On the Convergence of an Iteration Method in Timoshenko’s Theory of Plates
The boundary value problem for a Timoshenko system of differential equations describing the static behavior of a plate is considered. Two sought functions are expressed through the third one for which an integro-differential equation with the Dirichlet condition on the boundary is written. The application of the Galerkin method to the obtained problem leads to a nonlinear system of algebraic equations which is solved by iteration. The condition of iteration process convergence is established and its rate is estimated.
KeywordsTimoshenko equation Galerkin method Jacobi iteration Convergence of the iteration method
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