Kovalchuk S. Mechanics of deformation of composite beams with a curvilinear flat axis

The thesis is devoted to development of the elasticity and thermoelasticity theory for curvilinear composite beams with a flat axis of an arbitrary shape and stationary structure of cross section as well as the formation of an applied analytical method for determining the strain-stress state (SSS) of such elements under various mechanical loads and thermal actions. The thermoelasticity theory is developed in a natural curvilinear orthogonal coordinate system of a composite beam for which mathematical justification was given and construction methods for the defined beam shape were developed. The applied method for determining the thermoelastic SSS of curvilinear multilayer orthotropic beam that is consisted of any quantity of constant curvature sites was developed based on a number of obtained for the first time accurate analytical solutions to the problems of thermoelastic deformation of a multilayer beam part of constant zero and positive curvature under various mechanical loads and thermal actions. The accuracy of the developed method was confirmed by the comparison of calculation data with modeling results using the method of finite elements for a number of tests activities. The influence of shear and compression deformations and internal heat sources on the SSS components of multilayer curvilinear beams was investigated by using the developed method. The important effects of the increase of such elements strength and stiffness were highlighted.