Distribution methods for edge-face type setting

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

Suppose that you apply shear, in-plane, and out-of-plane force components to the edges of a planar region that lies in the (x,y) plane and the edges are divided into N element edges. Also suppose that the time, frequency, or temperature-dependent vector field that defines the magnitude of each force component evaluates to Qshear, Qin-plane, and Qout-of-plane.

A scalar field is used to define the spatial distribution of the force components. The scalar field can be represented as a function of two variables, g = g(x,y).

The value of the spatial distribution field at the midpoint of the ith element edge is:

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

where (xi,yi) are the coordinates of the midpoint of the ith element edge.

The force components that act at the edge midpoint of the ith element edge are each proportional to the value of the spatial distribution field and are weighted according to relative length.

{({f_{shear}})_i} = \left( {\frac{{{L_i}}}{L}} \right){g}({x_i},{y_i})

{({f_{in-plane}})_i} = \left( {\frac{{{L_i}}}{L}} \right){g}({x_i},{y_i})

{({f_{out-of-plane}})_i} = \left( {\frac{{{L_i}}}{L}} \right){g}({x_i},{y_i})

where Li is the length of the ith element edge, and L is the cumulative length of all the element edges. That is:

L = \sum\limits_{i = 1}^N {{L_i}}

The force components at the element edge midpoint are scaled as follows:

{({F_{shear}})i} = {S{shear}}{({f_{shear}})_i}

{({F_{in-plane}})i} = {S{in-plane}}{({f_{in-plane}})_i}

{({F_{out-of-plane}})i} = {S{out-of-plane}}{({f_{out-of-plane}})_i}

where the scaling factors, Sshear, Sin-plane, and Sout-of-plane, 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 midpoint of the ith element edge.{({F_{shear}})i} = {Q{shear}}\left( {\frac{{{L_i}}}{L}} \right){({F_{in-plane}})i} = {Q{in-plane}}\left( {\frac{{{L_i}}}{L}} \right){({F_{out-of-plane}})i} = {Q{out-of-plane}}\left( {\frac{{{L_i}}}{L}} \right)

Total per Object

The Total per Object and Geometric distribution distribution methods are identical except when you distribute the force over multiple edges of a face. The Geometric distribution method distributes the component magnitudes of the time, frequency, or temperature-dependent vector field, Qshear, Qin-plane, and Qout-of-plane, over the cumulative length of all the edges that you select. The Total per Object method distributes the component magnitudes of the time, frequency, or temperature-dependent vector field, Qshear, Qin-plane, and Qout-of-plane, over each edge that you select individually.For example, suppose that you select Total per Object as the distribution method, and you select two edges. For the shear component, the software distributes a force of Qshear over each edge. Similarly, the software distributes a force of Qin-plane over each edge, and a force of Qout-of-plane over each edge.Note: Because the edges may have different orientations, and forces add vectorially, the total applied shear force, in-plane force, and out-of-plane force may not be 2Qshear, 2Qin-plane, and 2Qout-of-plane, respectively.

Spatial

If you select Spatial as the distribution method, the scaling factors are:{S_{shear}} = \frac{{{Q_{shear}}}}{{\sum\limits_{i = 1}^N {\left| {{{({f_{shear}})}i}} \right|} }}{S{in-plane}} = \frac{{{Q_{in-plane}}}}{{\sum\limits_{i = 1}^N {\left| {{{({f_{in-plane}})}i}} \right|} }}{S{out-of-plane}} = \frac{{{Q_{out-of-plane}}}}{{\sum\limits_{i = 1}^N {\left| {{{({f_{out-of-plane}})}i}} \right|} }}The software uses the following equations to calculate the scaled force components that act at the midpoint of the ith element edge.{({F{shear}})i} = {Q{shear}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_i}\left| {g({x_i},{y_j})} \right|} }}} \right){({F_{in-plane}})i} = {Q{in-plane}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_i}\left| {g({x_i},{y_j})} \right|} }}} \right){({F_{out-of-plane}})i} = {Q{out-of-plane}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_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 midpoint forces, the following occurs:\sum\limits_{i = 1}^N {{{({F_{shear}})}i}} \ne {Q{shear}}\sum\limits_{i = 1}^N {{{({F_{in-plane}})}i}} \ne {Q{in-plane}}\sum\limits_{i = 1}^N {{{({F_{out-of-plane}})}i}} \ne {Q{out-of-plane}}

Spatial - Load Conservation

If you select Spatial - Load Conservation as the distribution method, the scaling factors are:{S_{shear}} = \frac{{{Q_{shear}}}}{{\sum\limits_{i = 1}^N {{{({f_{shear}})}i}} }}{S{in - plane}} = \frac{{{Q_{in - plane}}}}{{\sum\limits_{i = 1}^N {{{({f_{in - plane}})}i}} }}{S{out - of - plane}} = \frac{{{Q_{out - of - plane}}}}{{\sum\limits_{i = 1}^N {{{({f_{out - of - plane}})}i}} }}The software uses the following equations to calculate the scaled force components that act at the midpoint of the ith element face.{({F{shear}})i} = {Q{shear}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_i}g({x_i},{y_i})} }}} \right){({F_{in-plane}})i} = {Q{in-plane}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_i}g({x_i},{y_i})} }}} \right){({F_{out-of-plane}})i} = {Q{out-of-plane}}\left( {\frac{{{L_i}g({x_i},{y_j})}}{{\sum\limits_{i = 1}^N {{L_i}g({x_i},{y_i})} }}} \right)Note: If you select Spatial - Load Conservation as the distribution method, and the sum of an unscaled midpoint force component equals zero, the software issues an error message at export.

After the software calculates the scaled midpoint force components, it uses the element shape functions to distribute them to the nodes that define the element edges.

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 components type setting

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Distribution methods for edge-face type setting, Simcenter 3D 2021.1 Series

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