2023-11-02T04:28:40.000-0400

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Simcenter STAR-CCM+ Application Specific Solutions

The Center of Pressure (COP) of a body is defined as a point on the body about which the net moment is always zero.

The Center of Pressure (COP) of a body is defined as a point on the body about which the net moment is always zero, be it in any direction.

**Starting from Simcenter STAR-CCM+ 2020.3, a new "Center of loads" Report has been implemented in the code: we strongly suggest to use such report.**

If you are using a previous version and cannot upgrade it, the guidelines below provide you with a possible manual procedure.

Finding the center of pressure in 3D is not a straightforward as in 2D, since what you end up solving for is the equation of a line about which the net force acts, instead of the point which is obtained in a 2D case. Refer to the section below on the method to find the COP in 2D.

For 3D, the following image illustrates the geometry that we are solving on, where**Ft**=net force vector and **Mt**=net moment vector. The plane **Ï�** is the plane containing the vectors **Ft **and **Mt**. **M_tf **is the component of the moment orthogonal to **Ft **in the plane Ï�, while **M_to** is the component of **Mt **along **Ft**.

Note that the line we are solving for is the blue line below. Then the vector**rs**= position vector for points along this blue line. i.e. moment in any direction about points on the blue line is zero. Therefore, the blue line has the same direction cosines as the vector **Ft**.

To find the coordinates of the COP of a 2D body, the following mathematical formula is used:

If you are using a previous version and cannot upgrade it, the guidelines below provide you with a possible manual procedure.

Finding the center of pressure in 3D is not a straightforward as in 2D, since what you end up solving for is the equation of a line about which the net force acts, instead of the point which is obtained in a 2D case. Refer to the section below on the method to find the COP in 2D.

For 3D, the following image illustrates the geometry that we are solving on, where

Note that the line we are solving for is the blue line below. Then the vector

- Create a Force Report (Fx,Fy,Fz) for each direction x,y, and z. Include all of the body parts which you wish to consider.
- Create a Moment report for each axis (Mx,My,Mz).
- Create a new vector field function Force defined as: [$FxReport,$FyReport,$FzReport]. This is
**Ft**in the above figure. - Create a new vector field function Moment defined as: [$MxReport,$MyReport,$MzReport]. This is
**Mt**in the above figure. - Create a new scalar field function called "theta" to find the angle between the force and moment defined as: acos(dot($$Force,$$Moment)/(mag($$Force)*mag($$Moment)))
- Create a new scalar field function called "Moment_Force" to find the component of the moment which is perpendicular to the force (
**M_tf**above) defined as: mag($$Moment)*sin($theta) - We now need the position vector
**rs**. Create a new scalar field function called "rs_mag" to find the magnitude of rs defined as: ${Moment_Force}/mag($$Force) - Create a new vector field function called "rs" defined as: | $rs_mag*cross($${Force},$${Moment})/(mag($${Force})*mag($${Moment}))
- As noted previously, the| blue| line has the same direction cosines as the total force vector
**Ft**. - Create a new vector field function called "line_points" to parametrize the line about which the net force acts defined as: $$rs + K*($$Force/mag($$Force)), where K is any arbitrary number. Change K to get different points on the line.
- Create a new Maximum Report, and set the scalar field function to line_points[i]. Select the same parts that you used for the force reports. Repeat this step for the other direction j and k.
- Run the line_points reports with different values of k to get the 3D coordinates of some of the points on the line.
- Create Probe Points using Derived Parts, and enter the coordinates that you found in the step above for each point. Create a new geometry displayer for each point, and in a geometry scene, you will be able to see the line that these points make.
- To determine which point the net force acts about, you need another constraint. For example, you could calculate the X and Y coordinates as you would in the 2D case, then find the corresponding z point that is on the line.

To find the coordinates of the COP of a 2D body, the following mathematical formula is used:

This can be done using surface integral of force reports. Following is the procedure to go about it.

To verify the coordinates obtained, create a moment report and define Axis Origin as the coordinates of the center of pressure found and Axis about which moment is to be calculated. Irrespective of the defined direction for axis, the moment should come out to be zero.

NOTE:

- Set up two new reports to calculate total Force along x and y directions (name them
**Force_x**and**Force_y**respectively) on the boundaries of interest. - Now create two field functions:

**xF_y**defined as$$Centroid[0]*dot( [0,1,0] , ($Pressure)*$$Area )

**yF_x**defined as$$Centroid[1]*dot( [1,0,0] , ($Pressure)*$$Area )

- Create sum reports of the above two field functions

**XF_Y :**sum report of xF_y**YF_X :**sum report of yF_x

- Finally, to calculate the coordinates, create two expression reports,

**X_Coord**defined as$XF_YReport/$Force_yReport

**Y_Coord**defined as$YF_XReport/$Force_xReport

To verify the coordinates obtained, create a moment report and define Axis Origin as the coordinates of the center of pressure found and Axis about which moment is to be calculated. Irrespective of the defined direction for axis, the moment should come out to be zero.

NOTE:

- The field functions created above take care of only pressure forces, however; force report includes both pressure and shear forces. In most of the applications where the COP is of interest, the shear forces are usually negligible. However, if required, they can be taken into account by adding shear to pressure in the field function.
- The report/field-function names used here are for convenience purposes.