Membrane locking and CST triangle

[topcomer]

I often read on books that linear triangles do not have membrane locking for large deformations of plates/shells. I completely don't understand how this is possible. If one uses the well-known CST, stretching is measured as the increase in length of each edge of the triangle. Then, in the limit of the membrane stiffness going to infinity, clearly the solution cannot approximate any bending-dominated state, but rather it will be always rigid on general meshes (i.e. Minkowski theorem for convex bodies), allowing at most bending about few lines on very regular ones. What am I missing?

 

[Navin A S]

The thing you are missing is that linear triangles do not necessarily have the same stiffness in all directions. For example, in a triangular plate with a membrane locking behavior, the stiffness in the bending direction (the direction perpendicular to the plane of the triangle) may be much higher than the stiffness in the stretching direction (the direction parallel to the plane of the triangle). In this case, even though the overall stiffness of the triangle is finite, it will behave like an infinite stiffness in the bending direction, thus preventing large deformations in that direction.