Fracture analysis of two unequal collinear cracks weakening a piezo-electromagnetic media via complex variable approach

2020 ◽  
Vol 13 (1) ◽  
pp. 15-30
Author(s):  
Kamlesh Jangid
Author(s):  
Li Wang ◽  
Boris Diskin ◽  
Leonard V. Lopes ◽  
Eric J. Nielsen ◽  
Elizabeth Lee-Rausch ◽  
...  

A high-fidelity multidisciplinary analysis and gradient-based optimization tool for rotorcraft aero-acoustics is presented. Tightly coupled discipline models include physics-based computational fluid dynamics, rotorcraft comprehensive analysis, and noise prediction and propagation. A discretely consistent adjoint methodology accounts for sensitivities of unsteady flows and unstructured, dynamically deforming, overset grids. The sensitivities of structural responses to blade aerodynamic loads are computed using a complex-variable approach. Sensitivities of acoustic metrics are computed by chain-rule differentiation. Interfaces are developed for interactions between the discipline models for rotorcraft aeroacoustic analysis and the integrated sensitivity analysis. The multidisciplinary sensitivity analysis is verified through a complex-variable approach. To verify functionality of the multidisciplinary analysis and optimization tool, an optimization problem for a 40% Mach-scaled HART-II rotor-and-fuselage configuration is crafted with the objective of reducing thickness noise subject to aerodynamic and geometric constraints. The optimized configuration achieves a noticeable noise reduction, satisfies all required constraints, and produces thinner blades as expected. Computational cost of the optimization cycle is assessed in a high-performance computing environment and found to be acceptable for design of rotorcraft in general level-flight conditions.


1965 ◽  
Vol 32 (1) ◽  
pp. 59-66 ◽  
Author(s):  
Robert Greif ◽  
J. L. Sanders

An infinite stringer is assumed to be continuously attached to a sheet along a line perpendicular to a finite crack. At a great distance from the crack, the sheet is under a uniform tensile stress parallel to the stringer. The plane-stress solution for this problem is carried out by using the complex variable approach of Muskhelishvili to derive an integral equation which is then solved numerically on the IBM 7090 computer. In particular, the effect of the stringer on the strength of the stress singularity at the crack tip, and the maximum load-concentration factor in the stringer are found.


1993 ◽  
Vol 4 (2) ◽  
pp. 97-120 ◽  
Author(s):  
Vladimir M. Entov ◽  
Pavel I. Etingof ◽  
Dmitry Ya. Kleinbock

We study Hele–Shaw flows with a moving boundary and multipole singularities. We find that such flows can be defined only on a finite time interval. Using a complex variable approach, we construct a family of explicit solutions for a single multipole. These solutions turn out to have the maximal possible lifetime in a certain class of solutions.We also discuss the generalized Hele-Shaw model in which surface tension at the moving boundary is considered, and develop a method of finding steady shapes. This method yields new one-parameter families of stationary solutions. In the Appendix we discuss a connection between these solutions and a variational problem of potential theory.


1970 ◽  
Vol 4 (1) ◽  
pp. 29-37 ◽  
Author(s):  
D. E. Collett ◽  
R. C. Hewson-Browne ◽  
D. W. Windle

2011 ◽  
Vol 67 (1) ◽  
pp. 541-547 ◽  
Author(s):  
Jorge Duarte ◽  
Cristina Januário ◽  
Nuno Martins ◽  
Josep Sardanyés

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