The Stability of the Plates with Circular Inclusions under Tension
This paper deals with the problem of local buckling caused by uniaxial stretching of an infinite plate with a circular hole or with circular inclusion made of another material. As the Young’s modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible. This paper also shows the difference between them when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. Computational models show that instability modes are different both when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. The case when plate and inclusion have the same modulus of elasticity, but different Poisson’s ratio is investigated too. It is also discussed here the case when a plate with inclusion is under biaxial tension. For each ratio of the modulus of elasticity of plate versus inclusion it’s obtained the range of the load parameters for which the loss of stability is impossible.
Unable to display preview. Download preview PDF.
- Bauer SM, Kashtanova SV, Morozov NF, Semenov BN (2014) Stability of a nanoscale-thickness plate weakened by a circular hole. Doklady Physics 59(9):416–418Google Scholar
- Bauer SM, Kashtanova SV, Morozov NF, Semenov BN (2017) Stability loss in an infinite plate with a circular inclusion under uniaxial tension. Vestnik St Petersburg University, Mathematics 50(2):161–165Google Scholar
- Bochkarev A, Grekov M (2015) On symmetrical and antisymmetrical buckling of a plate with circular nanohole under uniaxial tension. Applied Mathematical Sciences 9:125–128Google Scholar
- Bochkarev AO, Grekov MA (2014) Local instability of a plate with a circular nanohole under uniaxial tension. Doklady Physics 59(7):330–334Google Scholar
- Deryugin YY, Lasko GV (2012) Field of stresses in an isotropic plane with circular inclusion under tensile stresses. Engineering 4:583–589Google Scholar
- Eshelby DE (1957) Definition of the stress field, which was creating by elliptical inclusion. Proceedings of the Royal Society A 241(1226):376Google Scholar
- Guz AN, Dishel’ MS, Kuliev GG, Milovanova OB (1981) Fracture and Stability of Thin Bodies with Cracks (in Russ.). Naukova Dumka, KievGoogle Scholar
- Kachanov M, Shafiro B, Tsurkov I (2003) Handbook of Elasticity Solutions. Kluwer Academic, DordrechtGoogle Scholar
- Muskhelishvili NI (1963) Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, GroningenGoogle Scholar
- Shimizu S (2007) Tension buckling of plate having a hole. Thin-Walled Structures 45(10):827–833Google Scholar