Abstract
The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.
Highlights
The existence of existence theorems makes it easy to prove the convergence of numerical methods to an exact real solution and contributes to a deep understanding of the studied mechanical phenomena
The existence theorem is proved within the framework of the shear model by S.P
A new analytical method is used, which consists in studying the original system of five equilibrium equations in classical Sobolev spaces under given boundary conditions by reducing it to a single nonlinear operator equation
Summary
The existence of existence theorems makes it easy to prove the convergence of numerical methods to an exact real solution and contributes to a deep understanding of the studied mechanical phenomena. The problem of convergence of the numerical solution to the exact (real) solution of the problem always comes to the fore The solution to this problem, as is known, is based on a rigorous mathematical study of the stressstrain state of thin-walled shell structures. At present, this problem is sufficiently fully studied in the framework of the simplest Kirchhoff-Love model [10,11,12,13,14,15,16,17]. The conformal mapping method is used to study a nonlinear problem for arbitrary flat shells under different boundary conditions
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