Penalty partial reduced selective integration: a new method to solve locking phenomena in thin shell steel and concrete structures

The shell structures are commonly used in many civil and industrial and long-span logistic applications. In this research we simply start by applying a degenerated finite element continuum approach. Then we propose a new alternative formulation by splitting the shear energy into two main components, the first one exactly integrated, whereas the second reduced integrated in a proper way. In this numerical and analytical research we present this advanced new approach (herein named penalty partial reduced selective integration) by adding weight coefficients to the splitting energy terms. As a consequence of this formulation, the unwanted locking events are definitively eliminated. A wide range of real and analytical examples, from scientific literature and practical engineering shell design situations, are analyzed and deeply investigated to better understand the level of accuracy and effectiveness of the formulation proposed. Furthermore, comparisons with well defined and established shell finite elements are made just to yield insight into the predictive capability of the penalty partial reduced selective integration, herein proposed and studied. Hence many examples are used to test this new formulation in order to analyze the numerical behavior of the approximate solution in dependence of the splitting parameters. A simple kind of methodological rules for choosing these numerical non-dimensional parameters are also given.