Numerical Solution for Dissimilar Confocally Elliptic Layers in Antiplane Elasticity

2016 ◽  
Vol 08 (05) ◽  
pp. 1650071 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
General Solution ◽  
Numerical Solution ◽  
Complex Variable ◽  
Final Solution ◽  
Shear Moduli ◽  
Numerical Examples ◽  
Antiplane Elasticity ◽  
The Matrix

This paper provides a general solution for confocally elliptic layers in antiplane elasticity. The studied medium is composed of many layers with different shear moduli. The remote stresses are applied at infinity. Complex variable method is used to study the problem. The continuity conditions for the displacement and the resultant force along the interfaces are suggested. By using the complex variable, the matrix transfer technique, and the boundary condition, the final solution is obtainable. Numerical examples are carried out to show the influence of the different shear moduli defined on different layers to the stress distribution.

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.

Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

2021 ◽  
pp. 108128652110112
Author(s):  
YZ Chen
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Logarithmic Potential ◽  
Boundary Integral ◽  
Scale Problem ◽  
Numerical Examples ◽  
Weakly Singular ◽  
Degenerate Scale ◽  
Antiplane Elasticity

This paper provides a numerical solution for the degenerate scale for a rigid curve in antiplane elasticity. The degenerate scale problem for the rigid curve is formulated on the usage of the logarithmic potential. After assuming the displacement to be a vanishing value along the rigid curve, the boundary integral equation (BIE) is formulated. The problem can be first formulated in the degenerate scale. After making a coordinate transform, we can obtain the relevant BIE in the ordinary scale. Finally, a numerical solution is achieved. Several numerical examples are provided. In addition, the degenerate scale problem for the multiple rigid curves is also solved.

scholarly journals A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Xuefeng Duan ◽  
Chunmei Li
Keyword(s):  
Iterative Algorithm ◽  
Projection Algorithm ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Von Neumann ◽  
Numerical Examples ◽  
Matrix Nearness Problem ◽  
Least Frobenius Norm Solution ◽  
Alternating Projection ◽  
The Matrix

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations AXB=E, CXD=F, which arises frequently in experimental design. If we choose the initial iterative matrix X0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.

Numerical Solution of Elastoplastic Torsion of a Shaft of Rotational Symmetry

1949 ◽  
Vol 16 (2) ◽  
pp. 139-148
Author(s):  
R. P. Eddy ◽  
F. S. Shaw
Keyword(s):  
Plastic Deformation ◽  
Stress Distribution ◽  
Numerical Solution ◽  
Rotational Symmetry ◽  
Relaxation Methods ◽  
Elastoplastic Boundary ◽  
Sufficient Magnitude ◽  
Elastoplastic Torsion ◽  
Von Mises

Abstract Using relaxation methods, an approximate numerical solution is found of the stress distribution in a shaft of rotational symmetry, which is subjected to a torque of sufficient magnitude to cause portions of the material to yield. It is assumed that the material of which the shaft is composed is isotropic and yields according to the condition of von Mises. The particular problem investigated is a shaft with a collar; results are presented showing the elastoplastic boundary, and the stress distribution, for two different amounts of plastic deformation.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

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