Grid Method for Microscale Discontinuous Deformation Measurement

The objective of this paper is to explore both grid method and Digital Image Correlation (DIC) technique for microscale and discontinuous displacement measurements, such as those associated with crack tips. First, the principle of the grid method is revisited. The grid method and DIC technique are then applied to computer generated images to calculate the displacement field around crack tips. Finally, the grid method is applied to actual experimental images of fracture tests which are conducted inside a Scanning Electron Microscope (SEM) chamber. A new technique is developed to generate microscale pattern that is suitable for both grid method and DIC technique. The displacement fields calculated from grid method are compared with those from DIC technique to identify the strengths and weaknesses of each technique for the microscale and discontinuous displacement measurements. It has been determined that grid method can obtain data closer to the discontinuity than DIC; however, DIC produces smoother displacement fields at the far field. Using this new pattern generation technique, both grid method and DIC technique can be applied to the fracture test at the microscale to complement with each other to achieve the best experiment results.     

Protonation of acenaphthoquinone. A novel peripheral 10 π-electron aromatic system

Acenaphthoquinone ($\text{1}$) undergoes ppotonation to afford the respective double protonation product $\text{2}$. The proton and carbon NMR parameters of $\text{2}$ are discussed.     

Characterization of the Mechanics of Compliant Wing Designs for Flapping-Wing Miniature Air Vehicles

Flapping-wing miniature air vehicles (MAVs) offer multiple performance benefits relative to fixed-wing and rotary-wing MAVs. This investigation focused on the problem of designing compliant wings for a flapping-wing MAV where only the spar configuration was varied to achieve improved performance. Because the computational tools needed for identifying the optimal spar configuration for highly compliant wing designs have yet to be developed, a new experimental methodology was developed to explore the effects of spar configuration on the wing performance. This technique optically characterized the wing deformations associated with a given spar configuration and used a customized test stand for measuring lift and thrust loads on the wings during flapping. This revealed that spar configurations achieving large and stable deformed volume during the flapping cycle provided the best combination of lift and thrust. The approach also included a sensitivity and reproducibility analysis on potential spar configurations. Results indicated that the wing shape and corresponding lift and thrust performance were very sensitive to slight changes in volume and 3-D shape associated with slight variations in the spar locations.     

Synthesis and ring-opening polymerization of novel bicyclic oxalactams: 2-oxa-5-azabicyclo[2.2.2]octan-6-one

A novel bicyclic oxalactam 2-oxa-5-azabicyclo [2.2.21 octan-6-one (2,5-BOL) was synthesized from sodium 3,4-dihydro-2H-pyran-2-carboxylate through a seven-step reaction sequence. Anionic ring-opening polymerization of 2,5-BOL was carried out in bulk at 12OOC or in dimethyl sulfoxide at 40, 60, and 80°C by using potassium pyrrolidonate and the N-benzoyl derivative of 2,5-BOL as catalyst and activator, respectively. The polymerization gave a new polyamide containing cis- and trans-2,5-linked tetrahydropyran rings in the main chain. The cis/trans ratio varied from 70/30 to 95 /5 depending on the reaction conditions. The polyamide having number average molecular weights of 3000–8000 was soluble in a variety of solvents including methanol, ethanol, dimethyl sulfoxide, dimethylformamide, chloroform, and dichloromethane. It began to decompose at 280–32OOC depending on the compositions of the cis- and trans-2,5-linked structural units. The anionic ring-opening polymerizability of 2,5-BOL was found to be much lower than its structural isomer, 8-oxa-6-azabicyclo[ 3.2.11 octan-7-one (8,6-BOL).     

A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces

The following theorem is proven:if E is a uniformly rotund Banach space with a Fréchet differentiable norm, C is a bounded nonempty closed convex subset of E, and T: C→C is a contraction, then the iterates {T ⁿx} are weakly almost-convergent to a fixed-point of T. Supported by NSF Grant MCS 76-08217.     

On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces

We prove that ifC is a bounded closed convex subset of a uniformly convex Banach space,T:C→C is a nonlinear contraction, andS _n =(I+T+…+T ⁿ⁻¹ )/n, then lim _n ‖S _n (x)−TS _n (x)‖=0 uniformly inx inC. T also satisfies an inequality analogous to Zarantonello’s Hilbert space inequality. which permits the study of the structure of the weak ω-limit set of an orbit. These results are valid forB-convex spaces if some additional condition is imposed on the mapping. Partially supported by NSF Grant MCS-7802305A01.     

Random products of contractions in metric and Banach Spaces

Suppose (X, d) is a metric space and {T₀,…, T_N} is a family of quasinonexpansive self-mappings on X. We give conditions sufficient to guarantee that every possible iteration of mappings drawn from {T₀,…, T_N} converges. As a consequence, if C₀,…, C_N are closed convex subsets of a Hilbert space with nonempty intersection, one of which is compact, and the proximity mappings are iterated in any order (provided only that each is used infinitely often), then the resulting sequence converges strongly to a point of the common intersection.