Finite Strip Modeling for Optimal Design of Folded Plate Structures

1050 A. Bergamini, F. Biondini / Engineering Structures 26 (2004) 1043–1054Fig. 7. Roof element. (a) Main dimensions and loads. (b) Optimal thickness distributions, wings with constant thickness and (c) wings with aterminal bulb.andthe thickness distribution shown in Fig. 8(b), has atotal volume Vðx opt Þ¼0:753 m 3 =m.4.4. Bridge deck with prestressed girdersThe bridge deck shown in Fig. 9(a), with lengthL ¼ 40:0 m, width B ¼ 12:0 m andheight H ¼ 3:0 m,is considered. Besides its self-weight and the weight ofthe non-structural elements g p ¼ 4kN=m 2 , the structureis subjectedto the four alternative loading conditionsshown in Fig. 9(a), with q ¼ 8:0 kN=m 2 . Boththe girders are prestressed with a cable whose profile isdescribed by a third degree polynomial curve. Thethickness distribution over the cross-section and thecables profile which minimize both the total volumeandthe prestressing force (w V ¼ w P ¼ 1:0), are searchedfor.To this purpose, the width of the finite stripsis assumedto be variable. Moreover, two different constraintsfor the global deformability index d(x) are considered,respectively with (1) d max;1 ¼ 0:75 and(2) d max;2 ¼ 0:50. The optimal thickness distributionandthe cable layout are shown for both cases (1) and(2) in Fig. 9(b) and(c), respectively. The correspondingoptimal values of the total volume andof the prestressingforce are Vðx opt;1 Þ¼3:783 m 3 =m and Pðx opt;1 Þ¼7:079 MN for case (1), Vðx opt;2 Þ¼4:286 m 3 =m andPðx opt;2 Þ¼8:482 MN for case (2). It can be noticedthat solution (1), being associatedto a less restrictiveconstraint on the d-index, leads to lower values of volumeandprestressing with respect to solution (2).In order to better highlight the main aspects of thedesign process, Figs. 10–14 show the characteristicsof the optimal solution (2) andthe correspondingevolution of the search procedure. In particular, Fig. 10shows the distribution along the longitudinal coordinatey of the maximum values attainedover all theloading conditions by the components of the behavioraldesign vectors g a (x) and g b (x), relatedto theFig. 8.Barrel vault. (a) Main dimensions and loads; (b) Optimal shape and thickness distribution.