Dragan Lukić

A numerical method for free vibration analysis of beams

In this paper, a numerical method for solution of the free vibration of beams governed by a set of second-order ordinary differential equations of variable coefficients, with arbitrary boundary conditions, is presented. The method is based on numerical integration rather than the numerical differentiation since the highest derivatives of governing functions are chosen as the basic unknown quantities. The kernelsof integral equations turn out to be Greens function of corresponding equation with homogeneous boundary conditions. The accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature. It is shown that good accuracy can be obtained even with a relatively small number of nodes.

Comparative study on earthquake-induced soil–tunnel structure interaction effects under good and poor soil conditions

The effects of soil–tunnel structure interaction are proved to be quite significant, particularly under earthquake excitation. The influence of earthquakes on a tunnel–ground interaction depends on the peak acceleration, the intensity and duration of the earthquake, and outmost on the relative rigidity between the tunnel and the ground. With an aim to study the effects of tunnel–ground interaction, two-dimensional simplified dynamic linear analyses have been undertaken using the finite element based commercial software ANSYS. The present study employs a continuous FE model in order to estimate the soil–structure interaction effects regarding tunnel structures under earthquake action, for the cases of both good and poor soil conditions. The earthquake loading is simulated under simple shear conditions obtained by means of a one-dimensional free-field site response analysis in the code EERA. The obtained numerical results are compared to the most frequently used analytical expressions, and by that, a capability of the models to simulate the most important aspects of the SSI effects is validated. Furthermore, a comparison of the results for the cases of dense and loose soil conditions is performed, and their reliability, considerable mutual differences, as well as significant factors influencing tunnel–ground interaction for both cases, are evaluated.

Free Vibration Analysis of Cross-Ply Laminated Thin-Walled Beams with Open Cross Sections: Exact Solution

AbstractThe objective of the present paper is to analyze the free vibrations of thin-walled beams with arbitrary open cross section, made of cross-ply laminates with midplane symmetry, by means of an exact solution. The theory of thin-walled composite beams is based on assumptions consistent with Vlasov’s beam theory and classical lamination theory. The governing differential equations for coupled bending-torsional vibrations were obtained using the principle of virtual displacements. To simplify the coupled system of differential equations, an ideal center of gravity and shear center were introduced. In the case of a simply supported thin-walled beam, the closed-form solution for the natural frequencies of free harmonic vibrations was derived. The frequency equation, given in determinantal form, is expanded in an explicit analytical form. To demonstrate the validity of this method, the natural frequencies of nonsymmetric thin-walled beams having coupled deformation modes are evaluated and compared with r...

Flexural-torsional vibration analysis of axially loaded thin-walled beam

The present paper considers the flexure-torsion coupled vibrations of axially loaded thin-walled beams with arbitrary open cross section, by means of an exact solution. The effects of axial force, warping stiffness and rotary inertia are included in the present formulations. In the case of simply supported thin-walled beam, a closed-form solution for the coupled natural frequencies of free harmonic vibrations was derived by using a general solution of the governing differential equations of motion based on Vlasov theory. The method is illustrated by its application to two test examples, to demonstrate the effects of bending-torsion coupling and axial force on the dynamic behavior of thin-walled beams. Compared with those available in the relevant literature, numerical results demonstrate the accuracy and effectiveness of the proposed method.

REASONS TO CHANGE THE TENDER PROJECT OF A TUNNEL DURING CONSTRUCTION

During construction, especially of tunnels, very often there is a need to change the tender technical documents, i.e. the documents upon which the construction permit is obtained and the tender is announced. The main reason for the change of documentation is, above all, unsuficient geotechnical investigations due to which technical solutions and calculations are inadequate. Very rearly documentation is changed due to errors in the calculation if the techncal review of documentation is correctly done. The paper presents an example of the change of documentation during construction and the reasons for that.

Analytical approach for resolving stress states around elliptical cavities

The determination of stress states around cavities in the stressed elastic body, regardless of cavity shapes, that may be spherical, cylindrical elliptical etc. in its analytical approach has to be based on selection of a stress function that will satisfy biharmonic equation, under given boundary conditions. This paper is concerned with formulation and solution of the cited differential equation using elliptical coordinates in conformity with the cavity shape of oblong ellipsoid [1]. It is therefore considered that the formulation of the stress tensor will be done in conformity to the cited coordinates. The paper describes basic statements and definitions in connection to harmonic functions used for determination of stress states around cavities formed in the stressed homogeneous space. The particular attention has been paid to the use of Legendre`s functions, with definitions and derivation of recurrent formulas, that have been used for determination of stress states around an oblong ellipsoidal cavity, [1]. The paper also includes the description of procedures used in forming series based on Legendre`s functions of the first order.