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Need to compute the derivative of S4R shell element stiffness matrix with respect to Young modulus

Need to compute the derivative of S4R shell element stiffness matrix with respect to Young modulus

Need to compute the derivative of S4R shell element stiffness matrix with respect to Young modulus

(OP)
Hi,

we use Abaqus shell elements of type S4R for modeling the concrete part of a reinforced concrete plate.

We need to know how to compute the derivative of S4R shell element stiffness matrix with respect to Young modulus.

For example, like what is done for 2D plane stress elements in eqs. (42b) and (43) in this paper. There, the derivative is computed from a definition of the element stiffness metrix as an integral of BTDB dxdy with B being a matrix of partial derivatives of element shape functions and with a 3x3 matrix D depending on Young's and shear modulus. However, we do not know if similar relations hold for S4R and if so, for what B and D matrices.

Any suggestion on how to do this or where to find this information?

Thank you in advance!

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