By Franklin Y Cheng; Yuanxian Gu
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Extra info for Computational mechanics in structural engineering : recent developments
Compromise So~lution ..... 4~. 0 Figure 5: Points in Pareto-Set Filter Figures 4 and 5 illustrate part of the solution. Figure 4 shows the points in the Pareto-set filter which gives the trade-offs between the two conflicting objectives. The two points (Min. W and Min. Ei) , determined by using a traditional optimal method, are drawn as reference points because they are the two end-points of the Pareto optimal set for this problem. Note that the points in the filter are on or very close to the Pareto optimal set.
Including the applications of advanced control theories, such as H2 control [Suhardjo et al (1992)], LQR and H~ static output feedback control [Wu et al (1998)], sliding mode control [Yang et al (1997)], etc. Today, full-scale active tuned mass dampers have been installed on many high-rise buildings in Japan [e. , Spencer & Sain (1997)]. 16th node (x, y, 0 DOF) • • ° 12th node (x, y, 0 DOF) Y x 9 D 10th node (x, y,O iSOF) 9th node (x, y,O DOF) l~i node (x, y, 0 DOF) (a) (b) (c) Fig. 1" (a) Configuration of Nanjing Tower; (b) cross-section of concrete leg; (c) Discrete Structural Model The structural properties of the Nanjing Tower in the along-wind direction, as modeled by a discrete 16-degree-of-freedom system shown in Fig.
14 and 15 from N~,h m( ~ ) ( a l , m 4. Evaluate aOhk 5. 17 to obtain h U~,~m(~) = 1,2) . ( a l , c t 2 , m : 1,2), and solve Eqn. ~,m(~)(a i , m= 1,2) for 3 < l < _ M . 6. Solve FE Eqn. 20 to obtain u0h°(x). 7. ~, in the formulations ( 31 )--( 35 ). 8. Evaluate the approximate displacements M(x) e h~ u Mh(x) in formulation ( 12 ) , the strains in formulation ( 36 ), and the stresses cr~ (x) in formulation ( 37 ). Numerical Results We have coded the computing program of the FE method based on TSA for 2-dimension case, and made some numerical experiments to verify its effectiveness.