AN INNOVATIVE SOLUTION IN CLOSED FORM AND NUMERICAL ANALYSIS FOR DISSIMILAR ELLIPTICAL INCLUSION IN PLANE ELASTICITY

2014 ◽  
Vol 06 (06) ◽  
pp. 1450080 ◽  
Author(s):  
Y. Z. CHEN
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Complex Potentials ◽  
Infinite Matrix ◽  
Elliptical Inclusion ◽  
The Matrix ◽  
Innovative Solution ◽  
Remote Loading

This paper provides a closed form solution for dissimilar elliptical inclusion in plane elasticity. A dissimilar elliptical inclusion is embedded in the infinite matrix with different elastic properties. The infinite matrix is applied by the constant remote loading. Complex variable method is used and two sets of the complex potentials are assumed in the analysis. One set is used for the matrix portion, and other for the inclusion portion. Catching the idea from the eigenstrain problem, we can assume the stresses in the inclusion to be constant. From the continuity conditions for stresses and displacements along the interface, we can get the two sets of the complex potentials in a closed form. In the analysis, an adequate form of the complex potential defined in the elliptical inclusion portion is analyzed in detail.

Degenerate Scale Problem for a Hypocycloid Hole in an Infinite Plate in Plane Elasticity

2016 ◽  
Vol 32 (4) ◽  
pp. N7-N10
Author(s):  
Y.-Z. Chen
Keyword(s):  
Boundary Condition ◽  
Conformal Mapping ◽  
Closed Form ◽  
Infinite Plate ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Scale Problem ◽  
Exterior Region ◽  
Degenerate Scale

AbstractBased on the conformal mapping, this paper provides a closed form solution for the degenerate scale of the hypocycloid hole in plane elasticity. In the derivation, we assume the vanishing displacements along the boundary in the degenerate scale problem. Some functions in the boundary condition are decomposed into three parts with particular behavior. Even the displacements are vanishing along the boundary of an exterior region, the displacements and stresses are not equal to zero in the exterior region. This is a particular feature in the degenerate scale problem.

A SIMPLE MODEL FOR FRACTURE IN A LAMINATED STRIP AND AN APPROXIMATE SOLUTION IN CLOSED FORM

1994 ◽  
Vol 05 (02) ◽  
pp. 219-221
Author(s):  
T.Y. Fan ◽  
M. Maier ◽  
S. Kerth
Keyword(s):  
Simple Model ◽  
Closed Form ◽  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Mapping Technique ◽  
Nonlinear Behaviour ◽  
Complex Variable Function ◽  
Variable Function ◽  
Material Nonlinear

This paper presents a simple model on the fracture of a laminated strip. Based on the method of complex variable function for solving plane elasticity and the confomal mapping technique, a closed form solution for the simplified model is constructed. The most important physical quantity for fracture analysis—the stress intensity factor—includes analytically the effects of structure geometry and the material constants. The analysis is very easily extended to solve the problem of material nonlinear behaviour and the problem of any 2n+1 layers with n+1 different materials. These may provide useful insight into the field of interlaminar fracture of composite materials.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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