Strip on elastic foundation described by different models, loaded by evenly distributed load

The problem of changing the size of the reactive pressures perceived by a strip at use of various models of the soil foundation and at various indicators of flexibility of the “strip-soil” system is investigated. The aim of the work is to obtain the form of plots of reactive pressures produced by the soil foundation on a strip loaded along its entire length with a uniformly distributed load. In determining the values ​​of reactive pressures and values ​​of bending moments, the data of a previously published work of one of the authors of the article, based on V.N. Zhemochkin method, is used. Analysis of the obtained calculation results showed that the shape of the plot of reactive pressures largely depends on both the index of flexibility of the foundation and the index of flexibility of the “strip-soil” system. The novelty of the research is that the calculation results are obtained using the traditional method of calculation (i.e., without taking into account the joint work of the “strip-soil” system and using 3 models of the soil base: linearly deformable half-plane, linearly deformable layer of finite thicknesses and the Winkler model. The obtained results of calculation will allow to design ground structures on the elastic foundation.

Finite Element Method Analysis Applied to Different Foundations Structures Systems

In the conventional static analysis of building frames, the base is idealised on rigid supports and the building is subdivided into three parts namely, the superstructure, the foundation and the ground soil, before design. In real life situations, the soil underneath the building undergoes deformations which may alter the performance of the structure. In this paper, it is studied the effect of soil type and foundation type on the response of a building frame system with both fixed base and flexible base. The Winkler model of soil-structure interaction is adopted to study the influence of soil flexibility and foundation rigidity on a 4 storey RC building with a regular plan resting on three types of soils namely, the light peat marshy ground, wet clay and medium gravel with fine sand. Three types of foundations are considered in the study: isolated footings, tied foundation and the raft (with and without overhangs) foundations. Winkler model is developed using springs by Finite Element Method in SAP2000. The settlement, the bending moment, the shear force and the axial force are the parameters placed forth for the comparative study. Results obtained reveal an increase in the response of the structure with respect to the soil flexibility and foundation rigidity.

Bending of an elastoplastic circular sandwich plate on an elastic foundation in a temperature field

Today, the development of the general theory of quasi-static deformation of three-layer structural elements, including plates, is not yet complete and is being intensively studied. Mathematical models of deformation under complex thermo-force and thermo-irradiation loads are created. The problems of strength, stability, and dynamic behaviour are considered. In strength calculations of three-layer structural elements, it is necessary to take kinematic hypotheses for each layer separately, which complicates the mathematical side of the problem but leads to significant refinement of the stress-strain state. The reaction of an elastic foundation is described by the Winkler model. The use of variational methods allows one to obtain a refined system of three differential equations of equilibrium in internal forces. The thermo-force bending of an elastoplastic circular sandwich plate with a light core connected to an elastic foundation is considered. The polyline normal hypotheses are used to describe the kinematics of a plate package that is not symmetric in thickness. In thin base layers, the Kirchhoff-Love hypotheses are accepted. In a light relatively thick core, the Timoshenko hypothesis is true, while the normal remains rectilinear, but rotates at some additional angle, the radial displacements change linearly in thickness. The differential equations of equilibrium are obtained using the Lagrange variation method. The statement of the boundary value problem in displacements is given in a cylindrical coordinate system. Numerical results for circular metal-polymer sandwich plates are presented.

Mechanical Characteristic Analysis of Buried Drainage Pipes after Polymer Grouting Trenchless Rehabilitation

The application of polymer grouting in underground pipeline rehabilitation is increasing gradually. The leakage and subsidence of buried pipelines could be repaired by polymer grouting technology. In order to analyse the calculation theory of the pipeline repairing process, the Winkler model and the Vlazov model of the pipe-soil-polymer interaction based on the elastoplastic theory are established, the calculation formulas of the pipe-soil interaction under polymer grouting are derived, and the MATLAB calculation program based on the transfer matrix method is compiled. Then the calculated values are compared with the pipeline experimental values, and the influence of different factors on the internal force and deformation of the polymer-repaired pipeline under different work conditions is discussed. The results show that the values and trends of the pipe deformation and circumferential bending moment calculated by the models are consistent with the experimental results, and the results obtained by the Vlazov model are closer to the experimental values. In addition, the void at the bottom of the pipeline has a large impact on the mechanical properties of the pipeline. However, polymer grouting can repair disengaged pipelines effectively and restore their mechanical properties. The proposed methods and calculation results are valuable for pipeline polymer repairing analysis and pipeline void repairing design.

GENERAL APPROACH TO THE DESIGN OF COMPLEX BAR AND PLATE SYSTEMS ON AN ARBITRARY ELASTIC FOUNDATION

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.

BENDING OF AN ELASTIC THREE-LAYER PLATE WITH A HOLE CONNECTED TO THE SOIL FOUNDATION

The relevance of this paper is explained by a demand for the development of mechanical and mathematical models and methods for calculating the stress-strain state of the sandwich structural elements. The statement of the boundary value problem on the deformation of a circular sandwich plate with a central hole, connected to the soil foundation, was given. To describe the kinematics of an asymmetric plate pack, the broken line hypotheses are accepted. In a relatively thick lightweight core, the normal does not change its length, remains rectilinear, but rotates through some additional angle. Tuff, coarse grained soil, granite, and gneiss are accepted as the soil foundation. The bearing reaction is described by the Winkler model. The system of equilibrium equations is obtained by the variational method. Its solution is written in displacements through Kelvin functions. A numerical parametric analysis of displacements and stresses in the plate is carried out, their dependence on the type of soil foundation is shown.

Analytical Models of Axially Loaded Blind Rivets Used with Sandwich Beams

The paper presents the novel use of analytical models of a beam on an elastic foundation. The one-parameter model (Winkler model) and the two-parameter models (Filonenko-Borodich and Pasternak models) were investigated. These models were used to describe the elastic response of axially loaded blind rivets used with sandwich structures. The elastic response related to the elastic strain energy is mentioned in the paper as the resilience modulus of the connection. The databases from laboratory pull-out tests were used to verify these models. One type of blind rivet (aluminum, with three clamping arms) and one type of sandwich beam were used. The sandwich beams used in the experiments consisted of two thin-walled and stiff external facings (zinc-coated steel) and a thick, soft core (polyisocyanurate foam—PIR). In the test the sandwich beams were subjected to static, axial pull-out loading. The research provides the quantitative comparison between the laboratory experiment and the analytical solutions from models adopted for this type of connection. Additionally, the failure mechanisms, the secant stiffness at the ultimate capacity, and the strain energy capacity of the elastic foundation at failure are considered. To the author’s knowledge, this approach has not been described in the literature so far.

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

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.