Extension of the strain energy updating technique to a multilayered shell model with adaptive displacements and fixed DOF

The strain energy updating technique (SEUPT) is extended to a new zigzag shell model with a hierarchical piecewise representation of displacements, which can adapt to a variation of solutions across the thickness. This model has the capability of being refined across the thickness without increasing the number of functional DOF (the traditional midplane displacements and shear rotations). The purpose of the SEUPT is to improve the accuracy of standard finite elements based on equivalent single-layer models with transverse shear deformations up to the level of the zigzag model. The strain and kinetic energies and the work of external forces are updated through a postprocessing iterative procedure by starting from a local interpolation of the results of the finite-element analysis. Because no derivatives of in-plane stresses are involved, updating is fast. The current version of the SEUPT obtains accurate predictions of interlaminar stresses from constitutive equations; thus, it does not require integration of local differential equilibriums, which is unwise for finite elements and can be inaccurate in certain cases. Because of its adaptive capability, the SEUPT efficiently treats thick laminated plates and shells with distinctly different properties of layers, strong anisotropy, and significant transverse normal stresses and strains. Accuracy is assessed by considering the stresses under static loading and the response to blast pulse loading of undamaged and damaged sandwich shells with laminated faces. The results show that the SEUPT preserves the accuracy of the zigzag shell model and efficiently improves the accuracy of standard finite elements.