for the entire structure or for a part of the entire structure, for example, some specific components. This is done using the command EL_GROUP.

The center of gravity and the moments of inertia are per default calculated in the global coordinate system. However, the user has the option to calculate the center of gravity and the moments of inertia in a local coordinate system. The local coordinate system is defined in the design response using the command CS_REF. For the calculation of the center of gravity both the directions and origin of the local coordinate system is used as reference whereas for the moments of inertia the directions of the axes of the local coordinate system is applied, see the following figure. The global coordinate system is applied if no local coordinate system is defined in the design response (DRESP). The volume for which the center of gravity is calculated is defined using EL_GROUP.



Remarks

  1. Only elements of the element group (EL_GROUP) listed in the tables of supported element types are applied in the calculation of the center of gravity.
  2. The physical density defined in the finite element input file is used in the calculation for the center of gravity.
  3. The moments of inertia for shell and membrane elements are calculated as true 3D elements in Tosca Structure using the thickness defined in the properties of the shell and membrane elements in the finite element file. Some finite element solvers and post-processors calculate the moments of inertia for shell and membrane elements as 2D elements without thickness.
  4. The physical density defined in the finite element input file is used in the calculation for the center of gravity and in the calculation for the moments of inertia.
  5. Internally, Tosca Structure calculates the center of gravity and the moments of inertia using more digits than can be observed in the finite element input file. A slight difference (<1%) between the center of gravity and the moments of inertia calculated using Tosca Structure and the finite element solver might be present.
  6. When Tosca Structure calculates the center of gravity and the moments of inertia only the elements shown in the tables of supported element types are included in the calculation. This might lead to a significant difference between the center of gravity and the moments of inertia calculated by Tosca Structure and the center of gravity and the moments of inertia calculated by the finite element solver, for example, if several beam elements are included in the calculation of the center of gravity and the moments of inertia.
  7. The coordinate system for the center of gravity and the moments of inertia is always interpreted as a Cartesian (rectangular) coordinate system, even if a cylindrical or spherical coordinate system was defined. To get close to a non-Cartesian coordinate system, you can define adequate "box constraints" using several constraints (for example, in x- and y-direction for a cylindrical coordinate system).

Definition

The design response (DRESP) for the center of gravity in the x-direction is defined like


DRESP
 ID_NAME  = ...
 DEF_TYPE = SYSTEM
 TYPE     = CENTER_GRAVITY_X
 EL_GROUP = ...
 CS_REF   = ...
END_

where the local coordinate definition (CS_REF) is optional. Default is the global coordinate system.

The design response (DRESP) for the center of gravity in the y-direction is defined like


DRESP
 ID_NAME  = ...
 DEF_TYPE = SYSTEM
 TYPE     = CENTER_GRAVITY_Y
 EL_GROUP = ...
 CS_REF   = ...
END_

where the local coordinate definition (CS_REF) is optional. Default is the global coordinate system.

The design response (DRESP) for the center of gravity in the z-direction is defined like


DRESP
 ID_NAME  = ...
 DEF_TYPE = SYSTEM
 TYPE     = CENTER_GRAVITY_Z
 EL_GROUP = ...
 CS_REF   = ...
END_

where the local coordinate definition (CS_REF) is optional. Default is the global coordinate system.

Examples of Commands for the Center of Gravity

For example, the design response (DRESP) for the center of gravity for the y-direction of the entire structure (ALL_ELEMENTS) calculated in the global coordinate system is defined like


DRESP
 ID_NAME  = DRESP_COG_Y_GLOBAL
 DEF_TYPE = SYSTEM
 TYPE     = CENTER_GRAVITY_Y
 EL_GROUP = ALL_ELEMENTS
END_

For example, the definition of the design response (DRESP) for the center of gravity for the y-direction of the substructure called EL_GROUP_2 is calculated in the local coordinate system number 23 like the following:


DRESP
 ID_NAME = DRESP_COG_X
 DEF_TYPE = SYSTEM
 TYPE = CENTER_GRAVITY_X
 EL_GROUP = EL_GROUP_2
 CS_REF = CS_23
END_