Balajee Ananthasayanam

Design of Cellular Shear Bands of a Non-Pneumatic Tire -Investigation of Contact Pressure

In an effort to build a shear band of a lunar rover wheel which operates at lunar surface temperatures (40 to 400K), the design of a metallic cellular shear band is suggested. Six representative honeycombs with aluminum alloy (7075-T6) are tailored to have a shear modulus of 6.5MPa which is a shear modulus of an elastomer by changing cell wall thickness, cell angles, cell heights and cell lengths at mesoscale. The designed cellular solids are used for a ring typed shear band of a wheel structure at macro-scale. A structural performance such as contact pressure at the outer layer of the wheel is investigated with the honeycomb shear bands when a vertical force is applied at the center of the wheel. Cellular Materials Theory (CMT) is used to obtain in-plane effective properties of a honeycomb structure at meso-scale. Finite Element Analysis (FEA) with commercial software ABAQUS is employed to investigate the structural behavior of a wheel at macro-scale. A honeycomb shear band designed with a higher negative cell angle provides a lower contact pressure along the contact patch associated with an in-plane shear flexible property.

Final Shape of Precision Molded Optics: Part I—Computational Approach, Material Definitions and the Effect of Lens Shape

Coupled thermomechanical finite element models were developed in ABAQUS to simulate the precision glass lens molding process, including the stages of heating, soaking, pressing, cooling and release. The aim of the models was the prediction of the deviation of the final lens profile from that of the mold, which was accomplished to within one-half of a micron. The molding glass was modeled as viscoelastic in shear and volume using an n-term, prony series; temperature dependence of the material behavior was taken into account using the assumption of thermal rheological simplicity (TRS); structural relaxation as described by the Tool-Narayanaswamy-Moynihan (TNM)-model was used to account for temperature history dependent expansion and contraction, and the molds were modeled as elastic taking into account both mechanical and thermal strain. In Part I of this two-part series, the computational approach and material definitions are presented. Furthermore, in preparation for the sensitivity analysis presented in Part II, this study includes both a bi-convex lens and a steep meniscus lens, which reveals a fundamental difference in how the deviation evolves for these different lens geometries. This study, therefore, motivates the inclusion of both lens types in the validations and sensitivity analysis of Part II. It is shown that the deviation of the steep meniscus lens is more sensitive to the mechanical behavior of the glass, due to the strain response of the newly formed lens that occurs when the pressing force is removed.

FINAL SHAPE OF PRECISION MOLDED OPTICS: PART II—VALIDATION AND SENSITIVITY TO MATERIAL PROPERTIES AND PROCESS PARAMETERS

In Part I of this study a coupled thermo-mechanical finite element model for the simulation of the entire precision glass lens molding process was presented. That study addressed the material definitions for the molding glass, L-BAL35, computational convergence, and how the final deviation of the lens shape from the mold shape is achieved for both a bi-convex lens and a steep meniscus lens. In the current study, after validating the computational approach for both lens types, an extensive sensitivity analysis is performed to quantify the importance of several material and process parameters that affect deviation for both lens shapes. Such a computational mechanics approach has the potential to replace the current trial-and-error, iterative process of mold profile design to produce glass optics of required geometry, provided all the input parameters are known to sufficient accuracy. Some of the critical contributors to deviation include structural relaxation of the glass, thermal expansion of the molds, TRS and viscoelastic behavior of the glass and friction between glass and mold. The results indicate, for example, the degree of accuracy to which key material properties should be determined to support such modeling. In addition to providing extensive sensitivity results, this computational model also helps lens molders/machine designers to understand the evolution of lens profile deviation for different lens shapes during the course of the process.

Modeling of Piezoelectric Materials on Rubber Beams

It is common to use piezoelectric materials to reduce vibrations or otherwise alter the dynamics of structures made of metal or composite materials. In contrast, this work addresses modeling of piezoelectric patches applied to a rubber substrate. An underlying goal of modeling, however, is to represent the significant physics of a problem with the simplest model possible. There were several simplified approaches to modeling piezoelectric actuation on classical beam and plate elements developed in the late 1980s and early 1990s. Of these, the pin force, extended pin force, and Euler-Bernoulli methods are assessed in this study. The basic concepts of the three approximation methods are developed, and the curvatures predicted by each is compared to predictions from a special-purpose finite element code. The final conclusion is that the constant-strain approaches (pin force and enhanced pin-force) are not accurate for very soft substrates. Future work includes adding the time dependence of rubber materials as well as the possibility of material of geometric nonlinearities.

Piezoelectric actuation of a compliant semi-infinite beam

Piezoelectric materials (PZT) are commonly used as actuators and sensors for vibration suppression in flexible metal or composite substrates. There are well-established techniques for modeling the actuation of PZTs when they are bonded to these structures. However, if the substrate material is much softer than the piezoelectric actuator/sensor, a higher level of modeling is needed to predict the local deformations at the interface. In this research, a finite-length piezoelectric element bonded perfectly to an infinite elastic strip is modeled. The specific goal was to quantify the actuation and sensing mechanics of piezoelectric devices on substrates potentially much softer than the piezoelectric element. Previous works have addressed membranes or plates bonded to an elastic half-space subjected to mechanical or thermal loads. Euler-Bernoulli beam theory is used to derive equations of equilibrium for the piezoelectric beam. These equations are then recast as integral equations for the interface displacement gradients and equated to the equivalent quantities for an elastic layer subject to distributed shear and normal tractions. The resulting singular integral equations are solved by expanding the interface tractions using a series of Chebyshev polynomials. First, certain sanity checks are performed to confirm the validity of the model by choosing a stiff substrate for which Euler-Bernoulli beam-assumptions holds good. For certain combinations of geometrical and material parameters, the substrate has a positive curvature, whereas the piezoelectric has a negative curvature and vice versa. After analyzing the forces acting on both piezoelectric and the substrate, the reasons for this behavior in soft substrates are justified here. Finally, the range of geometric parameters where the reversal of bending occurs in the piezoelectric is given.

Modeling of a piezoelectric beam on a semi-infinite elastic strip

We have developed a detailed model for a piezoelectric patch bonded perfectly to a semi-infinite substrate. There are well-established techniques for representing the effects of piezoelectric actuation on a flexible substrate by equivalent moments, but the accuracy of moments rely on classical beam behavior in both the actuation and substrate layers. The goal of the work presented here is to present a model capable of predicting both the actuation and sensing ability of a smart material on a general substrate. The piezoelectric layer is modeled by classical beam theory, but no kinematic assumptions other than plane strain are imposed on the substrate. Equilibrium is enforced between the piezoelectric patch and the surface tractions over the interface region, and standard Euler-Bernoulli beam theory is then used to form integral equations in terms of the displacement gradients at the interface with the substrate. Greens functions are then derived for a semi-infinite substrate using techniques from contact mechanics. There is no loss of generality in choosing a semi-infinite substrate since the effects of actuation by a patch disappear quickly outside the contact region. Preliminary results that both validate the current model and support the equivalent-moment action models for certain substrates are presented.