I notice that the solid-shell element (SOLSH190) gives me a weak buckling behaviour compared to solid and shell elements in some cases. In some specific cases, the buckling mode is unrealistic. Is this a bug?

The SOLSH190 used a fully-coupled 3-D stress stiffness in linear buckling and pre-stressed modal analyses; however, this method does not work well if the mesh is dominated with triangles or irregular quads. It was a limitation that has been corrected for 12.0. A decoupled method with membrane, thickness-normal, and transverse shears stress stiffness is now adopted.

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