Analysis of a stress singularity in a non-linear Flamant problem for certain models of a material |
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| Authors: | VM Mal’kov YuV Mal’kova |
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| Institution: | 1. Department of Mathematics, Institute of Mathematics, University of Rzeszów, ul. Rejtana 16A, 35-310 Rzeszów, Poland;2. M.P. University of Agriculture and Technology, Udaipur, India;3. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland;1. John A. Paulson School of Engineering and Applied Sciences, Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA;2. State Key Lab for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an 710049, China;1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria;2. Department of Civil Engineering, Aristotle University, Thessaloniki GR-54124, Greece |
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| Abstract: | A generalized plane problem in the non-linear theory of elasticity is considered for a half-plane loaded on the boundary with a concentrated external force (the non-linear Flamant problem). The properties of the material of the half-plane are described by different (known) models, and each model of the non-linearly elastic material generates its own specific boundary-value problem. Analytical solutions of the problems are obtained for two models of an incompressible material: the neo-Hookean model and the Bartenev–Khazanovich model, and a model of a compressible semi-linear (harmonic) material. The dependence of the stress state as a whole on the adopted model of the material and the effect of the model of the material on the form of the stress singularity in the neighbourhood of a pole are investigated. |
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