Avoiding locking in Reissner-Mindlin plates with high-order hierarchic bubble plus finite elements (Q1917863)

We prove that special finite elements of suitable degree do not exhibit any kind of locking phenomenon when used for the numerical solution of Reissner-Mindlin plate bending problems. The finite element is constructed by adding bubble functions to standard serendipity elements. The new elements, referred to as bubble plus elements, from the degree three onwards avoid the numerical locking. The mathematical proof of such a good behavior is based on a deep relation between the \({\mathcal C}^0\) bubble plus element of degree three for Reissner-Mindlin plates and the \({\mathcal C}^1\) element for Kirchhoff plates known as Bogner-Fox-Schmit element.