Bokov I. Stress-strain state of transversely isotropic plates under concentrated and local forces

The object of the study is stress-strain state of transversely isotropic plates, caused by concentrated and local forces. The subject of the study is a generalized theory of the {m,n}-approximation for transversely isotropic plates under concentrated and local forces. In the thesis the technique is developed for study of the stress-strain state of transversely isotropic plates under concentrated and local force effects using the refined theory of {m,n}-approximation. The three-dimensional equations of the elasticity theory are reduced to two-dimensional ones using the generalized theory of {m,n}-approximation. This theory is the most preferable for obtaining two-dimensional equations of the elasticity theory, since it is not based on any hypotheses, but uses the method of I.N. Vekua: decomposition of the unknown functions in Fourier series of Legendre polynomials. This approach allows us to take into account the transverse tangential and normal stresses. Using the two-dimensional integral Fourier transform and the inversion method using a special G-function, fundamental solutions of the static equations for transversely isotropic plates based on the {1,0}- and {1,2}-approximation theory are built for the first time. The distinctive features that characterized the influence of elastic parameters on stress-strain state of the transversely isotropic plates under concentrated force influences are studied. The influence of elastic parameters on the local stress-strain state of the transversely isotropic plate for various actions of the volume force normal component, and in dependence on geometry of local loading regions is investigated. Materials of research can be used at design developmental work and estimation of the operation parameters for thin-walled transversely isotropic materials under actions of concentrated and local forces. The results obtained are of theoretical and applied importance, and can be used in research institutes, design organizations and other research institutions related to research and design of thin-walled structural elements.