The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process.

Dynamics and buckling loads for a vibrating damped Euler–Bernoulli beam connected to an inhomogeneous foundation

In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle, beam buckling loads are computed for cases of harmonically perturbed types of inhomogeneities in the elastic foundation, for cases of point inhomogeneities in the form of concentrated springs in the elastic foundation, and for cases with rectangular inclusions in the elastic foundation. The investigation of the beam dynamics shows the possibility of internal resonances for particular values of the beam rigidity and longitudinal force. Such types of resonances, which are usually typical for nonlinear systems, are only possible for the beam due to its inhomogeneous foundation. The occurrence of so-called added mass effects near buckling instabilities under the influence of damping have been found. The analytical expressions for this “added mass” effect have been obtained for different damping models including space hysteresis types. This effect arises as a result of an interaction between the main mode, which is close to instability, and all the other stable modes of vibration.

NUMERICAL CALCULATION OF STRESS-STRAIN STATE OF EARTH DAM UNDER BASIC LOADS WITH ACCOUNT OF INHOMOGENEOUS FOUNDATION

design, construction and operation of earth hydrotechnical structures located in seismic regions require a continuous improvement of computational methods for calculating various loads (static and dynamic ones). On the basis of the developed methodology and the complex of applied programs, an earth dam (Tupolang HPP) is calculated for the basic loads (gravity forces, hydrostatics) taking into account the design features and the actual physical and mechanical characteristics of soil both at the structure and at its earth foundation ( the height of the structure is 165m).The problem is solved in a plane elastic statement by the numerical finite element method. As the result of the calculation the isolines were obtained of equal displacements (horizontal and vertical), stresses (normal, tangential, principal) over the area occupied by the structure and its inhomogeneous foundation. A number of physical conclusions were made regarding the construction of important structures on an inhomogeneous earth foundation.

Strength Evaluation of a Linear Extended Structure on a Statically Inhomogeneous Foundation

In this paper the Galerkin method are used to obtain approximate solution to the stochastic beam bending problem. The present method is used to analyze the static deflection of beams. The uncertainty is represented as a parameterized stochastic process. Galerkin’s method selects the weight function functions in a special way: they are chosen from the basis functions, i.e. w(x)Î{ji(x)}, ni=1. It is required that the following n equations hold true. From the approximate solution, first and second order derivatives of the response are used. This paper solves the problem of strength and safety evaluation of a linear extended structure lying on a statically inhomogeneous foundation and presents an engineering analysis method.This paper solves the problem of strength and safety evaluation of a linear extended structure lying on a statically inhomogeneous foundation and presents an engineering analysis method.