Thin plate quadrilateral element with independent rotational DOF

This paper presents a quadrilateral thin plate bending element with full compatibility of displacements and rotations at the nodes. A four-node finite element with independent translational and rotational degree of freedom (DOF) at each node is used. The shape functions for the approximation of the displacements and rotations are different and they are both determined from a complete polynomial of the fourth order. After satisfying conditions for the value of the functions and their first derivations at the element nodes, the shape functions consist of a fixed part satisfying the homogeneous differential equation and additional modes. The first one ensures high accuracy of the solution for the finite element with parallel opposite sides (rectangular, parallelogram). The additional modes in the shape functions of the rotational angle can be used for improving a solution in an arbitrarily quadrilateral finite element mesh. Described procedures ensure a high order of interpolation for the plate displacement. In both cases, finite element possesses twelve global degrees of freedom. The additional unknowns in the rotational shape functions of an arbitrarily quadrilateral element are eliminated on the element level

Wind load based on direct force measurements

Prikazana je horizontalna sila vjetra dobivena izravnim dinamičkim mjerenjem pomoću dinamičkog oscilatora na obronku planine Mosor, a obrađeni su tipovi vjetra bura i jugo. Uz dinamičke podatke o sili vjetra, srednjoj i fluktuirajućoj komponenti, izlučeni su spektri odgovora. Prikazana je razlika statičkog i dinamičkog djelovanja. Predložen je i približan postupak preslikavanja funkcije spektra odgovora sile vjetra s jedne na drugu lokaciju s poznatom srednjom brzinom vjetra.The horizontal wind force, measured directly on the Mosor Mountain foothills by dynamic oscillator, is presented. The wind types covered by the analysis are bura (bora) and jugo (sirocco). In addition to dynamic wind-force information, i.e. mean and fluctuating components, the response spectra are also derived. The difference between the static and dynamic action is presented. An approximate procedure for transferring wind force response-spectrum functions from one location to another, with the known mean wind speed, is proposed

Dinamička analogija za dokazivanje konvergencije rubnih zadaća ploča

This paper describes a procedure for proving the convergence and for estimating the numerical solution error of boundary value problems . The procedure is based on the transformation of a discrete boundary value problem in to an equivalent discrete dynamic eigenproblem. Discrete dynamic eigenproblem has physical meaning in convergence analysis because a mass represents the measure of domain discretization. The convergence and accuracy of numerical solution of boundary value problem depend on the convergence of discrete dynamic eigenproblem spectrum. The developed procedure is relatively simple, easy to perform ; in this paper it is used to evaluate the convergence and accuracy of numerical solution of the thin plate bending problem. The plate is discretized with four-node finite elements. One translational and two rotational degrees of freedom , which are independent of each other, are associated to each node of the plate. The shape func tions satisfy a homogenous differential equation of plate bending . The developed procedure gives the greatest global error which can appear for a chosen discretization . The performance of the proposed method is illustrated by the solution procedure of two examples: a simply supported square thin plate and a cantilever square thin plate.U ovome radu se opisuje postupak dokazivanja konvergencije i ocjene točnosti numeričkog rješenja rubnih zadaća. Postupak se temelji na transformaciji diskretne rubne zadaće u ekvivalentnu diskretnu dinamičku vlastitu zadaću. Diskretna dinamička vlastita zadaća im a fizikalno značenje jer masa predstavlja mjeru diskretizacije područja. Konvergencija i točnost numeričkog rješenja rubne zadaće ovisi o konvergenciji diskretne dinamičke vlastite zadaće. Razvijeni postupak je relativno jednostavan i lako izvediv , a u ovome radu je upotrijebljen za analizu konvergenci je i točnosti numeričkog rješenja tankih ploča. Ploča je diskretizirana s četvero čvornim konačnim elementima. Svakom čvoru ploče su pridruženi jedan translacijski i dva rotacijska stupnja slobode koji su međusobno neovisni . Bazne funkcije zadovoljavaju homogenu diferencijalnu jednadžbu savijanja ploča. Razvijenim postupkom dobivamo najveću moguću pogrešku koja se može pojaviti kod određene diskretizacije. Učinkovitost predloženog postupka je pri kazana u postupku rješavanja dva primjera: slobodno oslonjene kvadratne tanke ploče i ukliještene kvadratne tanke ploče

Sensitivity analysis of numerical parameters in FEM/DEM model for RC structures

The application of the finite-discrete element method (FEM/DEM) in the analysis of reinforced concrete (RC) structures is still in its early stages. Therefore, in this paper, sensitivity of the numerical model for analysis of RC structures based on the FEM/DEM method to the numerical parameters is presented. The accuracy of the solution, depending on the mesh refinement, crack spacing and penalty term, was analysed. The performed numerical analyses are useful in predicting the penalty parameter and mesh density in order to minimize numerical errors in analysis of RC structures with the FEM/DEM method. Validation of the numerical model for adopted numerical parameters was also shown by comparing numerical and experimental results

Comparison of two-dimensional and threedimensional analysis of reinforced and prestressed concrete structures

This paper presents the comparison of two-dimensional and three-dimensional analysis of the reinforced and prestressed concrete structures. The curved prestressing tendons and reinforcing bars, which are modelled by onedimensional finite element, are embedded into adequate two-dimensional and three-dimensional finite elements. The influence of the prestressing tendons on the concrete is modelled by distributed normal and tangential forces along the tendons and two concentrated forces at the anchors. The computation of the post-tensioned prestressed structures is organized in three phases: before, during and after prestressing of the tendons. A few numerical examples are given to compare the results obtained by these two analyses

Three-Dimensional Finite-Discrete Element Framework for the Fracturing of Reinforced Concrete Structures

This paper presents a three-dimensional numerical model based on finite-discrete element method for simulating cracking and predicting failure in reinforced concrete (RC) structures. Discrete representation of concrete cracks is coupled with a non-linear reinforcement model where reinforcing bars interact with concrete and slip due to crack opening and steel plastic deformation. Hence, it enables a simulation of complex material behaviour of concrete and steel in cracked zones and its influence on global structural behaviour. Several numerical examples are used to study the sensitivity of the model to different numerical and physical parameters and its capabilities in the analysis of RC structures

Wave properties of wind actions on structures

In this paper the wave properties of wind actions on structures analyzed on a single degree of freedom (SDOF) system are shown. The wave character of the action was examined by windows-wavelet analysis on several different measured data of wind actions. The constant and then the fluctuating action extracted from the wind force were analyzed by the wavelet transform. Fluctuating component of the wind action is represented by a harmonic function. The wavelet transform of wind action shows that the intensity of harmonic component decreases linearly with the number of cycles which implies that the resonance is not innate to wind action. All data of the wind action are obtained by measurements on SDOF oscillator. Time resolution varied from 0.01 to 0.00001 seconds. Significantly, the characteristics of wind action observed from the data on intensity of the averaging wind force are strongly connected with the length of the averaging wind force. The overall data of dynamic action show that the influence of wind is significantly higher for shorter periods of averaging. In this paper the term resonant spectra is used and the dynamic factor is based on them. The empirical relations for the value of the constant and the first harmonious component of the action are suggested. All results are compared with the classical spectra of the elastic force of SDOF system

Mathematical formulation of the space curvature of the tendon in the PC structures

This paper presents the mathematical formulation of the space curvature of the prestressing tendon in the nonlinear analysis of prestressed concrete (PC) structures. The nonlinear behaviour of prestressed tendons is described by the one dimensional elasto-viscoplastic model. The tendon element geometry is described by the second order space function which is determined by its projections. These elements make it possible to model arbitrarily curved prestressing tendons in space, thus they can be determined independently of the three-dimensional (3D) finite element mesh. This is very important in the case when the prestressing tendon can not be located in a plane. The transfer of prestressing force on the concrete was modelled numerically. The developed model makes it possible to compute prestressing structures in phases: before prestressing, during prestressing and after prestressing. The described models are implemented in the computer programme for a 3D analysis of the prestressed concrete structures where the structures are discretized by three-dimensional finite elements with an embedded one-dimensional element of prestressed tendons