@ARTICLE{Gilewski_W._Płytowy_2017, author={Gilewski, W. and Sitek, M.}, number={No 3}, journal={Archives of Civil Engineering}, pages={19-37}, howpublished={online}, year={2017}, publisher={WARSAW UNIVERSITY OF TECHNOLOGY FACULTY OF CIVIL ENGINEERING and COMMITTEE FOR CIVIL ENGINEERING POLISH ACADEMY OF SCIENCES}, abstract={The formulation of a plate finite element with so called ‘physical’ shape functions is revisited. The derivation of the ‘physical’ shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.}, type={Artykuły / Articles}, title={Płytowy element skończony o fizycznych funkcjach kształtu: poprawność sformułowania}, title={Plate finite element with physical shape functions: correctness of the formulation}, URL={http://www.journals.pan.pl/Content/103352/PDF-MASTER/ace-2017-0026.pdf.pdf}, keywords={płytowy element skończony, fizyczne funkcje kształtu, eliptyczność, zgodność, warunek inf-sup, Plate finite element, Physical shape functions, Ellipticity, Consistency, Inf-sup condition}, }