Numerical analisys of discontinuities in beam structures.

Stan, Florina ; Grozea, Marius-Alexandru ; Dobrescu, Corina 等

1. INTRODUCTION

Beam structures are widespreaded, representing efficient and safe solutions in civil and industrial structures, as well as in mechanical engineering. In many types of activities, a great variety of lifting and transport installations are used, which may execute lifting, moving, transport, bringing down, loading, discharging, assembling, turning, overturning operations etc. It is the case of the rolling bridges, cranes, elevators, waggons, spinning towers etc. The modelling and analisys of these structures as ensembles are quite simple due to the variety of the high-performance computer codes based on: displacement method, finite element method (Cioata, 2008) or algorythm based analytical methods.

Beam structures (Boiangiu & Alecu, 2008) have geometrical and constructive discontinuities and their calculus becomes difficult when referring to the junctions between the beams.

The paper presents the calculus with finite elements of a junction which is considered submodel and is isolated from the assembly of a complex structure.

The substructuring technique (Constantinescu & Sorohan, 2003) represents the sole method to get results close to reality, but the working methodologies are not developed enough.

The problem of discontinuities in the beam structures nodes presented in this paper involves deep investigations and the use of special calculus methods like the finite element method and some proper working methodologies because in these zones important stress concentrations often appear.

The working methodology used in this paper may be extended to any type of junction, no matter how complex.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

2. MODELLING OF FOUR STRAIGHT BEAM JUNCTION

The rectangular junction between two circular section beams (pipes) and two rectangular section beams was taken into consideration. The general view of the junction is shown in figure 1.

This junction is a substructure or a submodel and it is obtained from the structure ensemble by "cutting" at a certain distance from the center of the node. In the cutting sections, the efforts and displacements which were determined in a first stage for the structure ensemble may be introduced in the submodel. The dimensions of the submodel are shown in figure 2. The pipe with circular section broke through the one with rectangular section, the two components of the junction being assembled with 10 mm corner soldering.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The submodel was meshed with 21376 three dimensional brick finite elements, with eight nodes and three degrees of freedom per node, defined on a network of 28850 nodes. The submodel configuration and the meshing are presented in figure 3.

The XYZ global coordinate system, to which the model is related, is also figured.

The loads applied to the submodel are concentrated forces applied in nodes, on the circular section beam, as follows:

--a [F.sub.X] = 2 kN resultant force, applied on the face of the model with Z = 120 mm, on the X direction;

--a [F.sub.Z] = 2 kN resultant force applied on the face of the model with Z = 120 mm, on the Z direction;

--a [F.sub.Y] = -4.2 kN resultant force applied on the exterior face of the pipe, on a 50 mm length and a 30 mm width, on the Y direction.

The constraints of the submodel were defined by null displacements on the X, Y, Z directions in the inferior surface nodes of the rectangular section pipe (Y = 110 mm).

The measuring units for all the calculations were Newtons and Milimeters.

The elastic constants of the material (construction steel) were considered with the following values:

--the Young's modulus E = 2.1 x [10.sup.5] MPa;

--the shear modulus G = 8.1x [10.sup.4] N/[mm.sup.2];

--the Poisson's ratio v = 0.3.

3. RESULTS OF THE JUNCTION ANALISYS

The finite element analyses (Ghionea et al., 2008) yielded a great volume of information, from which only a small part is presented in a simple and suggestive form. In figure 4, the configuration of the deformed junction (with a multiplication factor of 300) as well as the map of the resultant (total) displacement values, are presented.

The general configuration of the stress state and the zone with the maximum equivalent stress are shown in figure 5. In figure 6, the variation of the von Mises equivalent stress along a part of the soldering between the two components of the junction is graphically represented.

Because the model of the analyzed junction is three dimensional and the meshing was realized with brick finite elements it is impossible to directly estimate the stress state in the model. To obtain an image of it, some sections with several planes are made, preferable with parallel planes with the global coordinate system of the model.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

4. CONCLUSIONS

1. Even if the analyzed junction is quite simple--geometrically and constructive--it required a great volume of work, to create the finite element model, to postprocess the results and to present them clearly.

2. The values of the stresses reveal phenomenon of stress concentration and important values of local stresses (Hadar et al., 2007) which in certain circumstances can be determined for correct estimations of the safety coefficient and of the reliability of the beam structure from which the analyzed junction was "detached".

3. The stress state configurations are clearly nonlinear, which motivates the interest and the engineering importance of the steps like the one shown above.

5. ACKNOWLEDGEMENT

The paper is conceveid in the frame of P.O.S.D.R.U. Programme--University POLITEHNICA of Bucharest.

6. REFERENCES

Boiangiu, M.& Alecu, A (2008), Bending Vibrations of Bars with Axial Forces, Annals of DAAAM for 2008 &Proceedings of the 19th International DAAAM Symposium 'Inteligent Manufacturing and Automation: Focus on Next Generation of Intelligent Systems and Solutions', Katalinic, B. (Ed), pp 133-134, ISSN 1726-9679, Trnava, Slovakia, October 2008, DAAAM International, Vienna

Cioata, V. G. (2008), Determining the Machining Error Due to Workpiece--Fixture System Deformation Using the Finite Element Method, Annals of DAAAM for 2008 & Proceedings of the 19th International DAAAM Symposium 'Inteligent Manufacturing and Automation: Focus on Next Generation of Intelligent Systems and Solutions', Katalinic, B. (Ed), pp 253-254, ISSN 1726-9679, Trnava, Slovakia, October 2008, DAAAM International, Vienna

Constantinescu, I.N. & Sorohan, St. (2003), Practica modelarii si analizei cu elemente finite, POLITEHNICA PRESS Publishing House, pp. 95-99, ISBN 973-8449-26-x, Bucharest

Ghionea, I, Munteanu, G. & Beznila, H (2008), Von Mises Stress Evaluation for a Mechanical Part Using the Catia Finite Element Method, Annals of DAAAM for 2008 &Proceedings of the 19th International DAAAM Symposium, Katalinic, B. (Ed), pp 549-550, ISSN 1726-9679, Trnava, Slovakia, October 2008, DAAAM International, Vienna

Hadar, A., Constantinescu, I.N., Jiga, G. & Ionescu, D.S. (2007), Some Local Problems in Laminated Composite Structures, Mat. Plast, Vol. 44, No. 4, pp. 354-360, ISSN 0025-5289, Bucharest