Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

2017 ◽  
Vol 38 (11) ◽  
pp. 1517-1532 ◽  
Author(s):  
S. Singh ◽  
K. Sharma ◽  
R. R. Bhargava
1959 ◽  
Vol 42 ◽  
pp. 1-2
Author(s):  
LL. G. Chambers

The use of the complex variable z( = x + iy) and the complex potential W(= U + iV) for two-dimensional electrostatic systems is well known and the actual system in the (x, y) plane has an image system in the (U, V) plane. It does not seem to have been noticed previously that the electrostatic energy per unit length of the actual system is simply related to the area of the image domain in the (U, V) plane.


1957 ◽  
Vol 24 (1) ◽  
pp. 122-124
Author(s):  
Gunadhar Paria

Abstract The problem of finding the stress distribution in a two-dimensional elastic body with parabolic boundary, subject to mixed boundary conditions, has been reduced to the solution of the nonhomogeneous Hilbert problem following the method of complex variable. The result has been compared with that for a straight boundary.


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.


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