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 theelement: 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.

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.

Investigation of influence of TiN thin film morphology on deformation inhomogeneities is an overall subject of the research. Numerical modelling approach that was selected for the study is based on the digital material representation concept, which gives an opportunity to directly replicate columnar microstructure morphology of an investigated thin film. Particular attention in this paper is put on the discussion of the influence of cellular automata neighbourhood on thin-film digital morphologies and their further deformation behaviour. Additionally, an evaluation of representativeness aspects of the digital models, in particular, the analysis of the influence of a number of columns, their dimensions and variations in their properties on the material behaviour during compression tests is also presented. The non-periodic boundary conditions are assumed during the investigation. Obtained data in the form of equivalent stress distributions as well as homogenized stress-strain curves from analyzed case studies are presented and discussed within the paper.