Dejan Zupan

University of Ljubljana · Faculty of Civil and Geodetic Engineering

The ageing of dams is one of the major challenges in specifically Slovenian and generally global dam engineering. Dams are exposed to environmental (climate) changes, as well as time-dependent effects, such as changes in the operating schedules of dams intended primarily for hydroelectric production. These changes can accelerate dams’ ageing and le...

This paper deals with the effects that displacements of the measuring pillar have on precise geodetic measurements. The changes in the position of the control points on the object or its surroundings can only be determined with well stabilized and stable reference points. These points are usually stabilized with measuring pillars which are not alwa...

We present a novel consistent singularity-free strain-based finite element formulation for the analysis of three-dimensional frame-like structures. Our model is based on a geometrically exact finite-strain beam theory, quaternion parametrization of spatial rotations, assumption that the strain measures are constant along the length of the element a...

We introduce a consistent displacement-based finite element formulation for the analysis of laminated composites with nonlinear interlaminar constitutive law. The computational model includes the nonlinear Reissner beam for modelling the bulk material and continuously distributed system of nonlinear springs to describe the connection between layers...

This paper presents the investigation of dynamic properties of a concrete gravity dam. Structural vibration measurements are an important part of structural monitoring, especially for the structures with high importance. The investigation started with the construction of the Brežice dam on the Sava River cascading system in Slovenia, where we have...

This paper presents the first application of the Laser Doppler Vibrometer (LDV) in non-stationary conditions within a hydropower plant powerhouse. The aim of this research is to develop a methodology to include non-contact vibration monitoring as part of structural health monitoring of concrete dams. We have performed in-situ structural vibration m...

To perform geodetic measurements of displacements of the ground and manmade constructions, stabilised reference points are needed from which control points on the object or its surroundings could be measured. Reference points are most commonly stabilised with reinforced concrete pillars; however, they are not always constructed in an appropriate ma...

The paper presents the design and static analysis of a high arch dam. A feasibility study was conducted on the dam in the 90s and a preliminary layout was designed. However, the dam’s construction phase has been never started. In this paper, the design and layout of the dam under consideration are in accordance with the US manuals for the design of...

In this paper, we present an original energy-preserving numerical formulation for velocity-based geometrically exact three-dimensional beams. We employ the algebra of quaternions as a suitable tool to express the governing equations and relate rotations with their derivatives, while the finite-element discretization is based on interpolation of vel...

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equ...

When some critical condition is reached at a material point of a solid body, a localized strain starts developing which makes the strain field discontinuous and highly accelerates local damaging of material. The present paper addresses this kind of strain localization in spatial geometrically exact beams. Here we propose a new beam finite element f...

This thesis presents the layout and the analysis of an arch dam. The dam was layout and designed at an optional location. We followed two US manuals for design of arch dams and designed our dam accordingly. These two manuals are published by United States Army Corps of Engineer (USACE) and Interior Department of United States Bureau of Reclamation...

In the paper we present a new finite-element formulation for the dynamic analysis of geometrically exact three-dimensional beams. We limit our studies to implicit time-integration schemes and possible approaches for increasing their robustness and numerical stability. In contrast to standard displacement-rotation based approach we present here a sp...

In the present paper the integration of angular velocities is studied. Both exact and approximate results are expressed in terms of rotational quaternions. Analytical solution is found using the theory of analytic differential systems. This exact solution serves as a suitable basis for derivation of various numerical methods. Approximative approach...

This paper presents the stability analyses of glulam arches subjected to distributed vertical loading. The present analysis employs a strain-based formulation of a nonlinear geometrically exact three-dimensional beam theory. The influence of the relative height of the arch on the lateral buckling load is studied. The buckling load is determined by...

Abstract This paper presents a new finite-element formulation for the dynamic analysis of three-dimensional beams. The formulation is based on the geometrically exact three-dimensional beam theory in which the strain vectors are the only unknown functions of the arc-length parameter. The classical Newmark time integration scheme extended to the mul...

In the paper, we present the Reissner–Simo beam theory in which the rotations are represented by quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered and the consistent energy complements of the rotational quaternions are employed, we derive the weak kinematic equat...

The rotational quaternions represent a unique four dimensional parametrization of rotations in the three dimensional Euclidean space. In the present paper they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parameterizing the rotation matri...

The analytical solution of a buckling force of a pretwisted delaminated composite column with a proper consideration of the extensional and bending stiffness coupling and transverse shear effect is presented. The system of homogenous linearized differential equations with nonconstant coefficients obtained for this problem is solved with the help of...

In the present paper we study the integration of rotations from the given angular velocities. The rotations are here represented by rotational quaternions. The quaternion representation of rotations is shown to be suitable for both analytical and numerical approach. Analytical solution is presented using the theory of analytic differential systems....

The rotational quaternions are the unique four-dimensional representation of rotations in three-dimensional Euclidean space. In the present paper on the dynamics of non-linear spatial beams, they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept...

The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the co...

Beam elements play an important role in modelling of various engineering structures. Their applicability is strongly dependent on the accuracy, robustness and efficiency of the numerical formulation. These properties prove to be of utmost importance especially when dealing with demanding initial or deformed geometry and material non-linearity. Many...

The present FEM formulation of the static and dynamic analysis of beam structures is novel in several respects. A completely new formulation of the three dimensional geometrically exact beam theory based on the quaternion algebra is proposed in which the rotations are fully replaced by the rotational quaternions. The same approach is used for both...

The present paper presents a consistent model of a three dimensional delaminated composite column with a proper consideration of the extensional and bending stiffness coupling and transverse shear effect to determine the axial buckling load. The exact analytical solution of the buckling force is obtained using the linearized stability theory. The t...

This paper presents the equations for the implementation of rotational quaternions in the geometrically exact three-dimensional beam theory. A new finite-element formulation is proposed in which the rotational quaternions are used for parametrization of rotations along the length of the beam. The formulation also satisfies the consistency condition...

The paper presents the wavelet-based discretization of the linearized finite-strain beam theory which assumes small displacements, rotations and strains but is capable of considering an arbitrary initial geometry and material behaviour. In the numerical solution algorithm, we base our derivations on the vector of strain measures as the only unknown...

The way the non-linear constitutive equations in the spatial beam formulations are solved, influences the rate of convergence and the computational cost. Three different approaches are studied: (i) the direct global approach, where the constitutive equations are taken to be the iterative part of the global governing equations, (ii) the local (or in...

The exact analytical solution of buckling in beams with multiple delaminations is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads, the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stabi...

The exact analytical solution of buckling in delaminated columns is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. In...

The paper deals with the characteristic value determination from relatively small samples. When the distribution and its parameters of a random variable are known, the characteristic value is deterministic quantity. However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples. Therefore the...

This paper presents the equations of the linearized geometrically exact three-dimensional beam theory of naturally curved and twisted beams. A new finite-element formulation for the linearized theory is proposed in which the strain vectors are the only unknown functions. The linear form of the consistency condition that the equilibrium and the cons...

The motion of a disk spinning on a horizontal surface has drawn a great deal of interest recently. The objectives of the researches are to find out what produces an increasing rattling sound and why the spinning ends so abruptly. In order to understand the behaviour of the spinning disk better, we derived a mathematical model of the rolling/sliding...

This paper presents a novel stress field and tangent material moduli integration procedure over a cross-section of a biaxially loaded concrete beam. The procedure assumes a sufficiently simple analytical form of the constitutive law of concrete, the polygonal shape of the boundary of the simply- or multi-connected cross-section and the monotonicall...

This paper introduces a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The formulation employs the generalized virtual work principle. In the resulting governing equations of the beam, the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive intern...

The standard test problem of MacNeal and Harder (Finite Elem. Anal. Des. 1 (1985) 3) for the verification of spatial beam finite elements, i.e. the deflection of the initially twisted beam, is commented through the analysis of three variants of initially twisted beams: (i) a linearly twisted beam with a constant cross-section; (ii) a non-linearly t...

This paper presents a new finite element formulation of the `geometrically exact finite-strain beam theory'. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced...

article introduces a new finite element formulation of the three-dimensional `geometrically exact finite-strain beam theory'. The formulation employs the generalized virtual work principle with the pseudo-curvature vector as the only unknown function. The solution of the governing equations is obtained by using a combined Galerkin-collocation algor...

A new finite element formulation of the `kinematically exact finite-strain beam theory' is presented. The finite element formulation employs the generalized virtual work in which the main role is played by the pseudo-curvature vector. The solution of the governing equations is found by using a combined Galerkin-collocation algorithm.

The paper deals with the characteristic value determination from relatively small samples. The characteristic value is usually determined with the assumption that the distribution and its parameters are known. The disadvantages of the method are described and the improved method is presented. Two improved point estimates as well as confidence inter...