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A general first-order formulation of the continuous sensitivity equations is introduced that improves the accuracy of the sensitivity boundary conditions. In the continuous sensitivity method, design or shape parameter gradients are computed from a continuous system of partial differential equations instead of the discretized system, which avoids the problematic mesh sensitivity calculations of discrete methods for shape variation problems. The first-order formulation for both the underlying elasticity and sensitivity equations is amenable to solution by a high-order polynomial least-squares finite element model. The continuous sensitivity boundary-value problem, which can be posed in local or total derivative form, is generally simpler in local sensitivity form for shape variation problems. Although the local form is not unique and total material sensitivities are generally desired for structural elasticity problems, the local sensitivity solution is easily transformed to a material derivative. The first-order formulation and the transformation to material derivatives are demonstrated for two elasticity example problems. The least-squares continuous sensitivity solutions are presented and compared with analytic sensitivities and finite difference results and should prove convenient validation benchmarks for other continuous sensitivity applications. DOI: 10.2514/1.44349

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the MoriTanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry. (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics. [DOI: 10.1115/1.2720908] Keywords: cell mechanics, stress fibers, homogenization, micromechanics, Mori-Tanaka method, finite element numerical simulation

A consistent third-order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed. The formulation has seven displacement functions and requires [C.sup.0] continuity in the displacement field. The exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate. A displacement finite element model is developed using Lagrange elements with higher-order interpolation polynomials. These elements preclude any effect of shear and membranes locking. Comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code.

The active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite material for the constraining layer of active constrained layer damping treatment is dealt with. The longitudinal PFRC material performs excellently in controlling the radiated sound from the vibrating flexible wall of the cavity and this control is attributed to the active constrained layer damping of the wall.

A novel work demonstrates the effect of delamination in smart laminated composite beams on the performance of active constrained layer damping (ACLD) treatment. A finite element model has been derived to formulate the dynamics of the composite beams integrated with a patch of ACLD treatment and a patch of piezoelectric film acting as a distributed sensor with and without the presence of delamination at different locations. Frequency response functions of the beams have been examined to observe the effect of delamination on the performance of ACLD treatment. It has been observed that the ACLD treatment improves the active damping characteristics of the beams, even in the presence of delamination, and that the responses of the beams are sensitive to the variation of the location of delamination. The responses due to active constrained layer damping presented may provide a useful guide to detect the presence of delamination in smart composite beams by the use of the existing numerical techniques.

An asymptotic theory for the vibration analysis of inhomogeneous monoclinic piezoelectric plates, by using small parameter expansion, is developed. Asymptotic results are compared to three-dimensional solution, for a piezoelectric bimorph strip.

In conventional analyses of composite laminates, the assumption of perfect bonding of adjoining layers is well accepted, although this is an oversimplification of the reality. It is possible that the bond strength may be less than that of the laminae. Thus, the study of weak bonding is an interesting focus area. In this study, an elastic bonding model based on three-dimensional theory of elasticity in a layerwise framework is used to study composite laminates. The differential quadrature (DQ) discretization is used to analyze the layerwise model. The present model enables the simulation of actual bonding stress states in laminated structures. The interfacial characteristics of transverse stress continuity as well as the kinematic continuity conditions are satisfied through the inclusion of the elastic bonding layer The present model is employed to investigate the free vibration of thick rectangular cross-ply laminates of different boundary conditions and lamination schemes. [DOI: 10.1115/1.1604838]

The harmonic vibration problem of functionally graded plates is studied by means of a three-dimensional asymptotic theory formulated in terms of transfer matrix. Instead of using multiple time scales expansion, the frequency is determined in a much simpler way that renders the asymptotic method to be practically validated for finding any higher-order solutions. This is illustrated by applying the refined formulation to a functionally graded rectangular plate with simply supported edges. The locally effective material properties are estimated by the Mori-Tanaka scheme. Accurate natural frequencies associated with flexural, extensional, and thickness-stretching modes are provided. DOI: 10.1061/(ASCE)0733-9399(2003) 129:8(896) CE Database subject headings: Plates; Vibration; Frequency; Material properties.