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Keywords: environmental effects, computational structural mechanics, inequality problems.

Summary

Engineering structures are often exposed to environmental actions which can cause significant damage [1]. Especially for metal structures, a main such defect is the strength degradation causing a reduction of the loads bearing capacity. To overcome such defects, sometimes cable-like members are used as a first strengthening and repairing procedure.

As well-known, the above cable-like members can undertake tension but buckle and become slack and structurally ineffective when subjected to a sufficiently large compressive force. Thus the governing conditions take an equality as well as an inequality form and the problem becomes nonlinear. So, the problem of structures containing as above cable-like members belongs to the so-called inequality problems of mechanics, as their governing conditions are of both, equality and inequality type [2].

In the early analysis attempts, many of these structures have been analyzed by a trial-and-error technique requiring repeated analysis of the structures for various loading systems. However, it should be noted that convergence to the correct solution by such iterative procedures is not always guaranteed. A more realistic treatment of the problem has been obtained using quadratic programming methods [3]. Further, the variational or hemivariational inequality concept has been used for the rigorous mathematical investigation of the problem [2].

The early numerical realizations of these approaches were based mainly upon the principle of minimum complementary energy. Thus, an equivalence principle for the analysis of statically undetermined structures with unilateral constraints has been proven by Nitsiotas [3].

On the other hand, most of the available computer programs are based on the displacement method. Consequently it seems more advantageous to combine the afore-mentioned equivalence principle with the displacement method to obtain a numerical procedure for the analysis of such structures.

The aim of this paper is to deal with the development of a simple numerical procedure for the static analysis of linearly elastic metal structures containing cable-like members by using a version of the stiffness (displacement) method of structural analysis. The present procedure is based on the finite element method and the equivalence principle, proposed by Nitsiotas in [3]. Using this principle, the analysis of such structures results in a linear complementarity problem (LCP), can with a reduced number of unknowns. The last problem can be solved by various effective quadratic programming algorithms. A numerical example shows the direct applicability on the computer and the effectiveness of the procedure presented herein.

References

1: Peavy H.S., Rowe D.R., Tchobanoglous G., "Environmental Engineering", McGraw-Hill, New York, 1985.
2: Panagiotopoulos P., "Hemivariational Inequalities. Applications in Mechanics and Engineering", Springer Verlag, Berlin, 1993.
3: Nitsiotas G., "Die Berechnung statisch unbestimmter Tragwerke mit einseitigen Bindungen", Ingenieur-Archiv, vol. 41, pp. 46-60, 1971. doi:10.1007/BF00536162

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 294 A Computational Stiffness Approach for Environmentally Damaged and Cable-Strengthened Metal Structures K.A. Liolios¹ and A.A. Liolios² ¹Ecological Engineering and Technology Laboratory, Department of Environmental Engineering, ²Structural Mechanics and Earthquake Engineering Laboratory, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece doi:10.4203/ccp.88.294 purchase the full-text of this paper Full Bibliographic Reference for this paper K.A. Liolios, A.A. Liolios, "A Computational Stiffness Approach for Environmentally Damaged and Cable-Strengthened Metal Structures", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 294, 2008. doi:10.4203/ccp.88.294 Keywords: environmental effects, computational structural mechanics, inequality problems. Summary Engineering structures are often exposed to environmental actions which can cause significant damage [1]. Especially for metal structures, a main such defect is the strength degradation causing a reduction of the loads bearing capacity. To overcome such defects, sometimes cable-like members are used as a first strengthening and repairing procedure. As well-known, the above cable-like members can undertake tension but buckle and become slack and structurally ineffective when subjected to a sufficiently large compressive force. Thus the governing conditions take an equality as well as an inequality form and the problem becomes nonlinear. So, the problem of structures containing as above cable-like members belongs to the so-called inequality problems of mechanics, as their governing conditions are of both, equality and inequality type [2]. In the early analysis attempts, many of these structures have been analyzed by a trial-and-error technique requiring repeated analysis of the structures for various loading systems. However, it should be noted that convergence to the correct solution by such iterative procedures is not always guaranteed. A more realistic treatment of the problem has been obtained using quadratic programming methods [3]. Further, the variational or hemivariational inequality concept has been used for the rigorous mathematical investigation of the problem [2]. The early numerical realizations of these approaches were based mainly upon the principle of minimum complementary energy. Thus, an equivalence principle for the analysis of statically undetermined structures with unilateral constraints has been proven by Nitsiotas [3]. On the other hand, most of the available computer programs are based on the displacement method. Consequently it seems more advantageous to combine the afore-mentioned equivalence principle with the displacement method to obtain a numerical procedure for the analysis of such structures. The aim of this paper is to deal with the development of a simple numerical procedure for the static analysis of linearly elastic metal structures containing cable-like members by using a version of the stiffness (displacement) method of structural analysis. The present procedure is based on the finite element method and the equivalence principle, proposed by Nitsiotas in [3]. Using this principle, the analysis of such structures results in a linear complementarity problem (LCP), can with a reduced number of unknowns. The last problem can be solved by various effective quadratic programming algorithms. A numerical example shows the direct applicability on the computer and the effectiveness of the procedure presented herein. References 1 Peavy H.S., Rowe D.R., Tchobanoglous G., "Environmental Engineering", McGraw-Hill, New York, 1985. 2 Panagiotopoulos P., "Hemivariational Inequalities. Applications in Mechanics and Engineering", Springer Verlag, Berlin, 1993. 3 Nitsiotas G., "Die Berechnung statisch unbestimmter Tragwerke mit einseitigen Bindungen", Ingenieur-Archiv, vol. 41, pp. 46-60, 1971. doi:10.1007/BF00536162 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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