Tarbiat Modarres University (T.M.U) In The Name of Allah

Transcription

1 In The Name of Allah

2 Optimum Design Program for Shape of Arch Dams (ODPSAD) Jalal Akbari PhD Candidate of Civil Engineering, Tarbiat Modares University,Iran M.T.Ahmadi Professor of Civil Engineering, Tarbiat Modares University, Iran H.Moharrami Assistant Professor of Civil Engineering, Tarbiat Modares University, Iran Peter Jan Pahl Professor of Civil Eng., TU Berlin,Germany ERCOFTAC 2006,5-7 April, Gran Canari, Spain

3 Outline Main Target Steps of ODPSAD Code Dynamic Loads & Optimization algorithm Design Variables Description Constraints & Objective Function Results Conclusion

4 Necessity &Target Because in our country (Iran) there are many new sites (150) for making new arch dams the necessity of shape optimization of arch dams is important in our country. Developing a practical and professional code for design optimum shape of arch dams with considering Engineering and construction necessities. Inputs: Arbitrary shape of canyon or topography data Height of arch dam material properties of rock and concrete Outputs: Optimum geometry of arch dam with satisfying design and construction demands

5 Main Steps of ODPSAD Program Geometry of Dam Geometry of arch dam is made with cubic Hermit splines. In this case characteristics such as ( thicknesses, radius, ) are known in 4 levels Hb=0, Hm=0.40*Hdam, Hu=0.75*Hdam, Hc=Hdam. In the arbitrary heights characteristics are determined with splines interpolation. Mesh Generation For 3 load cases ( dead load, hydrostatic load and Earthquake load) meshes are generated automatically with 8 node brick elements. Finite element analysis For above load cases finite element analysis is done with FEAPPv and stress results saved for optimization stage. Sensitivity analysis Gradients of objective function and constraints are carried out by finite difference method Optimization Enhanc design variables with one of optimization algorithms

6 Dynamic Load There are 3 sorts of dynamic load Time History Response Spectrum Equivalent Static Load in practice time history analysis is applied in form of shock, impact or harmonic loads so rarely is used in general form in optimization process. optimization for dynamic loads is time consuming process design space is disjoint for dynamic loads The number of constraints in time history load is increased dramatically With considering above notes Response spectrum load is used as dynamic load

7 Optimization Method There are 2 kinds method in arch dam shape optimization Gradient Based Methods GBM :(SLP,SQP,Penalty function, MFD,SD, ) Statistical Based Methods SBM :( GA,NN,ES,SA,.) Advantage and disadvantage of above methods Gradient computation in GBM is main drawback & time consuming process The probability of trapping in local optimum is high The rate of convergence in GMB is good In SBM gradient computation don t required The probability of trapping in local optimum is low In SBM The constraint problem must be changed to unconstraint problem In shape optimization and in the case that heavy finite element analysis is need the SBM are very weak NDV=40 NFEM=26000 Time= 325 h (13 day) 1.6 GHZ SBM(GA) NDV=40 NFEM=3000 Time= 433 h (1.4 day) 1.6 GHZ GBM (SQP)

8 C :Dam Coordinate system location (Cx,Cy,Cz) θ : The rotation of arch dam in site Tarbiat Modarres University (T.M.U) Design Variables There are 40 design variables in this optimization process

9 Tb,Tm,Tu,Tc : Thickness of crown cantilever in 4 levels Pb,Pm,Pu,Pc: Overhang parameters of crown in 4 levels

10 Rb,Rm,Ru,Rc: radius of curvature for crown cantilever at 4 stations

11 Tbr,Tmr,Tur,Tcr: Thickness of dam body at right abutment at 4 stations Tbl,Tml,Tul,Tcl: Thickness of dam body at left abutment at 4 stations

12 Sb,Sm,Su,Sc: Starting points of thickness variables zone in left side tb,tm,tu,tc : Starting points of thickness variables zone in right side

13 dbr,dmr,dur,dcr : Excavation in right abutment at 4 stations dbl,dml,dul,dcl : Excavation in left abutment at 4 stations

14 Gradient Computation Because there is not explicit formulation between design variables and objective function & constraints, these functions are approximated via Taylor expansion series. Nonlinear functions are replaced with sequential approximated quadratic (Objective function) and linear functions ( constrains) Gradient of objective function is computed with central finite difference method and gradient of constraints with forward finite difference method i To increase the rate of convergence, design variables are modified as bellow

15 Objective function & Constraints The volume of dam body and excavation volume at abutments is considered as objective function In shape optimization of arch dams, the 3 sorts of constraints should satisfy the demands of design and construction requirements: Geometrical constraints ( there are 7 constraints ) Stress constraints (there are variable constraints) Stability constraints ( there 8 constraints) In this research SQP (Sequential Quadratic Programming) algorithm is used as an optimizer

16 Geometrical constraints

17 Stress constraints

18 Location of elements & nodes for stress constraints evaluation

19 Stability Constraint

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21 Initial Design Variables Coordinate of site system Hdam =13 XS=0.0 YS=0.0 ZS=0.0 Coordinate of dam system XD= 0.0 YD=15.0 TETA=0. Overhangs in 4 levels Pc=1.00 Pu=0. Pm=0. Pb= 0. 5 Thickness of Crown Tc=. Tu=1. Tm=1. Tb=2. Radius of curvature. Rc= Ru=1 5 Rm= 5 Rb= 5. Thicknesses in right Tcr= Tur=15 Tmr=2 Tbr=30 Thicknesses in left Tcl= Tul=15 Tml=2 Tbl=30 Width Raito in right Sci=.5 Sui=.5 Smi= 5 Sbi=.5 Width Raito in left tci=.5 tui=.5 tmi=.5 tbi=.5 Excavation in abut. Dci=3 Dui=5; Dmi=6 Dbi=7 Material Properties Ec=22 Gpa Wc=2400 Ww=1000 Nu=.18 Er=8Gpa Valley shape nodes Trapezoidal shape

22 Geometry of Dam is made by 40 D.V

23 Geometry of Dam & Foundation is made by the same 40 D.V

24 Results

25 Evolution of crown cantilever shape

26 Volume(m3) Objective function convergence Iterations Crown cantilever Thickness Dam Height(m) Thickness(m) Initial Optimum

27 Conclusion This code has minimum interact with user ( user must guess suitable initial shape) In this code dynamic allocation and pointer capability of Fortran 90 is used The time consuming process in this research is gradient calculations because of using finite difference method instead of analytical sensitivity analysis or semi analytical method Good initial shape has very impact in number of iterations and convergence rate With starting from any arbitrary shape ( arbitrary design variables) optimum shape don t obtain. Suitable initial shape is required. The range of lower and upper limits of design variables in optimization algorithm have too effect in design variables enhancement so these limits must be select carefully. Using GUI and suitable post processor will develop in the future

28 Thanks for your attention