ОБЩИЙ ПОДХОД К РАСЧЕТ У СЛОЖНЫХ СТЕРЖНЕВЫХ И ПЛАСТИНЧАТЫХ СИСТЕМ НА ПРОИЗВОЛЬНОМ УПРУГОМ ОСНОВАНИИ

Abstract

This paper generalizes the method of static calculation of complex rod and plate systems on an arbitrary elastic foundation under the action of an external load, when modeling the foundation with various models, ranging from the classical Winkler model to a combined model consisting of the Winkler model and the Kogan two-layer model. The relevance and timeliness of the proposed work lies in the fact that the issues of calculating complex structures on an elastic foundation have not yet been fully investigated and there is no general approach to their calculation. The author knows the works of M.I. Gorbunova-Posadova, I.A. Simvulidi, G. Ya. Popova, S.N. Klepikova, S.D. Semenyuk, in which various approaches were used to study the design of simple rod structures, isolated foundation slabs, including mesh slabs, as well as spatial monolithic foundations, as a system of cross belts on an elastic foundation. The proposed technique is based on the Ritz variational method and the mixed method of structural mechanics using Zhemochkin’s influence functions. To determine the coefficients of the canonical equations and free terms of the mixed method of structural mechanics through the Zhemochkin method, the calculation uses the ratios for the deflections of plates or beams with pinching in their center. To simplify the relations of the Zhemochkin method in hinged-connected beams, it is convenient to introduce pinching with unknown displacements at the beginning or end of each beam. The numerical implementation of the general approach was carried out using the Mathematica computer program.