Variable Kinematic Modelling of Laminated Composite Plates

Abstract

SUMMARYA displacement-based variable kinematic global-local finite element model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. The displacement field hierarchy contains both a conventional plate expansion (2-D) and a full layerwise (3-D) 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. The VKFE is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm. These models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free-edge effects).

Multiscale enrichment based on partition of unity

“…Among the noteworthy SGEMs are the s-version of the finite element method [19,20,21,22] with application to strong [23,24] and weak [25,26,27,28] discontinuities, various multigrid-like scale bridging methods [29,30,31,32], the Extended Finite Element Method (XFEM) [33,34,35] and the Generalized Finite Element Method (GFEM) [36,37] both based on the Partition of Unity (PU) framework [38,39] and the Discontinuous Galerkin (DG) [40,41] method. Multiscale methods based on the concurrent resolution of multiple scales are often called as embedded, concurrent, integrated or hand-shaking multiscale methods.…”

Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method

“…In the analysis of composite materials, their particular anisotropic behavior must be taken into account to predict the directional properties. The CLT requires C 1 -continuity (Hermite interpolation) of the transverse deection and C 0 -continuity (Lagrange interpolation) of the in-plane displacements [28]. In CLT, good predictions can be made for in-plane stresses σ x , σ y , and τ xy and strains, however, interlaminar stresses σ z , τ xz , and τ yz are not obtainable because of the Kirchho assumption.…”

“…Through the homogenization procedure in the CLT, the stress resultants can be related to strains at the structural level in terms of the material elastic properties and the geometry of a plate. This means that the heterogeneous composite laminated plate is replaced implicitly by a single homogeneous plate, with the stiness and inertia properties of the new single homogeneous plate becoming equivalent to those of a heterogeneous laminated plate in the integral sense [28]. Also in the CLT, linear displacement eld (kinematic continuity between layers) and plane stress state are assumed owing to the small thickness compared to other dimensions.…”

“…Naturally, many researchers have used equivalent 2D plate theories such as classical lamination theory (CLT) and rst order shear deformation theory (FSDT) to analyze the behaviour of such structures [135]. Basically, the CLT and FSDT were derived from integration of the virtual work statement through the laminate thickness, so the heterogeneous laminate is treated as a single homogeneous layer [28]. Due to the homogenization characteristics resulting from equivalent stiness and inertia properties in the integral sense, the CLT and FSDT are not able to describe the kinematics of delamination with their original formulation.…”

First-Order Displacement-Based Zigzag Theories for Composite Laminates and Sandwich Structures: A Review

“…In closing this introductory overview of the zigzag approaches for the analysis of laminated composite laminates and sandwich structures, it should be noted that they belong to the more general modern approaches, known either as Multi-scale or Global-local approaches [86,87,88,89,90,91,92], where the displacement field within each layeris represented as a superposition of a layer-wise field, defined over each layer, and a global field spanning the entire laminate. Thus, the governing equations exhibit explicit coupling between effects associated with different (global and local) length scales.…”