Properties and layerwise modeling of the Harlequin variational theorem for composite structures

Abstract

The analysis of composite structures requires an accurate prediction of the displacements, strain, and (especially) stress fields. To meet this requirement, the Harlequin Variational Theorem of the First Family (HVTFF) was recently formulated by adopting the Partitioned Parametrized Variational Procedure (PPVP). This work introduces for the first time layerwise (LW) axiomatic models that simultaneously represent displacements, stresses, and strains within HVTFF framework. In addition, the physical meaning of the user-selected variational parameter appearing in the functional is assessed and its effects on the accuracy of the fields’ representations is determined. It is also shown that HVTFF can lead to pure displacement formulations or displacement-stress approaches typical of the Hellinger-Reissner Principle (HRP) and Reissner’s Mixed Variational Theorem (RMVT).