On the Vibration of Layered Sandwich Elastic Plates

Sandwich elastic plates have found increasing applications in civil, aerospace, military and offshore industries to enhance superior resistance to fatigue crack propagation, impact damage, local buckling and are very effective for vibration damping and noise reduction. Such structural application has significantly led to reduction in vulnerability of warships to blasts, ballistics, bomb and fire attacks. In engineering structures, one of the effective ways of damping vibration and noise attenuation, is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. Recent analysis and experimental investigation of vibration characteristics and damping properties of layered sandwich structures, are mostly limited to elastic beams. This paper is an attempt to extend such analytical investigations to layered sandwich plates. By employing contact mechanics and laminated thin plate theory, the generalised equation governing the vibration of two layered sandwich plates that are held together in pressurised environment is presented. In particular, by invoking operational methods for the case of linear interface pressure distribution, closed form analytical results for the system natural frequency and dynamic response under external excitation are reported for design analysis and applications.

A Novel Perspective in the Design of Cable-Driven Systems

This paper deals with a novel approach to the design of cable-driven systems. This kind of robots possesses several desirable features that distinguish them from common manipulators, such as: low-inertia, cost-effectiveness, safety, easy reconfiguration and transportability. One key-issue that arises from the unilateral actuation is the design for workspace optimization. Most previous researches on cable-driven systems design focused their attention on workspace analysis for existing devices. Conversely, we introduce a new approach for improving workspace by design, introducing movable pulley-blocks rather than increasing the number of cables. By properly moving the pulley-blocks, the end-effector can be always maintained in the best part of the working space, thus enhancing robot capabilities without the need for additional cables. Furthermore, the eventuality of cable interference is strongly reduced. In this paper, the novel design concept is applied to different planar point-mass cable-driven robots, with one or more translating pulley-blocks. The maximum feasible isotropic force, along with the power dissipation and the effective mass at the end-effector are employed to compare the performances of different configurations.

A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.

Modeling Two-Phase Flow in Porous Media Including Fluid-Fluid Interfacial Area

We present a new numerical model for macro-scale two-phase flow in porous media which is based on a physically consistent theory of multi-phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy’s law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid–fluid interfaces. An alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We show how parameters can be obtained for the alternative model using experimental data from a new kind of flow cell and present results of a numerical modeling study.

Fatigue of a Nanocomposite Laminate

A multi-scale carbon fiber reinforced polymer nanocomposite laminate, with strategically incorporated fluorine functionalized carbon nanotubes at 0.2 weight percent, is studied for improvements in strength, stiffness and fatigue life under both tension-tension fatigue (R = +0.1) and tension-compression fatigue (R = −0.1) loading. The nanotubes were incorporated into the carbon fabric, and laminates were fabricated using a high temperature vacuum assisted resin transfer molding process. The influence of the fluorinated functionalized carbon nanotubes on the evolution of damage and the resistance to catastrophic failure is credited for these mechanical property improvements.

Approximate Macroscale Constitutive Relations Using a Finite Element Based Constitutive Equations for Microscale Contact

Three dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity-asperity constitutive relations from a finite element model of their elastic-plastic interaction. Shoulder-shoulder asperity contact yields a slanted contact force consisting of both tangential (parallel to mean plane) and normal components. Multiscale modeling of the elastic-plastic rough surface contact is presented in which asperity-level FE-based constitutive relations are statistically summed to obtain total force in the normal and tangential direction. The equations derived are in the form of integral functions and provide expectation of contact force components between two rough surfaces. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. This is shown to yield upon statistical summation the cumulative effect resulting in the contact force between two rough surfaces with two components, one in the normal direction and a half-plane tangential component.

Humanoid Face Utilizing Rotary Actuator and Piezoelectric Sensors

Mimicking facial structure for a robotic head is a challenging issue and requires information on design and control of muscle actuation, architecture of the linkages between actuation points within skin, and deformation matrix with respect to global coordinates for a specific expression. This manuscript presents: (1) a functional relationship between deformation vector of facial control points and actuator parameter, skin elasticity and angular position of actuator. The actuation method is applicable to any rotary actuator technology utilized for facial expressions and takes into account the skin stiffness; (2) a prototype robotic head with embedded sensor to enhance interaction ability of humanoids; and (3) characterization of various facial expressions on a prototype robotic face.

A New and Consistent Approach for Deriving Brinson’s 1-D Constitutive Equation for Shape Memory Alloys

One of the first 1-D constitutive equations for shape memory alloys was presented by Brinson L.C in 1993 that became the base of later works typically. In Brinson’s equation, several proposed functions are considered in order to simplify the model and obtain the constitutive equation for SMA. In a recent paper V. R. Buravalla and A. Khandelwal (2007) have shown certain anomalies in Brinson’s model and have tried to present a modified model which unlike Brinson’s model satisfies the compatibility condition. However, their formulation, besides being lengthy, lacks clarity and in particular does not address proper expressions for transformation tensors Ωs and ΩT. In the present work, Brinson’s constitutive equation is derived from fundamental relations using a simple, clear-cut and straightforward approach. Without any extra and unnecessary assumption the consistency of the model is confirmed.

Three-Parameter Viscoelasticity Models for Ballistic Fabrics

Ballistic fabrics are made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra®. These fibers often behave viscoelastically in high strain rate deformations. The Kelvin-Voigt and Maxwell rheological models have been used to characterize such viscoelastic responses at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this study, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s−1 and 495 s−1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which shows that the two sets of results are in fairly good agreement. In particular, the comparison reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.

Design Optimization of Material Properties in a Particle-Filled Composite Material System

This work presents a methodology implementing random packing of spheres combined with commercial finite element method (FEM) software to optimize the material properties, such as Young’s modulus, Poisson’s ratio, coefficient of thermal expansion (CTE) of two-phase materials used in electronic packaging. The methodology includes an implementation of a numerical algorithm of random packing of spheres and a technique for creating conformal FEM mesh of a large aggregate of particles embedded in a medium. We explored the random packing of spheres with different diameters using particle generation algorithms coded in MATLAB. The FEM meshes were generated using MATLAB and TETGEN. After importing the nodes and elements databases into commercial FEM software ANSYS, the composite materials with spherical fillers and the polymer matrix were modeled using ANSYS. The effective Young’s modulus, Poisson’s ratio, and CTE along different axes were calculated using ANSYS by applying proper loading and boundary conditions. It was found that the composite material was virtually isotropic. The Young’s modulus and Poisson’s ratio calculated by FEM models were compared to a number of analytical solutions in the literature. For low volume fraction of filler content, the FEM results and analytical solutions agree well. However, for high volume fraction of filler content, there is some discrepancy between FEM and analytical models and also among the analytical models themselves.