approximate solution of certain nonlinear integro-differential equations of Kirchoff and Timoshenko type

Author: Eter Chichua
Keywords: Kirchhoff, Timoshenko, beam, plate
Annotation:

The following thesis deals with some problems of the beam and the symmetric plate with boundary and initial-boundary value. For the problems numerical methods are used, with their accuracies being examined. In the first chapter the nonlinear boundary problem for a Kirchhoff type static beam is stated. Corresponding differential equation, by the use of Green’s function, is reduced to an integral equation, which is solved with iterational method. The convergence of the method is established, speed of convergence is estimated, example is solved. In the second chapter boundary value problem, describing symmetrically loaded plate behavior, for a Timoshenko system of nonlinear differential equations is discussed. By the use of Galerkin method system of discrete equations is obtained, incorporating Jacobi-Cardano iteration for its solution. Theorem regarding the accuracy of iterational process is proved. Table of convergence conditions is composed. The third chapter inspects the initial-boundary problem for Timoshenko dynamic beam. To approximate the solution with respect to a spatial variable, the Galerkin method is used, the error is estimated.

Lecture files:

კირხჰოფისა და ტიმოშენკოს ტიპის ზოგიერთი არაწრფივი ინტეგრო-დიფერენციალური განტოლების მიახლოებითი ამოხსნა [ka]