Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

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.

Download Full-text

Generalized and Simplified Linear Closed-Form Solution of an Active Tensegrity Unit in the Form of Octahedral Cell

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.969.192 ◽

2014 ◽

Vol 969 ◽

pp. 192-198

Author(s):

Stanislav Kmeť ◽

Peter Platko

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Analysis ◽

Closed Form ◽

Closed Form Solution ◽

Point Load ◽

Form Solution ◽

Cable System ◽

Form Analysis ◽

Tensile Forces

Results of the generalized and simplified linear closed form solution of an active or adaptive tensegrity unit, as well as its numerical analysis using finite element method are presented in the paper. The shape of the unit is an octahedral cell with a square base and it is formed by thirteen members (four bottom and four top cables, four edge struts and one central strut). The central strut is designed as an actuator that allows for an adjustment of the shape of the unit which leads to changes of tensile forces in the cables. Due to the diagonal symmetry of the 3D tensegrity unit the closed-form analysis is based on the 2D solution of the equivalent planar biconvex cable system with one central strut under a vertical point load.

Download Full-text

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

International Journal of Applied Mechanics ◽

10.1142/s175882511450080x ◽

2014 ◽

Vol 06 (06) ◽

pp. 1450080 ◽

Cited By ~ 2

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.

Download Full-text

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

International Journal of Modern Physics C ◽

10.1142/s0129183194000192 ◽

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.

Download Full-text