Search academic texts

Information × Registration Number 0200U004002, 0197U018116 , R & D reports Title Mathematical modeling and numerical investigation of physic-machanic fields within the continuum with small nonuniformities popup.stage_title Head Savula Yarema Grygorovych, Registration Date 08-10-2001 Organization Ivan Franko National University of Lviv popup.description2 In this paper new mathematical models are developed for the research of the mechanics problems of the body's deformation with thin inclusions and thin coatings. This model permits the simultaneous use of the elasticity theory equations and Timoshenko type shell theory equations. The variational statements of the problems are presented, the numerical schemes of their solution are developed, and the effective software is constructed. For the numerical analysis the Finite Element Method (FEМ), Boundary Elements Method (BEМ) and their coupling are used. The numerical scheme and algorithm of the finite-boundary-elements hybrid approximations of the two-dimensional thermoplasticity problems is developed. According to these scheme and algorithm in the one part of the domain with plastic deformations the stress-strain state is investigated in the frame of small elastic-plastic deformations theory by means of the Finite Element Method. In the other part of the domain the Stress-strain State is investigated by means of the boundary elements direct method. For the investigation of the mechanics problems of the body's deformation in the case when one of the body's measurements is much less then others, the numerical -analytical approach is developed. This approach is based on the use of the three-dimensional elasticity theory equations, were the solution on one coordinate can be expanded into series of the Legendre polynomials and the Finite Element Method approximations are used with respect to the two other coordinates. For problems of elastic-plastic deformation of the thin-walled flexible bodies the mathematical model is developed, and the unconditionally stable scheme of a finite element method is suggested. For all mathematical models, and numerical schemes, which are suggested in this paper, their efficiency on numerical examples of the model problems is investigated. A comparison of the obtained results with the result, which are known in the literature is conducted. Product Description popup.authors popup.nrat_date 2020-04-02 Close