The problem of determining the stress-strain state rigidly fixed sandwich plate with transversely soft core in the presence of constraints (i.e., material nonlinearity) corresponding to the ideal elastic-plastic model for the core material is considered. Solvability of the generalized statement of the problem as a problem of finding the saddle point of some functionals is investigated.
By using the two-layer iterative method we obtain the basic characteristics of the equilibrium position of sandwich plate with a transversely soft filler in geometrical nonlinear one-dimensional statement. To solving problem we previously construct its finite-difference approximation Analysis of the results of numerical experiments is performed. Obtained data testify to the effectiveness of the proposed method.
The convergence of iterative methods for solving variational inequalities with monotonetype operators in Banach spaces is studied. Such inequalities arise in the description of deformation processes of soft rotational network shells. Certain properties of these operators, such as coercivity, potentiality, bounded Lipschitz continuity, pseudomonotonicity, and inverse strong monotonicity, are determined. An iterative method for solving these variational inequalities is proposed, its convergence is investigated, and the boundedness of the iterative sequence is proved. Moreover, it is proved that any weakly convergent subsequence of the iterative sequence converges to a solution of the original variational inequality.
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