Voropay N. Inverse non-stationary problems of elastic deformation plate and three-dimensional structural elements

The object of research is non-stationary deformation of elastic structural elements caused by the action of external impulse loads. The aim is developing methods of impulse loads identification, which acting on structural elements on the base of the different complexity models of elasticity theory. The methods are the finite difference method, the variational principle of Ostrogradskii-Hamilton, the Laplace and Fourier integral transformations, the theory of Fourier series, the theory of generalized functions, the theory of Volterra integral equations, regularization methods. New methods of inverse dynamic problems solving for the membrane-strip and the infinite long cylindrical membrane shell are created. The first time an analytical and numerical method for the identification of non-stationary concentrated load acting on the plate-strip in the theory of Kirchhoff is designed. Method for solving the problems of impulse loads identification in the first-order refined theory for a plate on the basis of one wave equation and infinite long cylindrical shells and plates with taking into account the transverse compression is developed. A new approach to solving inverse problems of non-stationary dynamics based on the equations of classical space elasticity theory and asymmetric elasticity theory for elastic bodies is proposed. The developed methods for indirect measurement of the external forces acting on structural elements provide information about the value and character of their changes vs. time. The implementation of the dissertation results is carried out in RPI "Hartron-Arcos". Range of application: aviation, rocket and cosmic construction, engineering industry, highway engineering.