symmetric_prism.tens

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[CONSTANTS]

  % Parametrization of a one-prism tower taken from 
  %    Stiffness formulations and necessary and sufficient
  %    conditions for exponential stability of prestressable structures
  %    Cornel Sultan
  %    International Journal of Solids and Structures 50 (2013)

   % The driving parameter: must be in [0,30deg]
   alpha := 5.6*PI/180

   % Structural parameters (taken from the matlab file)
   b := 1                      % Size of base/platform
   l := 3                      % Length of struts
   P := PARAMETER(PRETENSION)  % Pretension (taken from parameter file)
  
   rs := 0.05                 % Radius to represent struts
   rc := 0.0150               % Radius to represent cables

   % depending parameters
   sin_delta := b/(2*sqrt(3)*l*sin(alpha)) % sin(delta)

   % length of the elements
   V := sqrt(l^2+b^2-2*l*b*cos(alpha)*sin_delta)
   B := sqrt(3*l^2*sin_delta^2+b^2-3*l*b*sin_delta*cos(alpha)-sqrt(3)*l*b*sin_delta*sin(alpha))

   % print V
   % print B

   T_v_0 := (cot(alpha)-sqrt(3))*sqrt(3)/2

   % Compression for bars
   C_0 := l*T_v_0

   % normalizatin factor
   n := sqrt(3*(T_v_0^2*V^2+B^2+C_0^2))

   % Tension for cables
   T_v := P*T_v_0*V/n
   T_b := P*B/n
   C   := P*C_0/n
   
   % print T_v
   % print T_b
   % print C
   
   % stiffness as defined in the paper
   K_v_0 := 50
   K_b_0 := 10
   
   % The rest lengths for the different cables
   R_v := K_v_0*V/(T_v+K_v_0)
   R_b := K_b_0*B/(T_b+K_b_0)

   % The stiffness as in appears in our models
   K_v := K_v_0 / R_v
   K_b := K_b_0 / R_b

   % print K_v
   % print K_b
   % print R_v
   % print R_b

   % Margin. Used to increase the force, length, rest-length
   % from those in the initial configuration.
   % By using a large margins we ensure that the motion of
   % the structure is not hindered by theses limits, i.e.,
   % these limits will neve be active but the minimum
   % limit might be (cables must have at least 0 tension, etc).
   M := 20

   % Factor used to determine the minimum cable length. This
   % must be 0 or larger (we used 0.1 sometimes)
   ml := 0
   
   % Force range for struts
   min_fs :=-M*C
   max_fs :=  0

   % data for vertical cables 
   min_lc_v := ml*V
   max_lc_v := M*V
   min_r_v := 0
   max_r_v := M*R_v

   % data for top cables 
   min_lc_b := ml*B
   max_lc_b := M*B
   min_r_b := 0
   max_r_b := M*R_b
   
[STRUCTURE]

  strut s1 : n1 n2
             length l
             force [min_fs,max_fs]
             radius rs
          
  strut s2 : n3 n4
             length l
             force [min_fs,max_fs]
             radius rs
          
  strut s3 : n5 n6
             length l
             force [min_fs,max_fs]
             radius rs

  cable c1 : n1 n4                          % vertical
             length [min_lc_v,max_lc_v]
             stiffness K_v
             rest [min_r_v,max_r_v]
             radius rc

  cable c2 : n3 n6                          % vertical
             length [min_lc_v,max_lc_v]
             stiffness K_v
             rest [min_r_v,max_r_v]
             radius rc
              
  cable c3 : n5 n2                          % vertical
             length [min_lc_v,max_lc_v]
             stiffness K_v
             rest [min_r_v,max_r_v]
             radius rc

  cable c4 : n2 n4                          % platform
             length [min_lc_b,max_lc_b]
             stiffness K_b
             rest [min_r_b,max_r_b]
             radius rc

  cable c5 : n4 n6                          % platform
             length [min_lc_b,max_lc_b]
             stiffness K_b
             rest [min_r_b,max_r_b]
             radius rc
              
  cable c6 : n2 n6                          % platform
             length [min_lc_b,max_lc_b]
             stiffness K_b
             rest [min_r_b,max_r_b]
             radius rc
[COUPLE]
  % The orientation of the struts is related by a constant rotation
  % The force supported by the struts is all the same
  orientation: s1,[Rz(2*PI/3)]s2,[Rz(4*PI/3)]s3
  force      : s1,s2,s3
  
  % couple vertical cables: all have the same length, rest length, and
  % exerted tension
  length : c1,c2,c3
  rest   : c1,c2,c3
  force  : c1,c2,c3

  % couple platform cables: all have the same length, rest length, and
  % exerted tension
  length : c4,c5,c6
  rest   : c4,c5,c6
  force  : c4,c5,c6
  
[FIXED POINTS]
  % Fix the position of the bottom nodes
  n1(x)=0
  n1(y)=0
  n1(z)=0
  
  n3(x)=b*cos(pi/3)
  n3(y)=b*sin(pi/3)
  n3(z)=0
  
  n5(x)=b
  n5(y)=0
  n5(z)=0

[FORCES]
  % No force equilibrium in bottom nodes
  No null force : n1,n3,n5

[OBSTACLES]
  plane: box (-2,-2,-0.1)+(b+4,b*sin(pi/3)+4,0.05) green
  b1: sphere rs (0,0,-0.05) red
  b2: sphere rs (b*cos(pi/3),b*sin(pi/3),-0.05) red
  b3: sphere rs (b,0,-0.05) red

[COLLISIONS]
  do not check : all
  check : s1,s2
  check : s2,s3
  check : s1,s3