Complex Variable Method for Eigensolution Sensitivity Analysis

AIAA Journal ◽  
2006 ◽  
Vol 44 (12) ◽  
pp. 2958-2961 ◽  
Author(s):  
B. P. Wang ◽  
A. P. Apte
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method

Sensitivities Analysis Using the Semi-Analytic Complex Variable Method in Fracture Mechanics

2010 ◽  
Author(s):  
Weiya Jin ◽  
Brian H. Dennis ◽  
Bo Ping Wang
Keyword(s):  
Sensitivity Analysis ◽  
Fracture Mechanics ◽  
Linear System ◽  
Complex Variable ◽  
A Priori ◽  
Computational Cost ◽  
Complex Variable Method ◽  
Variable Method ◽  
Single Edge ◽  
Perturbation Size

In fracture mechanics, due to singularity existing on the crack tip, the corresponding sensitivity analysis of Stress Intensity Factor (SIF) is not clear whether the overall finite difference (OFD) or Semi-analytical Method (SAM) can obtain accurate sensitivities. The paper proposes the Semi-analytical Complex Variable Method (SACVM) to compute sensitivities of SIF and compares the sensitivities computed by the SACVM with those computed by the OFD and SAM in Center Cracked Tension (CCT) specimen and Single Edge Notched Tension (SENT) specimen. The results reveal that the OFD obtains oscillated sensitivities because of the ill-conditioned linear system. The sensitivities computed by the OFD and SAM are sensitive to the perturbation size out of a certain range. However, this certain range varies with different variable, and is not known a priori. The proposed SACVM can always obtain accurate, consistent sensitivities with little extra computational cost than the SAM. The SACVM is not sensitive to the perturbation size and is not affected by the ill-conditioned linear system. Therefore, the SACVM is recommended to deal with sensitivity analysis in the fracture mechanics.

On Bending of a Flat Slab Supported by Square-Shaped Columns and Clamped

1954 ◽  
Vol 21 (3) ◽  
pp. 263-270
Author(s):  
S. Woinowsky-Krieger
Keyword(s):  
Stress Distribution ◽  
Conformal Mapping ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Flat Slab ◽  
Flat Slabs ◽  
At Will

Abstract A solution is given in this paper for the problem of bending of an infinite flat slab loaded uniformly and rigidly clamped in square-shaped columns arranged to form the square panels of the slab. The complex variable method in connection with conformal mapping is used for this aim. Although not perfectly rigorous, the solution obtained is sufficiently accurate for practical purposes and, besides, it can be improved at will. Stress diagrams traced in a particular case of column dimensions do not wholly confirm the stress distribution, generally accepted in design of flat slabs.

The Stresses in a Thick Cylinder Having a Square Hole Under Concentrated Loading

1958 ◽  
Vol 25 (4) ◽  
pp. 571-574
Author(s):  
Masaichiro Seika
Keyword(s):  
Stress Distribution ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Numerical Examples ◽  
Concentrated Loading ◽  
Thick Cylinder ◽  
Square Hole

Abstract This paper contains a solution for the stress distribution in a thick cylinder having a square hole with rounded corners under the condition of concentrated loading. The problem is investigated by the complex-variable method, associated with the name of N. I. Muskhelishvili. The unknown coefficients included in the solution are determined by the method of perturbation. Numerical examples of the solution are worked out and compared with the results available.

scholarly journals Complex Variable Solutions for Forces and Displacements of Circular Lined Tunnels

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingbo Han ◽  
Yongxu Xia ◽  
Xing Wang ◽  
Lunlei Chai
Keyword(s):  
Rock Mass ◽  
Complex Variable ◽  
Earth Pressure ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Lateral Earth Pressure ◽  
Series Expression ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complex variable method for solving the forces and displacements of circular lined tunnels is presented. Complex potentials for the stresses and displacements are expressed in the term of series expression. The undetermined coefficients of the complex potentials are obtained according to the stress boundary conditions along the lining inner surface and the displacement and surface traction boundary condition along the lining and rock-mass interface. Solutions for the stresses and displacements of the tunnel lining and rock-mass are then established by applying Muskhekishvili’s complex variable method. In addition, forces solutions for linings are presented based on the tangential stress at the two boundaries. Examples are finally established to reveal the applicability and accuracy of the proposed method. The effects of the degrees from the tunnel crown to the invert, coefficient of the lateral earth pressure, and distance from the rock-mass to the interface on the regulations of the lining forces and rock-mass stresses are also thoroughly investigated.

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