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Abstract
This paper is devoted to a gradientelastic stress analysis of an infinite plate weakened by a cylindrical hole and subjected to two perpendicular and independent uniaxial tensions at infinity. The problem setting can be considered as an extension and generalization of the wellknown Kirsch problem of the classical elasticity theory which is here extended with respect to the external loadings and generalized with respect to the continuum framework. A closedform solution in terms of displacements is derived for the problem within the strain gradient elasticity theory on plane stress/strain assumptions. The main characters of the total and Cauchy stress fields are analyzed near the circumference of the hole for different combinations of biaxial tensions and for different parameter values. For the original Kirsch problem concerning a uniaxially stretched plate, the analytical solution fields for stresses and strains are compared to numerical results. These results are shown to be in a full agreement with each other and, in particular, they reveal a set of new qualitative findings about the scaledependence of the stresses and strains provided by the gradient theory, not common to the classical theory. Based on these findings, we finally consider the physicalness of the concepts total and Cauchy stress appearing in the strain gradient model.
Original language  English 

Pages (fromto)  351366 
Number of pages  42 
Journal  International Journal of Solids and Structures 
Volume  110111 
Early online date  2016 
DOIs  
Publication status  Published  Apr 2017 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Strain gradient elasticity
 Kirsch problem
 Cauchy sress
 Total stress
 Plane stress/strain problem
 Stress concentration
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Dive into the research topics of 'Gradientelastic stress analysis near cylindrical holes in a plane under biaxial tension fields'. Together they form a unique fingerprint.Projects
 3 Finished

Isogeometric adaptive methods for thinwalled structures– with applications from architectural and industrial design in structural and mechanical engineering
Niiranen, J., Balobanov, V., Khakalo, S., Shahzad, S. & Nguyen, T.
01/09/2016 → 31/08/2018
Project: Academy of Finland: Other research funding

Isogeometric adaptive methods for thinwalled structures with applications from architectural and industrial design in structural and mechanical engineering
01/09/2013 → 31/08/2018
Project: Academy of Finland: Other research funding

Isogeometric adaptive methods for thinwalled structures – with applications from architectural and industrial design in structural and mechanical engineering
Balobanov, V., Niiranen, J. & Khakalo, S.
01/09/2013 → 31/08/2016
Project: Academy of Finland: Other research funding