John Anthony Mitchell

A refined hybrid plate theory for composite laminates with piezoelectric laminae

In this paper, a refined theory of laminated composite plates with piezoelectric laminae is developed. The equations of motion of the theory are developed using an energy principle. This formulation is based on linear piezoelectricity, and includes the coupling between mechanical deformations and the charge equations of electrostatics. The theory developed herein is hybrid in the sense that an equivalent single-layer theory is used for the mechanical displacement field, whereas the potential function for piezoelectric laminae is modeled using a layerwise discretization in the thickness direction. For the equivalent single layer, the third-order shear deformation theory of Reddy is used. This hybrid feature is good in that it demonstrates a way in which multilayered smart skin piezoelectric structures may be analysed to accommodate multiple voltage inputs and/or sensor outputs.

A Study of Embedded Piezoelectric Layers in Composite Cylinders

A power series solution is presented for the static equilibrium equations of an axisymmetric composite cylinder under loadings due to surface mounted or embedded piezoelectric laminae. Both uniform and nonuniform distributions of the piezoelectric effect are studied and results are verified using a finite element model based on axisymmetric two-dimensional elasticity theory equations. A cylindrical truss element actuator is developed which may be used for damping vibrations of truss-type structures. Finally, the effects of a piezoelectric patch have been investigated. The axial forces generated at the fixed ends of a cylinder are found to be proportional to the length of the patch.

On refined nonlinear theories of laminated composite structures with piezoelectric laminae

In this paper geometrically nonlinear theories of laminated composite plates with piezoelectric laminae are developed. The formulations are based on thermopiezoelectricity, and include the coupling between mechanical deformations, temperature changes, and electric displacements. Two different theories are presented: one based on an equivalent-single-layer third-order theory and the other based on the layerwise theory, both of which were developed by the senior author for composite laminates without piezoelectric laminae. In the present study, they are extended to include piezoelectric laminae. In both theories, the electric field is expanded layerwise through the laminate thickness. The dynamic version of the principle of virtual displacements (or Hamilton’s principle) is used to derive the equations of motion and associated boundary conditions of the two theories. These theories may be used to accurately determine the response of laminated plate structures with piezoelectric laminae and subjected to thermomechanical loadings.

Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

The elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn3[combining macron]m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt-Reuss-Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pughs and Poissons ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are θD = 299.7, 415.6 and 356.9 K, respectively, while θD = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.

Modeling and Measurement of a Bistable Beam in a Microelectromechanical System

Design and fabrication of microelectromechanical systems (MEMS) can be costly, time consuming, and necessitating accurate models for their behavior. Current theoretical models of bistable beams in MEMS devices are limited to numerical or small deformation models and current measurement techniques are unable to fully characterize these devices as they only determine thresholds or have resolutions that are too coarse to adequately explore the force-deflection relationship of bistable mechanisms. Two analytical models are developed: a stepped Euler-Bernoulli beam and a large deformation model. To validate these models, a new technique for measuring in-plane mechanical properties of MEMS devices is introduced that measures normal and lateral forces against a probe tip, while electrostatic actuation and a force-feedback loop maintain the desired tip position. This allows true displacement-controlled measurements along two axes and facilitates automated positioning. Measurements validate the large deformation model and show that Euler-Bernoulli beam theory is inadequate for modeling the mechanisms bistable behavior. A parameter study in edge width using the large deformation model accounts for discrepancies between predicted and measured forces. The models utility is further demonstrated by an optimization study that redesigns the mechanism to be less sensitive to the edge width variation introduced in the manufacturing process.

Peridigm Users' Guide v1.0.0

Peridigm is Sandia’s primary open-source computational peridynamics code. It is a component software project, built largely upon Sandia’s Trilinos project and Sandia’s agile software components efforts. It is massively parallel, utilizes peridynamic state-based material models, Exodus/Genesis-format mesh input, Exodus-format output, and multiple material blocks. It performs explicit dynamic, implicit dynamic, and quasistatic analyses utilizing powerful nonlinear and linear solvers.

Study of Interlaminar Stresses in Composite Laminates Subjected to Torsional Loading

A computational procedure for accurate determination of interlaminar stresses in thick and thin composite laminates subjected to torsional loading is presented. A multilevel, recursively defined preconditioner in conjunction with the preconditioned conjugate gradient (PCG) algorithm is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element method. The computational procedure is used to model stress fields in thick and thin laminates in torsion using three-dimensional and quasi-three-dimensional models. Results indicate that the preconditioner developed here can be used to produce an efficient iterative solver for the determination of two- and three-dimensional stress fields in composite structures.

MEMS Passive Latching Mechanical Shock Sensor

This paper presents a novel micro-scale passive-latching mechanical shock sensor with reset capability. The device integrates a compliant bistable mechanism, designed to have a high contact force and low actuation force, with metal-to-metal electrical contacts that provide a means for interrogating the switch state. No electrical power is required during storage or sensing. Electrical power is only required to initialize, reset, self-test, or interrogate the device, allowing the mechanism to be used in low-power and long shelf-life applications. The sensor has a footprint of about 1 mm2 , allowing multiple devices to be integrated on a single chip for arrays of acceleration thresholds, redundancy, and/or multiple sense directions. Modeling and experimental results for a few devices with different thresholds in the 100g to 400g range are given. Centrifuge test results show that the accelerations required to toggle the switches are higher than current model predictions. Resonant frequency measurements suggest that the springs may be stiffer than predicted. Hammer-strike tests demonstrate the feasibility of using the devices as sensors for actual mechanical shock events.Copyright

A hierarchical iterative procedure for the analysis of composite laminates

A multilevel recursively defined preconditioner for use with the preconditioned conjugate gradient (PCG) algorithm is developed and applied to solve thin and thick laminated plate problems. The preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element (FE) method. Numerical studies have been conducted using quadrilateral elements for two-dimensional problems up to p=8 and serendipity brick elements for three-dimensional problems up to p=5. The efficiency of the iterative procedure is illustrated using bending response of laminated plates. The effects of element span ratios, convergence tolerance, polynomial order, material properties, and plate span ratios on the number of iterations required for convergence has been investigated. Results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two- and three-dimensional problems in structural mechanics.

Study of the effect of embedded piezoelectric layers in composite cylinders

An elasticity solution is presented for the static equilibrium equations of an axisymmetric composite cylinder under loadings due to surface mounted or embedded piezoelectric laminae. Both uniform and non-uniform distributions of the piezoelectric effect are studied and results are verified using a finite element analysis based on axisymmetric 2-D elasticity theory equations. A cylindrical truss element actuator is developed which may be used for damping vibrations of truss type structures. Finally, the effects of a piezoelectric patch have been investigated. The axial forces generated at the fixed ends of a cylinder are found to be proportional to the length of the patch.