Hello all.
I develop finite element analysis program for plane strain problem with python for my bachelor thesis.
I realized isoparametric CST (3-node triangle) with 1 Gauss integration point and LST (6-node triangle) with 3 Gauss int. points elements. Calculated displacements by my program match exactly with same problem in ABAQUS.
Then I've found strains and stresses in integration points and they match exactly with ABAQUS too. Now I need to extrapolate this results from int. points to nodes. I made it for CST element, found algorithms with extrapolation matrix for 4-node element , but can't find anything about extrapolating strains to nodes for LST element.
I don't really understand how can I make it with only 3 Gauss points and 6 nodes. Does anybody know something about extrapolation problem for LST element?
Any information will help me, thank you
(The illustraition taken from https://sameradeeb-new.srv.ualberta.ca/finite-element-analysis/one-and-two-dimensional-isoparametric-elements-and-gauss-integration/#reduced-gauss-integration-under-integration-for-two-dimensional-quadrilateral-isoparametric-elements17)
Dear Ilya Slovesnyj,
As I understood, the strains are calculated as first derivatives of approximated displacements (i.e. sums of nodal displacements multiplied by shape functions). Obviously, for linear elements the strains (and thus the stresses) are constant functions, while for quadratic elements they are bilinear ones. As I see, Abaqus merely uses the nodal values of these functions. Do the same thing.
If somebody will face a similar question, strains at node with coordinates (x, y) for isoparametric element:
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