Some issues of calculation of complex rod and plate systems on an elastic base

Oksana Kozunova,V Tur,N Matweenko

doi:10.1051/matecconf/202135000004

Abstract

This paper summarizes some issues of a new universal method for static calculation of complex rod and plate systems on an arbitrary elastic base under the influence of an external load, when modeling the base with various models, ranging from the classical Winkler model to the combined Winkler-Kogan model. The relevance and timeliness of the proposed work lies in the fact that the issues of calculating complex structures on an elastic base have not yet been fully investigated and there is no general approach to their calculation. The author knows the works of M. I. Gorbunov-Posadov, I. A. Simvulidi, B. N. Zhemochkin, G. Ya. Popov, S. N. Klepikov, S. D. Semenyuk, S. V. Bosakov, in which various approaches have been used to conduct research on the calculation of simple core structures, isolated foundation structures, including mesh slabs, as well as spatial monolithic foundations, as a system of cross belts on an elastic base. The proposed method is based on a mixed method of structural mechanics using the functions of the influence of an elastic medium in the relations of B. N. Zhemochkin. To simplify these relations, when determining the coefficients of canonical equations and free terms of the mixed method in the calculation of isolated and connected plates, the relations for deflections of plates with a normal pinched in the centre of the plate are used. For pivotally connected beams, it is convenient to introduce pinching with unknown displacements at the beginning or end of each beam, for frame rods-in their nodal connections. The numerical implementation of the general approach is performed using the Mathematica computer program.

Highlights

From the history of the development of static calculations of rod and plate systems on an elastic base, it can be seen that the methods of calculating the above structures were improved and refined as a result of scientific and technological progress [1,2,3,4,5,6]
The author suggests a general approach of structural mechanics for the static calculation of such complex systems, such as: 1) articulated rectangular plates on a combined Winkler-Kogan base, the model of which is proposed and tested in the works of the author [11, 18]; 2) articulated foundation beams based on Winkler, taking into account the physical nonlinearity of the beam material [19]; 3) articulated flat frames on an elastic Winkler base and on an elastic half-space [20]; 4) mesh foundation plates on a linearly deformable base, the calculation of which was numerically tested for an elastic half-space [21] and for an elastic isotropic layer [22]
The paper considers some issues of static calculation of articulated road slabs on a combined elastic base, articulated foundation beams on a Winkler base, taking into account the physical nonlinearity of the beam material, a hinged flat frame on a Winkler base and on an elastic half-space, as well as foundation mesh slabs on an elastic half-space and a homogeneous isotropic layer

Summary

Introduction

From the history of the development of static calculations of rod and plate systems on an elastic base, it can be seen that the methods of calculating the above structures were improved and refined as a result of scientific and technological progress [1,2,3,4,5,6]. The author suggests a general approach of structural mechanics for the static calculation of such complex systems, such as: 1) articulated rectangular plates on a combined Winkler-Kogan base, the model of which is proposed and tested in the works of the author [11, 18]; 2) articulated foundation beams based on Winkler, taking into account the physical nonlinearity of the beam material [19]; 3) articulated flat frames on an elastic Winkler base and on an elastic half-space [20]; 4) mesh foundation plates on a linearly deformable base, the calculation of which was numerically tested for an elastic half-space [21] and for an elastic isotropic layer [22]

The essence of the general approach

11 X o c 2

Problem 1

Conclusions