Mixed projection-mesh scheme of the finite-element method to solve boundary-value problems describing the non-isothermal processes of elastoplastic deformation |
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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: | A mixed projection-mesh scheme for solving a boundary-value problem of thermal plasticity is formulated in a quasi-static
statement 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 under study. The correctness and convergence of the mixed approximations for stresses, strains and
displacements are investigated as applied to the solution of nonlinear boundary-value problems that describe the non-isothermal
processes of active loading taking into account the initial strains dependent on the history of deformation and heating. The
properties of the projecting operators are studied in detail, and on this basis, the condition that ensures the existence,
uniqueness and stability of solution is formulated. The results of the analysis of special formulas of the interpolation-type
numerical integration are presented, the use of which considerably simplifies the computation procedure for solving equations
of the mixed method. The convergence and accuracy estimations are based on the results of the theory of the generalized boundary-value
problems and methods of the functional analysis. According to the estimations obtained, the accuracy of solution of a finite-dimensional
problem at the initial stages of loading should be sufficient to avoid the effect of increase of the first coefficients in
the expansion of the total error on the accuracy of solution of the elastoplastic problem at the subsequent stages of loading.
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Translated from Problemy Prochnosti, No. 3, pp. 87–117, May–June, 2007. |
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Keywords: | theory of plasticity finite-element method mixed scheme approximation stability convergence accuracy |
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