Miroslav Živković

A general beam finite element with deformable cross-section

A general beam finite element is proposed in the paper. The formulation of the element relies on the assumption that the beam-type structural response can be described by using the usual beam and 3D continuum theories. The beam behaviour is represented through the beam degrees of freedom of the global nodes on reference axis, and local effects are taken into account through the relative displacements of the cross-sectional nodes defining the in-plane and out-of-plane deformations of the cross-section. Consistent derivations for small and large displacements within incremental analysis are presented. The cross-section is modeled by segments (cross-sectional elements) and can be of arbitrary shape, including thick- and thin-walled types. The element is formulated as a superelement consisting of the isoparametric subelements (3D, shell, beam) with the relative displacements as the internal degrees of freedom of the element group, which is considered as a substructure. The relative displacements can be translations and rotations, depending on the type of the subelements. Continuity of the relative displacements is ensured within the element group, and connection of the beam elements with other finite element (FE) groups is realized through global (beam) degrees of freedom. Incompatible generalized displacements are implemented to subelements to improve their behavior. External loading of the element can correspond to global and cross-sectional nodes. The proposed beam superelement (BS) is easy for application within FE general purpose package (as our program PAK) in the preparation of input and in the postprocessing. A number of typical examples illustrate accuracy of results obtained by use of the beam superelement in linear and geometrically nonlinear analysis.

REGISTRATION AND SURFACE INSPECTION OF AUTOMOTIVE PRESSED PARTS BASED ON POINT CLOUD GENERATED BY OPTICAL MEASURING TECHNIQUES

Modern quality control has become unthinkable without optical measuring systems which are intensively used in automotive industry. This paper shows the analysis of preparation of models in terms of proper positioning in relation to the digitized model and the correct interpretation of the results of quality control. Experimental results verifying the method and the theory are shown. Part of tool for pressing and fabricated physical model of passenger car’s suspension control arm is compared to CAD model. Presented results of measurements show that the optical measuring systems are powerful tool for quality control, analysis and discovering of causes of faults.

The analysis of choice influence in fatigue failure criteria on integrity assessment of wagon structure

This paper presents the S-N approach to fatigue failure analysis of welded joints that integrates well with finite element modelling. Goodmans criterion and fatigue criterion based on the equivalent stress range were used for the analysis of the fatigue failure. Goodmans criterion and fatigue criterion based on the equivalent stress range, for determining fatigue safety factor, are implemented in the software package for finite element analysis PAK. Numerical calculation of fatigue safety factor was determined to assess the integrity of wagon structure parts according to the most commonly used European standards for wagon analysis. According to failure safety factors obtained by Goodmans criterion and fatigue criterion based on the equivalent stress range it should be noticed that both methods give good results. Both criteria give us adequate identification causes of cracking on the underframe of wagon for containers transportation. The obtained results and their well matching prove reliability of both fatigue failure criteria and that they can be used for integrity assessment of wagon structure parts.

Analitička, numerička i eksperimentalna procjena naprezanja kuglastog spremnika velikog obujma

Original scientific paper This paper presents designing of spherical tank using combination of analytical procedure with FEM analysis and experimental testing in order to minimize design time and verify design strength. Analytical procedure for calculation of the tank strength in the initial stages of design process is briefly presented. Based on analytical results, tank is dimensioned and FEM model is created. FEM analysis is used to identify areas with high concentration of stresses. FEM results showed that equivalent value of stress at the points of spherical tank support exceeds the values of yield stress, but this exceedance is not significant and in very small area, so overall design was deemed worthy. Experimental measurements verified FEM results that it is not necessary to reinforce the spherical tank at the points of support. After 8 months experiments were repeated giving the same results as the original measurements, thus justifying decision not to reinforce tank supports.

EMBANKMENT DAM STABILITY ANALYSIS USING FEM

This paper presents stability analysis of embankment dam with the surrounding heterogeneous rock mass using finite element method. In order to perform stability analysis of the dam and surrounding rock mass, several elastic-plastic material models for soil are customized and implemented in program package PAK. A 3D FE model of the embankment dam and the surrounding rock mass containing various material distributions according to their real distribution was made. The model includes a wider area around the dam in order to minimize the influence of the boundary conditions. The initial material parameters were determined using the identification of material parameters on the basis of the material from the dam body. Analysed dam is equipped with dam crest displacement transducers, as well as with transducers for the total and pore pressure in the clay core. Certain deviations have been noticed while comparing the measured values of these quantities with the results of the simulation. Since the analysed dam has been in operation for a long time, these deviations from the initial values of the parameters are caused due to the changes of the mechanical properties of materials during the dam operation. These changes are caused by several factors: the settlement of the dam and foundation, flushing of the material in the body of the dam and foundation, load changes, etc. In order to take into account the change of mechanical properties in materials and achieve the results of numerical simulation to describe the behaviour of the dam as close to the real behaviour, the calibration of the material parameters is carried out. Calibration of material parameters was performed using the measured displacements of the dam crest, as well as pore and total pressures in the clay core. Using the calibration we obtain new material parameters which give results of the numerical simulation that are closer to the behaviour of the real dam. In this manner we manage the dam safety and we can predict its future behaviour.