Effect of Element quality, Aspect Ratio, and Skewness on solution and results?
Hello there. We all know the specified ranges for the element quality, aspect ratio, orthagonal quality and skewness for the mesh elements, to be classified as good elements for modelling. But how will a low quality element, or with high skewness and aspect ratio affect my results? What is the background of it? How will a 'bad element' will cause the stresses within my model at that location to become illogical and absurd? What is the theory? How can they result in stress singularities as well?
Will bad elements also cause the displacements at those locations to be affected as well?
Best Answer

peteroznewman Member
Hello @Rameez_ul_Haq
A singularity is a characteristic of the geometry, such as an interior corner, and is independent of poor element shapes.
Low element quality affects stress much more than displacements. Stress is calculated from a difference of displacements, so small errors in displacement are magnified by the difference calculation.
Study the mathematical equations for the shape functions used in each element. These are created to work well for ideal element shapes, but the mapping from the ideal shape to the actual shape degrades the accuracy of those shape functions. There are more ways a quadratic element can go wrong than a linear element because the assumption is that a midside node is expected to at the center of the line connecting the corner nodes and it might stray far from that point. You don't need to know the details, since as you say, there are measurement tools with acceptable limits on the various metrics to allow you to judge the quality of the mesh.
Keep in mind that element quality metrics are only one source of error in the overall model. A much larger effect is discretization error, which occurs by using elements that are too large (but may have ideal shapes) in areas of high stress gradient. Another error is in oversimplified boundary conditions or connections between parts.
Answers
Hello @Rameez_ul_Haq
A singularity is a characteristic of the geometry, such as an interior corner, and is independent of poor element shapes.
Low element quality affects stress much more than displacements. Stress is calculated from a difference of displacements, so small errors in displacement are magnified by the difference calculation.
Study the mathematical equations for the shape functions used in each element. These are created to work well for ideal element shapes, but the mapping from the ideal shape to the actual shape degrades the accuracy of those shape functions. There are more ways a quadratic element can go wrong than a linear element because the assumption is that a midside node is expected to at the center of the line connecting the corner nodes and it might stray far from that point. You don't need to know the details, since as you say, there are measurement tools with acceptable limits on the various metrics to allow you to judge the quality of the mesh.
Keep in mind that element quality metrics are only one source of error in the overall model. A much larger effect is discretization error, which occurs by using elements that are too large (but may have ideal shapes) in areas of high stress gradient. Another error is in oversimplified boundary conditions or connections between parts.