The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability Equations

A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions

Bifurcation and collapse analysis of stringer and ring-stringer stiffened cylindrical shells with cutouts

Results for cylindrical configurations using the STAGS computer program were presented. Discontinuities were imposed upon the shell's skin by incorporating symmetrical cutout openings. In addition, the surface is stiffened with both stringer and ring-stringer arrangements. The cutout problem has been shown to be highly nonlinear for smooth surface shells, but it was found that bifurcation and collapse loads are close when one is considering stiffened skin configurations. In order to arrive at this conclusion, it was necessary to evaluate the following: (1) comparison between smeared and discrete stiffener theory for linear solutions, (2) numerical finite difference convergence as directed toward buckling determination, (3) collapse load results with the various skin stiffeners. A linear bifurcation study relating to stiffening effects around cutout areas present within stringer and ring-stringer shell surfaces was included. Comparisons were made between a variety of geometric positions considering cutout frame and thickened skin additions

Biological Investigation of Wing Motion of the Manduca Sexta

An investigation was conducted assessing the feasibility of reproducing the biological flapping motion of the wings of the hawkmoth, Manduca sexta (M.sexta) by artificially stimulating the flight muscles for Micro Air Vehicle research. Electromyographical signals were collected using bipolar intramuscular fine wire electrodes inserted into the primary flight muscles, the dorsal longitudinal and dorsal ventral muscles, of the adult M.sexta. These signals were recorded and associated with wing movement using high speed video. The signals were reapplied into the corresponding muscle groups with the intention of reproducing similar flapping motion. A series of impulse signals were also directed into the primary flight muscles as a means of observing muscle response through measured forewing angles. This study pioneered electromyographic research on M.sexta at the Air Force Institute of Technology with tests conducted with fine wire electrodes. Through this process, the research showed the deformational structural changes that take place when a wing is removed from an insect and proved that muscular stimulation is a viable method for generating wing movement. This study also assisted in developing an understanding related to the role that a thorax-like fuselage could play in future micro aircraft designs. This study has shown that partial neuromuscular control of the primary flight muscles of M.sexta is possible with electrical stimulants which could be used to directly control insect flight

An Experimental Technique for the Evaluation of Strain Dependent Material Properties of Hard Coatings

A novel vibration experiment consisting of a free-free boundary condition, an electromagnetic excitation source, a vacuum chamber, and a laser vibrometer based surface measurement system has been developed that permits high levels of excitation on highly damped specimens with a minimal amount of unwanted systematic error. While some of the aspects of this experiment are not unique, when combined with a processing technique that accounts for the nonlinearities present in the system, this experiment permits, accurate measurement of strain dependent stiffness and damping properties of hard coatings at high strain levels. This procedure has been demonstrated using a titanium beam that has been coated with a free-layer damping treatment of Magnesium Aluminate Spinel. The results indicate that Magnesium Aluminate Spinel has both nonlinear stiffness and damping properties. The stiffness asymptotes to a minimum value around 650 microstrain while the damping is a maximum around 100 microstrain. Additionally, the data contained herein cover a larger strain range for this material than previously reported

Modeling and Simulation Techniques Used in High Strain Rate Projectile Impact

A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison in physical and computational performance. The second analysis technique relied on a mixed model that still made use of some Lagrangian modeling, but included smoothed particle hydrodynamics techniques as well, which are mesh free. The inclusion of the smoothed particle hydrodynamics was intended to address some of the known issues in Lagrangian analysis under high displacement and deformation. A comparison of the models was first performed against experimental results as a validation of the models, then the models were compared against each other based on closeness to experimentation and computational performance

Adiabatic Shear Banding in Nickel and Nickel-Based Superalloys: A Review

This review paper discusses the formation and propagation of adiabatic shear bands in nickel-based superalloys. The formation of adiabatic shear bands (ASBs) is a unique dynamic phenomenon that typically precedes catastrophic, unpredicted failure in many metals under impact or ballistic loading. ASBs are thin regions that undergo substantial plastic shear strain and material softening due to the thermo-mechanical instability induced by the competitive work hardening and thermal softening processes. Dynamic recrystallization of the material’s microstructure in the shear region can occur and encourages shear localization and the formation of ASBs. Phase transformations are also often seen in ASBs of ferrous metals due to the elevated temperatures reached in the narrow shear region. ASBs ultimately lead to the local degradation of material properties within a narrow band wherein micro-voids can more easily nucleate and grow compared to the surrounding material. As the micro-voids grow, they will eventually coalesce leading to crack formation and eventual fracture. For elevated temperature applications, such as in the aerospace industry, nickel-based superalloys are used due to their high strength. Understanding the formation conditions of ASBs in nickel-based superalloys is also beneficial in extending the life of machining tools. The main goal of the review is to identify the formation mechanisms of ASBs, the microstructural evolutions associated with ASBs in nickel-based alloys, and their consequent effect on material properties. Under a shear strain rate of 80,000 s−1, the critical shear strain at which an ASB forms is between 2.2 and 3.2 for aged Inconel 718 and 4.5 for solution-treated Inconel 718. Shear band widths are reported to range between 2 and 65 microns for nickel-based superalloys. The shear bands widths are narrower in samples that are aged compared to samples in the annealed or solution treated condition

Computational Based Investigation of Lattice Cell Optimization under Uniaxial Compression Load

Structural optimization is a methodology used to generate novel structures within a design space by finding a maximum or minimum point within a set of constraints. Topology optimization, as a subset of structural optimization, is often used as a means for light-weighting a structure while maintaining mechanical performance. This article presents the mathematical basis for topology optimization, focused primarily on the Bi-directional Evolutionary Structural Optimization (BESO) and Solid Isotropic Material with Penalization (SIMP) methodologies, then applying the SIMP methodology to a case study of additively manufactured lattice cells. Three lattice designs were used: the Diamond, I-WP, and Primitive cells. These designs are all based on Triply Periodic Minimal Surfaces (TPMS). Individual lattice cells were subjected to a uniaxial compression load, then optimized for these load conditions. The optimized cells were then compared to the base cell designs, noting changes in the stress field response, and the maximum and minimum stress values. Overall, topology optimization proved its utility under this loading condition, with each cell seeing a net gain in performance when considering the volume reduction. The I-WP lattice saw a significant stress reduction in conjunction with the mass and volume reduction, marking a notable increase in cell performance

Property Estimation in FGM Plates Subject to Low-Velocity Impact Loading

A property estimation sequence is presented for determining local elastic properties of a two-phased, two-constituent functionally graded material (FGM) plate subject to impact loading. The property estimation sequence combines the use of experimentally determined strain histories, finite element simulations of the experimental impact events, and an analytical model of the impact tests. The experimental, computational, and analytical models are incorporated into a parameter estimation framework, based on optimization theory, to solve for material properties of individual graded layers in the FGM plate specimens. Abstract excerpt © MS