In-plane torsional stiffness in a macro-panel element for practical finite element modelling. (August 2018) - Li, T.Q.; Ward, T.; Lewis, W.J.
Highlights: We address the problem of finite element modelling of in-plane torsional stiffness arising in a situation where beam and shell element connections induce in-plane torsional effects in the shell. Previous work concerning a model based on Allman/Cook formulation is found to be lacking sufficient accuracy in predicting these effects. Our proposed macro-panel element resolves the problem of the in-plane torsional stiffness of the shell being adversely affected by the size of the finite elements, while retaining the quality of a finely meshed model needed to represent the normal and shear stresses accurately. Additional benefits arising from the proposed model are: (i) much simpler modelling process and (ii) much simpler analysis of results, which makes the model attractive for use in practice. Abstract: Finite element (FE) analysis produces results, which, in most cases, gain in accuracy, as the size of the FE mesh is reduced. However, this is not necessarily the case when beam and shell element connections induce in-plane torsional effects in the shell. In such situations, shell elements either do not allow for an in-plane torsional stiffness, or, when present, the in-plane torsional stiffness is incorrectly affected by the sizes of the elements. To overcome this problem, we propose a macro- panel element that has fewer degrees of freedom, includes a new model for in-plane torsional stiffness, and produces results with sufficient accuracy to meet engineering requirements. The panel element is based on the principle of sub-structuring, i.e., the panel is meshed internally by smaller shell elements. As shown in the paper, the proposed panel element can be quite large, yet, it can give accurate analysis results. This work helps to overcome a common dilemma in practical use of finite element analysis, where finite element theory requires element sizes to be sufficiently small, but practical considerations suggest the use of large-size elements that simplify the modelling process and reduce excesses in generated results. A model built using macro-panel elements is equivalent to the model built using smaller shell elements, with the normal and shear stresses in the former being the same as the stresses in the finely meshed shell element model, We identify a number of performance benefits that become available as a consequence of modelling the shell elements at a higher level of abstraction.