Hierarchical modeling of laminated composite plates using variable kinematic finite elements and mesh superposition

Abstract

A hierarchical, 2-D, displacement-based, global/local finite element model is developed to permit an accurate, efficient analysis of localized 3-D effects in laminated composite plates. The model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level.

First, by superimposing a hierarchy of assumed displacement fields within the same finite element domain, a new variable kinematic, finite element is developed. The displacement field hierarchy contains both a conventional 2-D plate expansion and a full layerwise expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. Since the resulting model is hierarchic, these different element types can easily be connected together in the same computational domain to permit simultaneous multiple model analysis.

Despite the obvious utility of variable kinematic finite elements, a multiple model analysis based solely on the use of these elements has a significant restriction: all subregions of the computational domain must maintain in-plane mesh compatibility along subregion boundaries. This restriction necessitates the use of 2-D transition zones.

In an effort to avoid the problems associated with 2-D transition zones, hierarchical, multiple assumed displacement fields are used at the mesh level in a finite element mesh superposition scheme. In this application of the finite element mesh superposition technique. the variable kinematic elements are used to form the independent, local, overlay meshes that can be superimposed on a pre-existing mesh of conventional 2-D plate elements. Due to the hierarchical nature of the resulting composite displacement field, the overlay mesh and the original mesh need not have compatible discretization. Thus the specifications and superimposed location of the overlay mesh can be tailored to fit the needs of the analyst regardless of the global mesh topology.

The resulting model is used to analyze a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free edge effects, delamination fronts, and adhesive bonds).