There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

Fundamentals of Rock Mechanics

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

Impact of incident angles of earthquake shear (S) waves on 3-D non-linear seismic responses of long lined tunnels

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 capabi...

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

Testing and finite element analysis of reinforced concrete column footings failing by punching shear

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 Green's 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.

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A numerical method for free vibration analysis of beams

Dynamic analysis of thin-walled closed-section beams

The paper is related to the determination of stress and strain fields around unsupported, stress free surface of an ellipsoidal cavity situated in a stressed elastic continuum. This is a most common requirement for the estimate of structural safety of underground rock excavations. The analytical approach elaborated in the paper avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. The significant simplifications of all expressions from definition of the problem to its resolving have been achieved by application of ellipsoidal coordinates. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.

Dragan Lukić

Papers

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

Testing and finite element analysis of reinforced concrete column footings failing by punching shear

A numerical method for free vibration analysis of beams

Dynamic analysis of thin-walled closed-section beams

Stress–strain field around elliptic cavities in elastic continuum