The 6node triangular element and the 4node quadrangular have the same order (p=2), so which one has better accuracy and why?
The approximative capability of 6-node triangular elements seems to be better due to presense of full set of quadratic approximation functions: x*y, x2, y2 compared to 4-node quadrilateral elements (only x*y). Also they allow to represent curved surfaces and edges more adequate.
Dear Eirini,
It again depends on the problem for which you are assigning these elements. If its stress concentrated region, considering the fact that your problem will be 2D model, quadrangular element even after having 4-node. As we know triangular elements (whether its 1st order or 2nd order or even higher order) are not preferred at high concentration regions. So, everything is depending on the problem with is it singularity region or not.
Dear Eirini Pitsiougka ,
If your concern is only accuracy, LST (6-noded triangular elements) gives an accurate result than 4-noded quadrilateral element for plane stress applications. This is because in 4-noded quadrilateral element, the absence of the mid-surface node yields spurious average mid-surface strain during bending, which is approximately zero. And this falsified mid-surface strain causes excessive bending stiffness. However, in LST element the presence of mid-surface node increases the number of integration point that eliminates the gradient in mid-surface strain which provides an accurate solution. I hope the attached figure (from reference 1) will elaborates the above discussion precisely.
But for problems associated with large nodes and vibration, LST is not recommended this is due to large number of equation and unknowns in LST than 4-noded element.
You can refer the following materials:
1. A First Course in the Finite Element Method, 4th edition, by Daryl L. Logan
2. A Six-Node Curved Triangular Element and a Four-Node Quadrilateral Element for Analysis of Laminated Composite Aerospace Structures, by C. Wayne Martin and David M. Breiner
I feel 6-noded triangle gives better accuracy and predict the correct stress variation with respect to the applied load in plane stress and plane strain condition as compared to 4-noded quadrilateral. The reason for 6-noded triangle is predicting better response mainly because of quadratic terms in the displacement function as compared to 4-noded quadrilateral element and also the strain predicted by 6-node triangle is linear strain. This phenomenon can be verified by performing numerical analysis of a beam subjected to vertical load using these two elements and analysis results will show the 6-noded triangle predicted response is having a better prediction of stress variation (because of linear strain) and 4-noded element predict constant stress.
It depends. LST element has a slightly better accuracy than Q4 element in terms of displacement.
for plate problems, the 6-nodded triangle and Q4 have almost the same order of accuracy.
I preffer Q4 element especially for stress pridection.
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