EXPERIMENTAL-THEORETICAL CALCULATION OF THE STRESS-DEFORMED STATE OF THE BAR ON THE ELASTIC BASIS

Any strip foundation, and sometimes a slab foundation can be consideredas a be a mon an elastic base. And if with calculation of a beam – the tape base problems practically do not a rise because loading on the tape base as a rule is evenly distributed, and means and the base be haves, a sabsolutelyrigid beam. Then when considering a section of the foundation with unevenlyapplied load, some problems may arise. Today there are many publications on studies of the use of beams with an elastic base in the field of construction and the application of the features of the method of calculating the stress-strain state in the field of design. As is known, from classical soil mechanics, when a load is applied to a flexible slab, its center gives a draft of 1.24-1.57 times greater than the edges. Note that this effect can be explained by the contour work of the base and its uneven stiffness in the central and peripheral zone of the slab foundation. It should be noted that today in most cases the method of BN Zhemochkin [6] is used as the basis for the analytical solution of the problem of the interaction of the beam with the elastic base, which combines an engineering approach and strict solutions of the theory of elasticity. According to research, the method is based on the replacement of the continuous problem of the interaction of the foundation beam with the soil base, discrete, with a limited number of calculated sections within the beam and approximation of the smooth reactive pressure curve stepped with a constant value within a single section. Such simplifications allow to calculate various engineering problems on interaction of beams and plates, including with difficult geometry with the set degree of accuracy, bypassing difficult differential and integral calculations.

APPROXIMATION OF THE METHOD OF FOCUSED DEFORMATIONS TO THE PRACTICE OF APPLICATION OF SOLID FOUNDATIONS ON AN ELASTIC BASIS

The article discusses the application of solid foundation slabs in the base and the theoretical justification for the approximation of the method of concentrated deformations in the design of solid foundations on an elastic foundation.

ANALYSIS OF COMBINED PLATES WITH ALLOWANCE FOR CONTACT WITH ELASTIC FOUNDATION

The paper covers the problems of combined plates with circular base and consisting of a few sections with different laws of thickness variation. Analytical methods of analysis of similar structures are not yet devel­oped. The present work suggests the analytical method for solving of the stated problems, the contact with the elas­tic subgrade is also considered. The above-mentioned approach is shown on the example of the analysis of the bot­tom of the cylindrical reservoir, resting on the elastic subgrade. The inner part of this construction is represented by the ring plate of variable thickness which increases along the direction from the internal boundary. The outer part is represented by the ring plate of the constant thickness. The influence of the elastic basis and the upper part of the reservoir is taken into consideration. The solutions for stresses and deflections of the combined plate are given in closed form in terms of Bessel functions. The conditions of the plate’s sections conjugation are fulfilled.

Bending by explosion of a multilayered concrete beam on a visco-elastic basis

In this work, the problem of bending of a multilayered concrete beam of arbitrary cross-section by explosive loading on a visco-elastic basis is considered. It is assumed that different grades of concrete can be realized in layers in the cross-section. The property of concrete resistance to tension and compression is considered in work. It is assumed that the dynamic loading is caused by consecutive explosion of two charges over the middle of the span of beam. The distribution of bending moments and deflections of the beam at each time is determined. The time of the end of motion and the residual deflection of beam are found.

Methods of calculating the deflection of an orthotropic inhomogeneous plate on an elastic basis

The problem of elastic equilibrium of an orthotropic nonhomogeneous rectangular plate on an elastic basis (one-parameter Winkler model) is considered, hingedly fixed from all sides. We use the Navier method for finding the deflection function at each step of the iterative process and perturbation methods and successive approximations as iterative methods for solving the problem. The suitability of the method of successive approximations and the method of perturbations for the numerical solution of the problem of determining the stress-strain state of such a plate, the limits of the applicability of these methods, their accuracy and convergence of the iterative process in solving the deformation problems of heterogeneous orthotropic plates have been analyzed. The dependence of the deflection on the mechanical and geometric parameters of the plate and the base is established. It was found that the Poisson ratio practically does not affect the stress state of the plate (when the Poisson ratio is changed two times, the difference between the intensities of the shear stresses does not exceed 10%), it is possible to consider it as a constant using the methods of successive approximations and disturbances. It is also established that the method of successive approximations and the method of perturbations has a limit on the nature of inhomogeneity, the convergence essentially depends on the nature of the heterogeneity.

Stress Analysis of Post-Buckled Sandwich Panels

The paper presents a method to assess stresses in sandwich plates with periodic microstructure in the post-buckling region. The fundamental assumption is that the microstructure is linear elastic and von Karman non-linearity is present only at macro-, i.e. panel-scale. This enables response evaluation by equivalent homogenous continuum with constant stiffness properties. It is shown that the homogenization cancels shear-induced, odd-terms in microstructural field variables such as displacements and stresses. These are of fundamental importance when strength of the panel must be assessed. The localization approach utilised here neglects the actual position of the microstructure and thus is able to capture only the maximum values of these stress fluctuations. The validation of the present approach is carried out with 3D FE analyses and a good agreement is shown. The shear-induced periodic stresses are of fundamental importance when the strength in the post-buckling region is assessed based on linear elastic basis.