Strain-Displacement matrix [B] of SOLID185 element #3442

derne058 · 2024-09-30T16:06:35Z

derne058
Sep 30, 2024

Hi everyone,

I'm working in a project and I need to calculate the strain-displacement matrix [B] for SOLID185 element. To check if [B] is consistent, I recalculate again the deformation vector using [B] and nodal displacement (in this case, those extrapolated at Gaussian points using "mapdl.eresx("NO")" command) as:

{deformation} = [B] {u}, where {deformation} is 6x1, [B] is 6x24 and {u} is 24x1.

The nodal displacements for the selected element are ordered as: {u} = {u1x, u1y, u1z, ..., u8x, u8y, u8z}. Here, 1,2,...,8 indicate the node ordering used in ANSYS. Using the equation above, the values of deformation vector are completely different from those calculated at the same points by ANSYS.

The [B] matrix is calculated using the shape functions given in ANSYS Theory reference for SOLID185, and it is built using the following steps:

For selected element, get the node and its associated coordinates and Gauss point (i.e., node I = (-1 ,-1, -1) in natural coordinate
system)
Calculate shape function derivatives w.r.t. natural coordinate system at considered Gauss point
Calculate the Jacobian, the inverse of Jacobian and its determinant (they are used to transform shape function derivatives in the global coordinate system)
Calculate shape function derivatives w.r.t. global coordinate system
Calculate [B] matrix

I've checked the code that I developed several times and I don't see any errors or problems (maybe so, I'm not 100% sure!), everything seems consistent to me.

Do you think ANSYS uses other hidden points? Am I missing some piece of theory? Has anyone already done something similar (even using different elements)?