Dear Members,

I was trying to study the behaviour of Abaqus S4 shell element. In an attempt to do so, I came across the paper by Dvorkin and Bathe as shown in the first image inserted below. I was trying to solve for the SHEAR case for a thickness of t=0.001 in the given distorted mesh. As per the paper, the transverse displacement (U3) should follow a linear distribution.

The displacement component U3 obtained for shear load Q=1  in Abaqus is not linear as shown below:

After refining the mesh to 1000x1000 elements, the displacement contour becomes linear, however, the tip displacement converges to a much different value (0.00297) as follows:

I made the above investigation during the process of implementing an MITC4 shell element. The above patch test solved using my implementation fetches the following result for U3 displacement:

As evident from the above displacement contour, the tip U3 displacement using my implementation with 5 distorted elements is same as the converged solution of Abaqus (0.00297) using 1000x1000 elements. To justify the numerical solution, I worked out a theoretical derivation leading to the same tip displacement as below:

Does the above observation mean that the results obtained using 5 distorted element in ABAQUS is inaccurate? Does it mean that Abaqus S4 shell element does not quality SHEAR patch test in above Dvorkin's and Bathe's paper? 

I kindly request the members to share their expert opinion in this regard.

(N.B.: For thickness t=1, Abaqus results are as per the research paper and also match my implementation)

Thanks with kind regards,

Aakash