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@semprelibera 2018-06-23T05:01:06.000000Z 字数 14106 阅读 1689

OpenSEES悬臂梁滞回模拟

assignment

  1. # --------------------------------------------------------------------------------------------------
  2. # Example 2. 2D cantilever column, static pushover
  3. # fiber section, nonlinearBeamColumn element
  4. #           Silvia Mazzoni & Frank McKenna, 2006
  5. #
  6. #    ^Y
  7. #    |
  8. #    2       __ 
  9. #    |          | 
  10. #    |          |
  11. #    |          |
  12. #  (1)       LCol
  13. #    |          |
  14. #    |          |
  15. #    |          |
  16. #  =1=      _|_  -------->X
  17. #
  19. # SET UP ----------------------------------------------------------------------------
  20. # units: N, mm, sec
  21. wipe;                   # clear memory of all past model definitions
  22. file mkdir DataHyst;                # create data directory
  23. model BasicBuilder -ndm 2 -ndf 3;       # Define the model builder, ndm=#dimension, ndf=#dofs
  26. # define GEOMETRY -------------------------------------------------------------
  27. #######
  28. # 把这里改成Gill试验中的构件几何尺寸
  29. #######--------------------------start
  30. set LCol 1200;      # column length
  31. set Weight 1815000.;        # superstructure weight
  32. # define section geometry
  33. set HCol 550;       # Column Depth
  34. set BCol 550;       # Column Width
  35. #######---------------------------end
  36. # calculated parameters
  37. set PCol $Weight; 		# nodal dead-load weight per column
  38. #######
  39. #重力加速度改成9.81N/kg
  40. #######------start
  41. set g 9.81;			# g.
  42. #######------end
  43. set Mass [expr $PCol/$g];		# nodal mass
  44. # calculated geometry parameters
  45. set ACol [expr $BCol*$HCol];					# cross-sectional area
  46. set IzCol [expr 1./12.*$BCol*pow($HCol,3)];          # Column moment of inertia
  48. # nodal coordinates:
  49. node 1 0 0;         # node#, X, Y
  50. node 2 0 $LCol         
  52. # Single point constraints -- Boundary Conditions
  53. fix 1 1 1 1;            # node DX DY RZ
  55. # nodal masses:
  56. mass 2 $Mass  1e-9 0.;     # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
  58. # Define ELEMENTS & SECTIONS -------------------------------------------------------------
  59. set ColSecTag 1;            # assign a tag number to the column section 
  60. # define section geometry
  61. ########
  62. #改保护层信息以、纵筋数量、纵筋面积
  63. ########---------start
  64. set coverCol 40.;           # Column cover to reinforcing steel NA.
  65. set numBarsCol 4;           # number of longitudinal-reinforcement bars in each side of column section. (symmetric top & bot)
  66. set barAreaCol 452.4 ;      # area of longitudinal-reinforcement bars
  67. ########----------end
  69. ########
  70. #这里混凝土和纵筋的材料性质信息需要按照Gill试验进行修改
  71. ########---------------start
  72. # MATERIAL parameters -------------------------------------------------------------------
  73. set IDconcU 1;          # material ID tag -- unconfined cover concrete
  74. set IDreinf 2;              # material ID tag -- reinforcement
  75. # nominal concrete compressive strength
  76. set fc -23.1;               # CONCRETE Compressive Strength (+Tension, -Compression)
  77. set Ec [expr 57000*sqrt(-$fc*1.45e2)*6.89e-3]; 		# Concrete Elastic Modulus (the term in sqr root needs to be in psi
  78. # unconfined concrete
  79. set fc1U 		$fc;           # UNCONFINED concrete (todeschini parabolic model), maximum stress
  80. set eps1U   -0.003;         # strain at maximum strength of unconfined concrete
  81. set fc2U        [expr 0.2*$fc1U];		# ultimate stress
  82. set eps2U	-0.01;			# strain at ultimate stress
  83. set lambda 0.1;				# ratio between unloading slope at $eps2 and initial slope $Ec
  84. # tensile-strength properties
  85. set ftU [expr -0.14*$fc1U];           # tensile strength +tension
  86. set Ets [expr $ftU/0.002];			# tension softening stiffness
  87. # -----------
  88. set Fy 375.;				# STEEL yield stress
  89. set Es 287500.;				# modulus of steel
  90. set Bs 0.03;				# strain-hardening ratio 
  91. set R0 18;				# control the transition from elastic to plastic branches
  92. set cR1 0.925;				# control the transition from elastic to plastic branches
  93. set cR2 0.15;				# control the transition from elastic to plastic branches
  94. uniaxialMaterial Concrete02 $IDconcU $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets;	# build cover concrete (unconfined)
  95. uniaxialMaterial Steel02 $IDreinf $Fy $Es $Bs $R0 $cR1 $cR2;                # build reinforcement material
  96. ########---------------end
  99. # FIBER SECTION properties -------------------------------------------------------------
  100. # symmetric section
  101. #
  102. #                        y
  103. #                        ^
  104. #                        |     
  105. #             ---------------------     --   --
  106. #             |   o     o     o    |     |    -- cover
  107. #             |                       |     |
  108. #             |                       |     |
  109. #    z <--- |          +           |     H
  110. #             |                       |     |
  111. #             |                       |     |
  112. #             |   o     o     o    |     |    -- cover
  113. #             ---------------------     --   --
  114. #             |-------- B --------|
  115. #
  116. # RC section: 
  117.    set coverY [expr $HCol/2.0];	# The distance from the section z-axis to the edge of the cover concrete -- outer edge of cover concrete
  118.    set coverZ [expr $BCol/2.0];    # The distance from the section y-axis to the edge of the cover concrete -- outer edge of cover concrete
  119.    set coreY [expr $coverY-$coverCol]
  120.    set coreZ [expr $coverZ-$coverCol]
  121.    set nfY 16;          # number of fibers for concrete in y-direction
  122.    set nfZ 4;           # number of fibers for concrete in z-direction
  124. ########
  125. #这里布置纵筋钢筋
  126. ########------------start
  127.    section fiberSec $ColSecTag   {;	# Define the fiber section
  128. 	patch quad $IDconcU $nfZ $nfY -$coverY $coverZ -$coverY -$coverZ $coverY -$coverZ $coverY $coverZ; 	# Define the concrete patch
  129. 	layer straight $IDreinf $numBarsCol $barAreaCol -$coreY $coreZ -$coreY -$coreZ;	# top layer reinfocement
  130. 	layer straight $IDreinf $numBarsCol $barAreaCol  $coreY $coreZ  $coreY -$coreZ;	# bottom layer reinforcement
  131.    # layer straight $IDreinf $numBarsCol $barAreaCol  $coreY $coreZ -$coreY  $coreZ; # left layer reinforcement
  132.    # layer straight $IDreinf $numBarsCol $barAreaCol  $coreY -$coreZ -$coreY -$coreZ; # right layer reinforcement
  133.     };  # end of fibersection definition
  134. ########----------end
  137. # define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
  138. set ColTransfTag 1;             # associate a tag to column transformation
  139. geomTransf Linear $ColTransfTag  ;     
  141. # element connectivity:
  142. set numIntgrPts 5;                              # number of integration points for force-based element
  143. element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag;   # self-explanatory when using variables
  145. # Define RECORDERS -------------------------------------------------------------
  146. recorder Node -file DataHyst/DFree.out -time -node 2 -dof 1 2 3 disp;       # displacements of free nodes
  147. recorder Node -file DataHyst/DBase.out -time -node 1 -dof 1 2 3 disp;       # displacements of support nodes
  148. recorder Node -file DataHyst/RBase.out -time -node 1 -dof 1 2 3 reaction;       # support reaction
  149. recorder Drift -file DataHyst/Drift.out -time -iNode 1 -jNode 2 -dof 1   -perpDirn 2 ;  # lateral drift
  150. recorder Element -file DataHyst/FCol.out -time -ele 2 globalForce;                      # element forces -- column
  151. recorder Element -file DataHyst/ForceColSec1.out -time -ele 1 section 1 force;              # Column section forces, axial and moment, node i
  152. recorder Element -file DataHyst/DefoColSec1.out -time -ele 1 section 1 deformation;             # section deformations, axial and curvature, node i
  153. recorder Element -file DataHyst/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force;     # section forces, axial and moment, node j
  154. recorder Element -file DataHyst/DefoColSec$numIntgrPts.out -time -ele 1 section 1 deformation;     # section deformations, axial and curvature, node j
  157. # define GRAVITY -------------------------------------------------------------
  158. pattern Plain 1 Linear {
  159.    load 2 0 -$PCol 0
  160. }
  162. # Gravity-analysis parameters -- load-controlled static analysis
  163. set Tol 1.0e-8;         # convergence tolerance for test
  164. constraints Plain;          # how it handles boundary conditions
  165. numberer Plain;         # renumber dof's to minimize band-width (optimization), if you want to
  166. system BandGeneral;     # how to store and solve the system of equations in the analysis
  167. test NormDispIncr $Tol 6 ; 		# determine if convergence has been achieved at the end of an iteration step
  168. algorithm Newton;			# use Newton's solution algorithm: updates tangent stiffness at every iteration
  169. set NstepGravity 10;  		# apply gravity in 10 steps
  170. set DGravity [expr 1./$NstepGravity];  # first load increment;
  171. integrator LoadControl $DGravity;	# determine the next time step for an analysis
  172. analysis Static;			# define type of analysis static or transient
  173. analyze $NstepGravity;      # apply gravity
  174. # ------------------------------------------------- maintain constant gravity loads and reset time to zero
  175. loadConst -time 0.0
  177. puts "Model Built"
  179. # STATIC PUSHOVER ANALYSIS --------------------------------------------------------------------------------------------------
  180. #
  181. # we need to set up parameters that are particular to the model.
  182. set IDctrlNode 2;           # node where displacement is read for displacement control
  183. set IDctrlDOF 1;            # degree of freedom of displacement read for displacement contro
  184. set Dmax [expr 0.03*$LCol];		# maximum displacement of pushover. push to 10% drift.
  185. set Dincr [expr 0.00001*$LCol];        # displacement increment for pushover. you want this to be very small, but not too small to slow down the analysis
  186. ########
  187. #这里输入位移加载的幅值
  188. ########---------------start
  189. set Amp1 3.0
  190. set Amp2 6.0
  191. set Amp3 10.0
  192. set Amp4 20.0
  193. set Amp5 34.0
  194. ########---------------end
  195. # create load pattern for lateral pushover load
  196. set Hload $Weight;				# define the lateral load as a proportion of the weight so that the pseudo time equals the lateral-load coefficient when using linear load pattern
  197. pattern Plain 200 Linear {;			# define load pattern -- generalized
  198. 	load 2 $Hload 0.0 0.0;  # define lateral load in static lateral analysis
  199. }
  201. # ----------- set up analysis parameters
  202. # CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/617.htm)
  203. #          Plain Constraints -- Removes constrained degrees of freedom from the system of equations (only for homogeneous equations)
  204. #          Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints 
  205. #          Penalty Method -- Uses penalty numbers to enforce constraints --good for static analysis with non-homogeneous eqns (rigidDiaphragm)
  206. #          Transformation Method -- Performs a condensation of constrained degrees of freedom 
  207. constraints Plain;      
  209. # DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/366.htm)
  210. #   determines the mapping between equation numbers and degrees-of-freedom
  211. #          Plain -- Uses the numbering provided by the user 
  212. #          RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm 
  213. numberer Plain
  215. # SYSTEM (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/371.htm)
  216. #   Linear Equation Solvers (how to store and solve the system of equations in the analysis)
  217. #   -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology. 
  218. #          ProfileSPD -- Direct profile solver for symmetric positive definite matrices 
  219. #          BandGeneral -- Direct solver for banded unsymmetric matrices 
  220. #          BandSPD -- Direct solver for banded symmetric positive definite matrices 
  221. #          SparseGeneral -- Direct solver for unsymmetric sparse matrices 
  222. #          SparseSPD -- Direct solver for symmetric sparse matrices 
  223. #          UmfPack -- Direct UmfPack solver for unsymmetric matrices 
  224. system BandGeneral
  226. # TEST: # convergence test to 
  227. # Convergence TEST (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/360.htm)
  228. #   -- Accept the current state of the domain as being on the converged solution path 
  229. #   -- determine if convergence has been achieved at the end of an iteration step
  230. #          NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration 
  231. #          NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration 
  232. #          EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration 
  233. set Tol 1.e-5;                        # Convergence Test: tolerance
  234. set maxNumIter 6000;                # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
  235. set printFlag 0;                # Convergence Test: flag used to print information on convergence (optional)        # 1: print information on each step; 
  236. set TestType NormDispIncr ; # Convergence-test type
  237. test $TestType $Tol $maxNumIter $printFlag;
  239. # Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/682.htm)
  240. #          Linear -- Uses the solution at the first iteration and continues 
  241. #          Newton -- Uses the tangent at the current iteration to iterate to convergence 
  242. #          ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence 
  243. set algorithmType Newton
  245. #algorithm $algorithmType;        
  246. algorithm Newton -initial
  247. # Static INTEGRATOR: -- determine the next time step for an analysis  (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/689.htm)
  248. #          LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain 
  249. #          DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain 
  250. #          Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized 
  251. #          Arc Length -- Specifies the incremental arc-length of the load-displacement path 
  252. # Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects 
  253. #          Newmark -- The two parameter time-stepping method developed by Newmark 
  254. #          HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method 
  255. #          Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement 
  256. analysis Static
  257. integrator DisplacementControl  $IDctrlNode   $IDctrlDOF $Dincr
  259. # ANALYSIS  -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/manuals/usermanual/324.htm)
  260. #          Static Analysis -- solves the KU=R problem, without the mass or damping matrices. 
  261. #          Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant. 
  262. #          variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when 
  263. #                 there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable.
  264. #analysis Static
  266. #  ---------------------------------    perform Static Pushover Analysis
  267. ########
  268. #这里设置具体的位移加载方式
  269. ########---------------------start
  270. set Nsteps [expr int($Amp1/$Dincr)];        # number of pushover analysis steps
  271. set ok [analyze $Nsteps];                # this will return zero if no convergence problems were encountered
  272. integrator DisplacementControl $IDctrlNode $IDctrlDOF [expr -1*$Dincr]
  273. set Nsteps [expr int(2*$Amp1/$Dincr)];
  274. set ok [analyze $Nsteps];
  275. integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
  276. set Nsteps [expr int(($Amp1+$Amp2)/$Dincr)];
  277. set ok [analyze $Nsteps];
  278. integrator DisplacementControl $IDctrlNode $IDctrlDOF [expr -1*$Dincr]
  279. set Nsteps [expr int(2*$Amp2/$Dincr)];
  280. set ok [analyze $Nsteps];
  281. integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
  282. set Nsteps [expr int(($Amp2+$Amp3)/$Dincr)];
  283. set ok [analyze $Nsteps];
  284. integrator DisplacementControl $IDctrlNode $IDctrlDOF [expr -1*$Dincr]
  285. set Nsteps [expr int(2*$Amp3/$Dincr)];
  286. set ok [analyze $Nsteps];
  287. integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
  288. set Nsteps [expr int(($Amp3+$Amp4)/$Dincr)];
  289. set ok [analyze $Nsteps];
  290. integrator DisplacementControl $IDctrlNode $IDctrlDOF [expr -1*$Dincr]
  291. set Nsteps [expr int(2*$Amp4/$Dincr)];
  292. set ok [analyze $Nsteps];
  293. integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
  294. set Nsteps [expr int(($Amp4+$Amp5)/$Dincr)];
  295. set ok [analyze $Nsteps];
  296. integrator DisplacementControl $IDctrlNode $IDctrlDOF [expr -1*$Dincr]
  297. set Nsteps [expr int(2*$Amp5/$Dincr)];
  298. set ok [analyze $Nsteps];
  299. integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr
  300. set Nsteps [expr int($Amp5/$Dincr)];
  301. set ok [analyze $Nsteps];
  302. ########------------------------end
  305. # ---------------------------------- in case of convergence problems
  306. if {$ok != 0} {      
  307. # change some analysis parameters to achieve convergence
  308. # performance is slower inside this loop
  309. 	set ok 0;
  310. 	set controlDisp 0.0;		# start from zero
  311. 	set D0 0.0;		# start from zero
  312. 	set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
  313. 	while {$Dstep < 1.0 && $ok == 0} {	
  314. 		set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
  315. 		set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
  316. 		set ok [analyze 1 ]
  317. 		if {$ok != 0} {
  318. 			puts "Trying Newton with Initial Tangent .."
  319. 			test NormDispIncr   $Tol 2000  0
  320. 			algorithm Newton -initial
  321. 			set ok [analyze 1 ]
  322. 			test $TestType $Tol $maxNumIter  0
  323. 			algorithm $algorithmType
  324. 		}
  325. 		if {$ok != 0} {
  326. 			puts "Trying Broyden .."
  327. 			algorithm Broyden 8
  328. 			set ok [analyze 1 ]
  329. 			algorithm $algorithmType
  330. 		}
  331. 		if {$ok != 0} {
  332. 			puts "Trying NewtonWithLineSearch .."
  333. 			algorithm NewtonLineSearch .8
  334. 			set ok [analyze 1 ]
  335. 			algorithm $algorithmType
  336.         }
  337.     }
  338.     };      # end if ok !0
  340. puts "DonePushover"
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