Zelensky A. Models and methods of analytic theory of non-thin plates and shallow shells under static loading

The object of the research is the analytic and numerical dependences of the stress-strain state of non-thin physically linear and non-linear homogeneous and laminated plates and shells of mechanical-geometric parameters, the type of the loading and the models of the versions of the analytical theory into boundary problems of static. The aim of the research is the development and construction of new versions and their models of non-thin plates and shells and based-developing methods of the solutions for boundary problems for these elements according al components of stress-strain state and border effects. The new variants and models of theory of the plates and shells subjected to arbitrary static loading are constructed in context of three-dimensional theory of elasticity. The three-dimensional problem of the theory of elasticity for plates and shells is reduced to the two-dimensional one using the Reissner's variation principle and linked-up equations, method of series expansion of SSS components on lateral coordinate with the use of Legendre-Polynom. Us a new problem formulation the three-dimensional boundary problem for orthotropic and physically non-linear plates and shallow shells with the use of perturbations method is reduced to the infinite recurrent sequence of two-dimensional linear boundary problems. The method of solutions of the systems of differential equations are the systems are obtained on the base of the built variants of theory: the operator method the trigonometric series method, the method of diminution of differential equation degree, the method of special functions. The stress-strain state of using plates and shells is analyzed. The results of research are inculcated in the process of study and can be used for calculation with the highest level of the strength and the longevity of construction in the design organization and in the research ones as well.