862019 The Quality of Mesh Plays a Key Role in the Accuracy of the Results

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The quality of mesh plays a key role in the accuracy of the results The software uses two

important checks to measure the quality of elements in a mesh

bull Aspect Ratio Check For a solid mesh numerical accuracy is best achieved by amesh with uniform perfect tetrahedral elements whose edges are equal in length

For a general geometry it is not possible to create a mesh of perfect tetrahedralelements Due to small edges curved geometry thin features and sharp corners

some of the generated elements can have some of their edges much longer thanothers When the edges of an element become much different in length the

accuracy of the results deteriorates

The aspect ratio of a perfect tetrahedral element is used as the basis for

calculating aspect ratios of other elements The aspect ratio of an element isdefined as the ratio between the longest edge and the shortest normal dropped

from a vertex to the opposite face normalized with respect to a perfect

tetrahedral By definition the aspect ratio of a perfect tetrahedral element is 10

The aspect ratio check assumes straight edges connecting the four corner nodesThe aspect ratio check is automatically used by the program to check the quality

of the mesh

bull Jacobian Check Parabolic elements can map curved geometry much more

accurately than linear elements of the same size The mid-side nodes of the

boundary edges of an element are placed on the actual geometry of the model Inextremely sharp or curved boundaries placing the mid-side nodes on the actual

geometry can result in generating distorted elements with edges crossing over

each other The Jacobian of an extremely distorted element becomes negative Anelement with a negative Jacobian causes the analysis program to stop

The Jacobian check is based on a number of points located within each element

The software gives you a choice to base the Jacobian check on 4 16 29 Gaussian

points or At Nodes

It is recommended to set Jacobian check to At Nodes when using the p-method to solve static problems

The Jacobian ratio of a parabolic tetrahedral element with all mid-side nodes

located exactly at the middle of the straight edges is 10 The Jacobian ratioincreases as the curvatures of the edges increase The Jacobian ratio at a pointinside the element provides a measure of the degree of distortion of the element

at that location The software calculates the Jacobian ratio at the selected number

of Gaussian points for each tetrahedral element Based on stochastic studies it isgenerally seen that a Jacobian Ratio of forty or less is acceptable The software

adjusts the locations of the mid-side nodes of distorted elements automatically to

make sure that all elements pass the Jacobian check

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For high order shells the Jacobian check uses 6 points located at the nodes