Abstract: The problem of layout and shape optimization of stiffeners in plates loaded in plane and in bending Kirchhoff's plates is considered in the paper. Two types of reinforcement are analyzed here, namely introduction of elements made of stiffer material like fibers or beams and introduction of ribs. The problem of minimization (maximization) of arbitrary objective functional of displacements, strains, stresses or reactions with constraint imposed on the structure cost is considered. Using adjoint method, expressions for sensitivities with respect to introduction of stiffeners are derived and on this basis conditions of modification are formulated. In order to find optimal reinforcement, heuristic algorithm is proposed in the paper. At first, using information from sensitivity analysis, initial localization of a new fiber or rib is determined. Next, in order to correct their positions and to determine other parameters characterizing stiffened structure standard optimization is performed. Usually, optimal position of the stiffener only a little differs from the initial position. Numerical examples illustrate applicability of the method. (c) 2007 Elsevier Ltd. All rights reserved.
B I B L I O G R A F I A1. Pedersen, P., "On optimal orientation of orthotropic materials", Struct Optim, vol. 1, 2, 1989, p.101-106
2. Landriani, G.S.& Rovati, M., "Optimal design for 2-D structures made of composite materials", ASME J Eng Mater Technol, vol. 113, 1991, p.55-63
3. Thomsen, J., "Optimization of composite disks", Struct Optim, vol. 3, 2, 1992, p.89-98
4. Burczyński T, Szczepanik M, Kuś W. Evolutionary optimization of stiffeners location in 2-D structures. In: Proceedings of the 16th international conference on computer methods in mechanics (on CD-ROM), Częstochowa, Poland, 2005.
5. Dems, K.& Mróz, Z.& Szeląg, D., "Optimal design of rib-stiffeners in disks and plates", Int J Solids Struct, vol. 25, 9, 1989, p.973-998
6. Lam, Y.C.& Santhikumar, S., "Automated rib location and optimization for plate structures", Struct Multidisc Optim, vol. 25, 1, 2003, p.35-45
7. Marczewska I, Sosnowski W, Marczewski A, Bednarek T. Topology and sensitivity-based optimization of stiffened plates and shells. In: Proceedings of the fifth world congress of structural and multidisciplinary optimization (on CD-ROM), Lido di Jesolo, Italy, 2003.
8. Stok, B.& Mihelic, A., "Two-stage design optimisation of shell structures", Struct Eng Rev, vol. 8, 1996, p.91-97
9. Tenek, L.& Hagiwara, I., "Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization", Comput Meth Appl Mech Eng, vol. 115, 1994, p.111-124
10. Krog, L.A.& Olhoff, N., "Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigenfrequency objectives", Comput Struct, vol. 72, 1999, p.535-563
11. Sokołowski, J.& Żochowski, A., "On topological derivative in shape optimization", SIAM J Control Optimiz, vol. 37, 4, 1999, p.1251-1272
12. Hashin, Z., "Analysis of composite materials - a survey", J Appl Mech (ASME), vol. 50, 1983, p.481-505
13. Jones, R.M., "Mechanics of composite materials", 1975
14. Lewiński, T., "A note on averaging of stiffnesses of thin elastic periodic plates", Eng Trans, vol. 34, 3, 1986, p.337-352
15. Kączkowski Z. Plates. Static calculations. Warszawa: Arkady
2000 [in Polish].
16. Woźniak, C. (Eds.), Mechanics of elastic plates and shells [in Polish], 2001
17. Lewiński, T.& Telega, J.J., "Plates, laminates and shells: asymptotic analysis and homogenisation", 1999
18. Szteleblak W, Bojczuk D. Optimisation of rib layout in plate structures. In: Proceedings of the 16th international conference on computer methods in mechanics (on CD-ROM), Częstochowa, Poland, 2005.
19. Mróz, Z.& Bojczuk, D., "Finite topology variations in optimal design of structures", Struct Multidisc Optim, vol. 25, 3, 2003, p.153-173
20. Dems, K.& Mróz, Z., "Shape sensitivity analysis and optimal design of physically nonlinear plates", Arch Mech, vol. 41, 4, 1989, p.481-501 
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