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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. ã Aspect Ratio Check. For a solid mesh, numerical accuracy is best achieved by a mesh 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 tetrahedral elements. Due to small edges, curved geometry, thin features, and sharp corners, some of the generate
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  The quality of mesh plays a key role in the accuracy of the results. The software uses twoimportant checks to measure the quality of elements in a mesh. ã 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, theaccuracy 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 droppedfrom a vertex to the opposite face normalized with respect to a perfecttetrahedral. By definition, the aspect ratio of a perfect tetrahedral element is 1.0.The aspect ratio check assumes straight edges connecting the four corner nodes.The aspect ratio check is automatically used by the program to check the qualityof the mesh. ã Jacobian Check  . Parabolic elements can map curved geometry much moreaccurately 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 actualgeometry 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 nodeslocated exactly at the middle of the straight edges, is 1.0. 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 elementat 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 softwareadjusts the locations of the mid-side nodes of distorted elements automatically tomake sure that all elements pass the Jacobian check.  For high order shells, the Jacobian check  uses 6 points located at the nodes.
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