Distribution methods for magnitude and direction or normal type settings

To demonstrate how the distribution methods differ when the Type setting is Magnitude and Direction or Normal, consider the following example.

Suppose that you apply a force to a planar region that lies in the (x,y) plane and is divided into N element faces. Also suppose that the time, frequency, or temperature-dependent scalar field that defines the magnitude of the force evaluates to some value, Q.

The spatial distribution field is a scalar field that can be represented as a function of two variables, g = g(x,y).

The value of the spatial distribution field at the centroid of the ith element face is:

{g_i} = g({x_i},{y_i})

where (xi,yi) are the coordinates of the centroid of the ith element face.

The force that acts at the element centroid of the ith element face is proportional to the value of the spatial distribution field and is weighted according to relative area.

{f_i} = \left( {\frac{{{A_i}}}{A}} \right)g({x_i},{y_i})

where Ai is the area of the ith element face, and A is the total area of the planar region. That is:

A = \sum\limits_{i = 1}^N {{A_i}}

The centroidal forces, fi, are scaled as follows:

{F_i} = S{f_i}

where Fi are the scaled centroidal forces and the scaling factor, S, depends on the distribution method that you select.

Geometric distribution

If you select Geometric distribution as the distribution method, the spatial distribution is uniform. The software uses the following equation to calculate the scaled force that acts at the centroid of the ith element face.{F_i} = Q\left( {\frac{{{A_i}}}{A}} \right)

Total per Object

The Total per Object and Geometric distribution distribution methods are identical except when you distribute the force over a region that is comprised of multiple objects. The Geometric distribution method distributes the magnitude of the time, frequency, or temperature-dependent scalar field, Q, over the cumulative region. The Total per Object method distributes the magnitude of the time, frequency, or temperature-dependent scalar field, Q, over each object that comprises the region individually.For example, suppose that you select Total per Object as the distribution method, and you select a region that is comprised of two objects. The software distributes a force of Q over each object, so that the total force applied is 2Q.

Spatial

If you select Spatial as the distribution method, the scaling factor is:S = \frac{Q}{{\sum\limits_{i = 1}^N {\left| {{f_i}} \right|} }}The software uses the following equation to calculate the scaled force that acts at the centroid of the ith element face.{F_i} = Q\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{A_i}\left| {g({x_i},{y_j})} \right|} }}} \right)Note: If you select Spatial as the distribution method, and both positive and negative values exist for the unscaled centroidal forces, the following occurs:\sum\limits_{i = 1}^N {{F_i}} \ne Q

Spatial - Load Conservation

If you select Spatial - Load Conservation as the distribution method, the scaling factor is:S = \frac{Q}{{\sum\limits_{i = 1}^N {{f_i}} }}The software uses the following equation to calculate the scaled force that acts at the centroid of the ith element face.{F_i} = Q\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{A_i}g({x_i},{y_i})} }}} \right)Note: If you select Spatial - Load Conservation as the distribution method, and the sum of the unscaled centroidal forces equals zero, the software issues an error message at export.

After the software calculates the scaled centroidal forces, it uses the element shape functions to distribute them to the nodes that define the connectivity of the element faces.

Learn more

Special considerations for specifying magnitude and distribution in separate fields

Distribution methods for components type setting

Distribution methods for edge-face type setting

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Distribution methods for magnitude and direction or normal type settings, Simcenter 3D 2021.1 Series

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