Distribution methods for components type setting

To demonstrate how the distribution methods differ when the Type setting is Components, consider the following example.

Suppose that you apply force components 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 vector field that defines the magnitude of the force components evaluates to Qx, Qy, and Qz.

For the Spatial and Spatial - Load Conservation methods, 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})

The force components that act at the element centroid of the ith element face are each proportional to the value of the spatial distribution field and are weighted according to relative area.

{({f_x})_i} = {({f_y})_i} = {({f_z})_i} = \left( {\frac{{{A_i}}}{A}} \right)g({x_i},{y_i}) = {f_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 force components are scaled as follows:

{({F_x})_i} = {S_x}{f_i}

{({F_y})_i} = {S_y}{f_i}

{({F_z})_i} = {S_z}{f_i}

where the scaling factors, Sx, Sy, and Sz, depend 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 equations to calculate the scaled force components that act at the centroid of the ith element face.{({F_x})_i} = {Q_x}\left( {\frac{{{A_i}}}{A}} \right){({F_y})_i} = {Q_y}\left( {\frac{{{A_i}}}{A}} \right){({F_z})_i} = {Q_z}\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 component magnitudes of the time, frequency, or temperature-dependent vector field, Qx, Qy, and Qz, over the cumulative region. The Total per Object method distributes the magnitudes of the time, frequency, or temperature-dependent vector field, Qx, Qy, and Qz, 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. For the x-component, the software distributes a force of Qx over each object, so that the total x-component of force applied is 2Qx. Similarly, the total y-component and z-component of force applied are 2Qy and 2Qz, respectively.

Spatial

If you select Spatial as the distribution method, the scaling factors are:{S_x} = \frac{{{Q_x}}}{{\sum\limits_{i = 1}^N {\left| {{f_i}} \right|} }}{S_y} = \frac{{{Q_y}}}{{\sum\limits_{i = 1}^N {\left| {{f_i}} \right|} }}{S_z} = \frac{{{Q_z}}}{{\sum\limits_{i = 1}^N {\left| {{f_i}} \right|} }}The software uses the following equations to calculate the scaled force components that act at the centroid of the ith element face.{({F_x})i} = {Q_x}\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}\left| {g({x_i},{y_j})} \right|} }}} \right){({F_y})i} = {Q_y}\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}\left| {g({x_i},{y_j})} \right|} }}} \right){({F_z})i} = {Q_z}\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_x})}i}} \ne {Q_x}\sum\limits{i = 1}^N {{{({F_y})}i}} \ne {Q_y}\sum\limits{i = 1}^N {{{({F_z})}_i}} \ne {Q_z}

Spatial - Load Conservation

If you select Spatial - Load Conservation as the distribution method, the scaling factors are:{S_x} = \frac{{{Q_x}}}{{\sum\limits_{i = 1}^N {{f_i}} }}{S_y} = \frac{{{Q_y}}}{{\sum\limits_{i = 1}^N {{f_i}} }}{S_z} = \frac{{{Q_z}}}{{\sum\limits_{i = 1}^N {{f_i}} }}The software uses the following equations to calculate the scaled force components that act at the centroid of the ith element face.{({F_x})i} = {Q_x}\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}g({x_i},{y_i})} }}} \right){({F_y})i} = {Q_y}\left( {\frac{{{A_i}g({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}g({x_i},{y_i})} }}} \right){({F_z})i} = {Q_z}\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 an unscaled centroidal force component equals zero, the software issues an error message at export.

For the Spatial - Components and Spatial - Components - Load Conservation methods, the spatial distribution field is a vector field that can be represented as three two-variable functions:

{g_x} = {g_x}({x_i},{y_i})

{g_y} = {g_y}({x_i},{y_i})

{g_z} = {g_z}({x_i},{y_i})

The values of the spatial distribution field at the centroid of the ith element face are:

{({g_x})_i} = {g_x}({x_i},{y_i})

{({g_y})_i} = {g_y}({x_i},{y_i})

{({g_z})_i} = {g_z}({x_i},{y_i})

The force components that act at the element centroid of the ith element face are each proportional to the value of the spatial distribution field and are weighted according to relative area.

{({f_x})_i} = \left( {\frac{{{A_i}}}{A}} \right){g_x}({x_i},{y_i})

{({f_y})_i} = \left( {\frac{{{A_i}}}{A}} \right){g_y}({x_i},{y_i})

{({f_z})_i} = \left( {\frac{{{A_i}}}{A}} \right){g_z}({x_i},{y_i})

The centroidal force components are scaled as follows:

{({F_x})_i} = {S_x}{({f_x})_i}

{({F_y})_i} = {S_y}{({f_y})_i}

{({F_z})_i} = {S_z}{({f_z})_i}

where the scaling factors, Sx, Sy, and Sz, depend on the distribution method that you select.

Spatial - Components

If you select Spatial - Components as the distribution method, the scaling factors are:{S_x} = \frac{{{Q_x}}}{{\sum\limits_{i = 1}^N {\left| {{{({f_x})}i}} \right|} }}{S_y} = \frac{{{Q_y}}}{{\sum\limits{i = 1}^N {\left| {{{({f_y})}i}} \right|} }}{S_z} = \frac{{{Q_z}}}{{\sum\limits{i = 1}^N {\left| {{{({f_z})}i}} \right|} }}The software uses the following equations to calculate the scaled force components that act at the centroid of the ith element face.{({F_x})i} = {Q_x}\left( {\frac{{{A_i}{g_x}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}\left| {{g_x}({x_i},{y_j})} \right|} }}} \right){({F_y})i} = {Q_y}\left( {\frac{{{A_i}{g_y}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}\left| {{g_y}({x_i},{y_j})} \right|} }}} \right){({F_z})i} = {Q_z}\left( {\frac{{{A_i}{g_z}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}\left| {{g_z}({x_i},{y_j})} \right|} }}} \right)Note: If you select Spatial - Components 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_x})}i}} \ne {Q_x}\sum\limits{i = 1}^N {{{({F_y})}i}} \ne {Q_y}\sum\limits{i = 1}^N {{{({F_z})}_i}} \ne {Q_z}

Spatial - Components - Load Conservation

If you select Spatial - Components - Load Conservation as the distribution method, the scaling factors are:{S_x} = \frac{{{Q_x}}}{{\sum\limits_{i = 1}^N {{{({f_x})}i}} }}{S_y} = \frac{{{Q_y}}}{{\sum\limits{i = 1}^N {{{({f_y})}i}} }}{S_z} = \frac{{{Q_z}}}{{\sum\limits{i = 1}^N {{{({f_z})}_i}} }}The software uses the following equations to calculate the scaled force components that act at the centroid of the ith element face.{({F_x})i} = {Q_x}\left( {\frac{{{A_i}{g_x}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}{g_x}({x_i},{y_i})} }}} \right){({F_y})i} = {Q_y}\left( {\frac{{{A_i}{g_y}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}{g_y}({x_i},{y_i})} }}} \right){({F_z})i} = {Q_z}\left( {\frac{{{A_i}{g_z}({x_i},{y_j})}}{{\sum\limits{i = 1}^N {{A_i}{g_z}({x_i},{y_i})} }}} \right)Note: If you select Spatial - Components - Load Conservation as the distribution method, and the sum of an unscaled centroidal force component equals zero, the software issues an error message at export.

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

Note:

Depending on how you define the magnitude of the boundary condition, Pre/Post may not use the scale factors in the Scale Factors group of the Force or Moment dialog box, which appear when the Type setting is Components.

• When you define the magnitude with a constant value or a time, frequency, or temperature-dependent field that evaluates to a constant value, the software multiplies the magnitude by the scale factor to obtain the load to distribute.

• When you define the magnitude with a time, frequency, or temperature-dependent field, depending on the solver, the software either:Multiplies the magnitude by the scale factor to obtain the load to distribute.Writes the scale factor and the field data to the solver input file separately.

Learn more

Special considerations for specifying magnitude and distribution in separate fields

Distribution methods for magnitude and direction or normal type settings

Distribution methods for edge-face type setting

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Distribution methods for components type setting, Simcenter 3D 2021.1 Series

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