The transition matrix

To calculate the transition matrix from the forces and moments to the local stresses it is necessary to invert the influence matrix SFi,j to get a mapping from forces to nominal stresses. The inverse matrix is given by . The next step is to read in the 2D stress tensors of interest for each load case in order to generate a nominal stress matrix Sk,j. The transformation matrix Tk,i is the given by:

Tk,i = Sk,j SFj,t

This way the resulting transformation matrix Tk,i is able to map the applied load forces Li to the matching local stress component σk by calculating:

σk = Tk,iLi

For a durability analysis, all you need to know are the stresses at the green points for the shell model and the transition matrix, in order to calculate the local stresses in the seam weld.

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The transition matrix, Simcenter 3D 2021.1 Series

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