This research develops an asymptotically optimal method for solving the fourth-order elliptic boundary value problem in complex geometries, focusing on plate bending.
Subject of research: mathematical model of plate bending under longitudinal-transverse load. Purpose of research: to develop an asymptotically optimal method for solving a fourth-order elliptic boundary value problem in a geometrically complex domain in the presence of a Dirichlet boundary condition. Research method: the paper develops a method of iterative extensions to find the bending of a plate under longitudinal and transverse load on an elastic base. Objectof research: the bending of a plate described by a mathematical model in the form of an elliptical boundary value problem of the fourth order in a field of geometrically complex shape with the obligatory presence of a Dirichlet boundary condition. Research findings: a method was developed that is asymptotically optimal in terms of the number of operations, based on the iterative expansion method for calculating plate bending under longitudinal-transverse load. The problem being solved continued fictitiously, the continued problem was approximated by finite element methods and partial approximation. The solution of a discrete extended problem was iteratively approached by solutions of extended problems. The asymptotic optimality of the proposed method has been experimentally verified by computer calculations.
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Ebel et al. (2025) studied this question.
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