Electric-current-induced thermal stress around a non-circular rigid inclusion in a two-dimensional nonlinear thermoelectric material

We analyze the contribution of surface elasticity and electric current density on the thermal stress distribution around a circular nano-hole in a thermoelectric material. Using complex variable methods, we obtain closed-form solutions describing the corresponding thermoelastic fields in the vicinity of the nano-hole. Our results indicate that the effect of surface elasticity is to generate significant normal and shear stresses on the boundary of the hole, allowing for the ability to either suppress or enhance hoop stress depending on the sign of the corresponding surface material constant. In addition, we find that positive hoop stress generated on the boundary by the remote electric current density can be neutralized by the incorporation of positive surface elasticity. In the case of the remaining boundary stress components, both surface elasticity and electric current density are found to enhance normal stress, while the maximum shear stress depends largely on the contribution of surface elasticity.

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Optimal control of the location of a thin rigid inclusion in the equilibrium problem of an inhomogeneous two-dimensional body with a crack

Sibirskii zhurnal industrial'noi matematiki ◽

10.33048/sibjim.2019.22.106 ◽

2018 ◽

Vol 22 (1) ◽

pp. 53-62

Author(s):

N. P. Lazarev ◽

G. M. Semenova

Keyword(s):

Optimal Control ◽

Equilibrium Problem ◽

Rigid Inclusion ◽

Two Dimensional ◽

Thin Rigid Inclusion

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The Influence of the Shape and Rigidity of an Elastic Inclusion on the Transverse Flexure of Thin Plates

Journal of Applied Mechanics ◽

10.1115/1.4009260 ◽

1943 ◽

Vol 10 (2) ◽

pp. A69-A75

Author(s):

Martin Goland

Keyword(s):

Stress Distribution ◽

Future Study ◽

Rigid Inclusion ◽

Elastic Inclusion ◽

Thin Plates ◽

Elastic Plates ◽

Perforated Plates ◽

Circular Rigid Inclusion ◽

Special Cases ◽

Elastic Inclusions

Abstract The purpose of this paper is to investigate the influence of several types of inclusions on the stress distribution in elastic plates under transverse flexure. An “inclusion” is defined as a close-fitting plate of some second material cemented into a hole cut in the interior of the elastic plate. Depending upon the properties of the material of which it is composed, the inclusion is described as rigid or elastic. In particular, the solutions presented will deal with the effects of circular inclusions of differing degrees of elasticity and rigid inclusions of varying elliptical form. Since the rigid inclusion and the hole are limiting types of elastic inclusions, and the circular shape is a special form of the ellipse, plates with either a circular hole or a circular rigid inclusion are important special cases of this discussion. It is hoped that the present analysis of several types of inclusions will aid in a future study of perforated plates stiffened by means of reinforcing rings fitted into the holes.

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