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SUMMARYThe layerwise laminate theory of Reddy' is used to develop a layerwise, two-dimensional, displacementbased, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3-D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2-D-type data structure that provides several advantages over a conventional 3-D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

A review of equivalent–single–layer and layerwise laminated plate theories and their finite element models is presented. The layerwise theory advanced by the senior author is presented and a variable displacement finite element model and mesh superposition techniques are described. A simultaneous multiple model approach that is based on the variable kinematic theory and the mesh superposition method are also described. The objective of the simultaneous multiple model approach is to match the most appropriate mathematical model with each subregion based on the physical characteristics, applied loading, expected behavior, and level of solution accuracy desired in that subregion. Thus solution economy is maximized without sacrificing the solution accuracy.

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).

This paper presents the initial results of a research project concerning the mechanism of head injury. In order to begin to define the mechanism, it is necessary to determine mechanical properties of the various skull bones, organize them into constitutive equations, and develop a structural model of the skull. The material presented is concerned primarily with the development of experimental procedures and the results which have been obtained. The specimen-testing program has been split into four parts: (1) The procural of 3/4-in. and ll/2-in.-diam plugs from human skulls at autopsy and the precise determination of specimen location and orientation; (2) the fabrication and strain gaging of small test specimens for basic tension, compression, tension-compression, and shear tests; (3) the conducting of tests; and (4) the correlation of experimental findings with microscopic structure by standard and nonstandard techniques of histology.

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SUMMARYAn adaptive finite element procedure is developed for modelling transient phenomena in elastic solids, including both wave propagation and structural dynamics. Although both temporal and spatial adaptivity are addressed, the novel feature of the formulation is the use of mesh superposition to produce spatial refinement (referred to as s-adaptivity) in transient problems. Spatial error estimation is based on superconvergent patch recovery of higher-order accurate stresses and is used to guide mesh adaptivity, while the temporal error estimation is based on the assumption of linearly varying third-order time derivatives of the displacement field and is used to adjust the time step size for the HHT-variant of the Newmark direct numerical integration method. Spatial adaptivity of the mesh is performed using a hierarchical h-refinement scheme that is efficiently implemented using a structured version of finite element mesh superposition. This particular spatial adaptivity scheme is extremely fast and consequently makes it feasible to repeatedly update both the mesh and the time increment as required in an adaptive transient analysis. This work represents the initial effort in applying this type of spatial adaptivity to transient problems. Three example problems are given to demonstrate the performance characteristics of the s-adaptive procedure.

The effects of accurately accounting for transverse shear strain, transverse normal strain, and discrete layer kinematics on the computed global response of actuated plates are investigated using a hierarchical displacement-based, two-dimensional (2-D) finite element model that is developed specifically for composite laminates. The hierarchical model is used to obtain the first-order shear deformation model, a higher-order cubic equivalent-singlelayer model, a type-I layerwise model, and a type-II layerwise model as special cases. Each of the first three models uses a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the models differ significantly in their assumed distribution of transverse shear strain. The type-II layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects. The scope of the study is restricted to homogeneous plates with surface-mounted actuators covering a wide range of span-to-thickness ratios. The results clearly demonstrate that as the span-to-thickness ratio of the actuated region decreases, discrete layer kinematics become very important for accurately characterizing the global response of the actuated plate. The set of laminate kinematic assumptions utilized by a particular model influence the predicted global response primarily through the so-called local kinematic effect where a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and localized transverse normal deformation in the vicinity of the actuator edges, thereby reducing the amount of actuation energy that is available for producing the intended global deformation mode.