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Keywords: plastic analysis, frames, collapse mechanisms, collapse load factor, genetic algorithm.

Summary

The minimum and maximum principles are the basis of all the general analytical methods for plastic analysis and design, Baker, Horne and Heyman [1]. The most widely applicable method of analysis based on the minimum principle is that of the combination of elementary mechanisms, developed by Neal and Symonds [2,3].

Plastic analysis and design of rigid-jointed frames has been cast in the form of linear programming by Charnes and Greenberg [4], as early as 1951. Further progress in the field is due to Heyman [5], Baker and Heyman [6], Jennings [7], Theirauf [8], and Kaveh [9], among many others. Considerable progress has been made in the past decade, a complete report of which may be found in Munro [10] and Livesley [11].

In the method of combination of mechanisms, for a given frame and loading, every possible collapse mechanism can be regarded as the combination of certain number of independent mechanisms. The number of independent mechanisms, IM, is given by IM = NCS - DSI, where NCS and DSI are the number of potential plastic hinge positions (critical sections) and DSI is the degree of static indeterminacy of the frame.

For each possible collapse mechanism, a work equation can be written down from which the corresponding value of the load factor $\lambda$ is found. The actual mechanism is distinguished from among all the possible mechanisms by the fact that it has the lowest corresponding value of $\lambda$ , by the kinematic theorem, Neal [12]. The independent mechanisms with low values of $\lambda$ are therefore examined to form a mechanism, which gives an even lower value for $\lambda$ .

In this article, a direct method is developed rather than using a mathematical programming approach which has its own difficulties. In this approach an additional degree of freedom (DOF) is added to each member of the main structure. Therefore each element contains five degrees of freedom, consisting of four independent translation DOFs and two dependent rotation DOFs. The external work and internal work are then calculated and using the principle of virtual work, the load factor for each mechanism is obtained.

Once the basic collapse mechanisms and their load factors are calculated, the genetic algorithm is used to combine the mechanisms and identify the one corresponding to the least possible load factor. Examples are included to illustrate the efficiency of the present method compared to the use of simple genetic algorithm.

Genetic algorithm is shown to be a suitable tool for calculating the collapse load factor of frames. The hybrid crossover-mutation of this article reduces the number of generations needed for optimization and increases the speed of convergence to the load factor. This also enables to perform analysis for those frames for which the simple genetic algorithm fails to converge.

References

1: Baker J., Horne M.R, and Heyman J., The Steel Skeleton; Plastic Behaviour and Design, Cambridge at the University Press, Vol. 2, 1956.
2: Neal, B.G. and Symonds P.S., The rapid calculation of plastic collapse loads for a framed structures, Proc. Instits Civ. Engrs, Part 3, Vol. 1, 1952. doi:10.1680/ipeds.1952.12270
3: Neal, B.G. and Symonds P.S., The calculation of collapse loads for framed structures, J. Instits Civ. Engrs, Vol. 35, 1950-1. doi:10.1680/ijoti.1951.12699
4: Charnes A. and Greeberg H.J., Plastic collapse and linear programming, Summer Meeting of the American Mathematical Society, 1959.
5: Heyman, J. On the minimum weight design of a simple portal frame, International Journal of Mechanical Science, 1960:1:121-134. doi:10.1016/0020-7403(60)90034-5
6: Baker J. and Heyman, J. Plastic Design of Frames, Fundamentals, Vol. 1, Cambridge, Cambridge University Press, 1969.
7: Jennings, A. Adapting the simplex method to plastic design, In: Marris, LJ, editor. Proceedings of Instability and Plastic Collapse of Steel Structures, 1983, pp 164-173.
8: Thierauf, G. A method for optimal limit design of structures with alternative loads, Computational Methods in Applied Mechanics in Engineering, 1987:16:134-149. doi:10.1016/0045-7825(78)90039-7
9: Kaveh, A. Optimal Structural Analysis. RSP (John Wiley), UK, 1997.
10: Munro, J. Optimal plastic design of frames In Proceedings of NATO, Waterloo: Advanced Study in Engineering Plasticity by Mathematical Programming, 1977.
11: Livesley, R.K. Linear programming in structural analysis and design. In: Gallagher RH et al editors, Optimum Structural Design, Chapter 6, New York, Wiley, 1977.
12: Neal, B.G., The Plastic Methods of Structural Analysis, 3rd Edition, Science Paperbacks, London Chapman and Hall, 1977.

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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: 78 PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON THE APPLICATION OF ARTIFICIAL INTELLIGENCE TO CIVIL AND STRUCTURAL ENGINEERING Edited by: B.H.V. Topping Paper 33 Collapse Load Factor for Rigid-Plastic Analysis of Frames using a Genetic Algorithm A. Kaveh and K. Khanlari Building and Housing Research Center, Tehran, Iran doi:10.4203/ccp.78.33 purchase the full-text of this paper Full Bibliographic Reference for this paper A. Kaveh, K. Khanlari, "Collapse Load Factor for Rigid-Plastic Analysis of Frames using a Genetic Algorithm", in B.H.V. Topping, (Editor), "Proceedings of the Seventh International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 33, 2003. doi:10.4203/ccp.78.33 Keywords: plastic analysis, frames, collapse mechanisms, collapse load factor, genetic algorithm. Summary The minimum and maximum principles are the basis of all the general analytical methods for plastic analysis and design, Baker, Horne and Heyman [1]. The most widely applicable method of analysis based on the minimum principle is that of the combination of elementary mechanisms, developed by Neal and Symonds [2,3]. Plastic analysis and design of rigid-jointed frames has been cast in the form of linear programming by Charnes and Greenberg [4], as early as 1951. Further progress in the field is due to Heyman [5], Baker and Heyman [6], Jennings [7], Theirauf [8], and Kaveh [9], among many others. Considerable progress has been made in the past decade, a complete report of which may be found in Munro [10] and Livesley [11]. In the method of combination of mechanisms, for a given frame and loading, every possible collapse mechanism can be regarded as the combination of certain number of independent mechanisms. The number of independent mechanisms, IM, is given by IM = NCS - DSI, where NCS and DSI are the number of potential plastic hinge positions (critical sections) and DSI is the degree of static indeterminacy of the frame. For each possible collapse mechanism, a work equation can be written down from which the corresponding value of the load factor $\lambda$ is found. The actual mechanism is distinguished from among all the possible mechanisms by the fact that it has the lowest corresponding value of $\lambda$ , by the kinematic theorem, Neal [12]. The independent mechanisms with low values of $\lambda$ are therefore examined to form a mechanism, which gives an even lower value for $\lambda$ . In this article, a direct method is developed rather than using a mathematical programming approach which has its own difficulties. In this approach an additional degree of freedom (DOF) is added to each member of the main structure. Therefore each element contains five degrees of freedom, consisting of four independent translation DOFs and two dependent rotation DOFs. The external work and internal work are then calculated and using the principle of virtual work, the load factor for each mechanism is obtained. Once the basic collapse mechanisms and their load factors are calculated, the genetic algorithm is used to combine the mechanisms and identify the one corresponding to the least possible load factor. Examples are included to illustrate the efficiency of the present method compared to the use of simple genetic algorithm. Genetic algorithm is shown to be a suitable tool for calculating the collapse load factor of frames. The hybrid crossover-mutation of this article reduces the number of generations needed for optimization and increases the speed of convergence to the load factor. This also enables to perform analysis for those frames for which the simple genetic algorithm fails to converge. References 1 Baker J., Horne M.R, and Heyman J., The Steel Skeleton; Plastic Behaviour and Design, Cambridge at the University Press, Vol. 2, 1956. 2 Neal, B.G. and Symonds P.S., The rapid calculation of plastic collapse loads for a framed structures, Proc. Instits Civ. Engrs, Part 3, Vol. 1, 1952. doi:10.1680/ipeds.1952.12270 3 Neal, B.G. and Symonds P.S., The calculation of collapse loads for framed structures, J. Instits Civ. Engrs, Vol. 35, 1950-1. doi:10.1680/ijoti.1951.12699 4 Charnes A. and Greeberg H.J., Plastic collapse and linear programming, Summer Meeting of the American Mathematical Society, 1959. 5 Heyman, J. On the minimum weight design of a simple portal frame, International Journal of Mechanical Science, 1960:1:121-134. doi:10.1016/0020-7403(60)90034-5 6 Baker J. and Heyman, J. Plastic Design of Frames, Fundamentals, Vol. 1, Cambridge, Cambridge University Press, 1969. 7 Jennings, A. Adapting the simplex method to plastic design, In: Marris, LJ, editor. Proceedings of Instability and Plastic Collapse of Steel Structures, 1983, pp 164-173. 8 Thierauf, G. A method for optimal limit design of structures with alternative loads, Computational Methods in Applied Mechanics in Engineering, 1987:16:134-149. doi:10.1016/0045-7825(78)90039-7 9 Kaveh, A. Optimal Structural Analysis. RSP (John Wiley), UK, 1997. 10 Munro, J. Optimal plastic design of frames In Proceedings of NATO, Waterloo: Advanced Study in Engineering Plasticity by Mathematical Programming, 1977. 11 Livesley, R.K. Linear programming in structural analysis and design. In: Gallagher RH et al editors, Optimum Structural Design, Chapter 6, New York, Wiley, 1977. 12 Neal, B.G., The Plastic Methods of Structural Analysis, 3rd Edition, Science Paperbacks, London Chapman and Hall, 1977. 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 £82 +P&P)
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