Analysis of boundary-value problems describing the non-isothermal processes of elastoplastic deformation taking into account the loading history |
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Authors: | A. Yu. Chirkov |
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Affiliation: | (1) Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine |
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Abstract: | We discuss the theory and approximate methods for solving boundary-value problems of thermoplasticity in a quasi-static formulation when the process of non-isothermal elastoplastic deformation of a body is a sequence of equilibrium states. In this case, the stress-strain state depends on the loading history, and the process of inelastic deformation is to be observed over the whole time interval being studied. The boundary-value problem is stated as a non-linear operator equation in the Hilbertian space. The conditions that provide the existence, uniqueness and continuous dependence of the generalized solution on the applied loads and initial strains are defined. A convergence of the methods of elastic solutions and variable elastic parameters is studied to solve the boundary-value problems describing the non-isothermal processes of active loading taking into account the initial strains dependent on the deformation history and heating. __________ Translated from Problemy Prochnosti, No. 1, pp. 69–99, January–February, 2006. |
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Keywords: | theory of plasticity stress and strain deviators non-isothermal processes elastoplastic deformation simple loading thermomechanical surface boundary-value problem iterative methods convergence accuracy |
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