The Inf-Sup Condition Tests for Shell/Plate Finite Elements / Testy Warunku Inf-Sup Do Oceny Płytowych I Powłokowych Elementów Skonczonych

Development of high-performance finite elements for thick, moderately thick, as well as thin shells and plates, was one of the active areas of the finite element technology for 40 years, followed by hundreds of publications. A variety of shell elements exist in the FE codes, but “the best” finite element is still to be discovered. The paper deals with an evaluation of some existing shell finite elements, from the point of view of the third of three requirements to be satisfied by the element: ellipticity, consistency and inf-sup condition. It is difficult to prove the inf-sup condition analytically, so, a numerical verification is proposed. A set of numerical tests is considered for shell and plate problems. Two norm matrices and a selection of the stiffness matrices (bending, shear and membrane dominated) are analysed. Finite elements from various computer systems can be evaluated and compared with the use of the proposed tests.