About

To find the shape/form of a highly geometry-nonlinear structure.

pip install TwoD-Form-Finding

Checklist

Before init a new model from SAP2000...

• Constrains must be pinned, i.e. Ux, Uy, Uz fixed ONLY
• If using special groups for different properties, make sure the group name has been assigned to target frames.
• If doing form-finding based on self-weight, iteration is needed, and mass source shall be defined in SAP2000. See eg double oval form found by dead

Get Started

1. Initiate an MxN 2d web model

Open this file and start to rock!!!
eg_2d-pretensioned-net

• Initiate an instance
  aaa = TwoDShapeFinding(m, n, 2)
  • m is the node number in X dir.
  • n is the node number in Y dir.
  • "2" means node distance is 2.
    > The unit sys is KN.m.C
• Set constrains
  aaa.set_fix(*constrain)
  • "constrains" is a list of column and row numbers, e.g.
    [[0, 0], [2, 4],...]
  • To add additional constrains
    aaa.set_fix([20, 20], [10, 10]) # optional for additional constrains
• Set joint loads
  aaa.set_init_F(*loading)
  • "loading" is a list of column, row and joint force, e.g.
    [[1, 1, 1], [5, 6, 10],...]
  • Joint loads are considered positive in the gravity direction.
  • One can just set initial loads of all 0 by
    aaa.set_init_F()
• Set boundary conditions
  aaa.set_init_z(*boundary_z)
  • "boundary_z" means to define initial z coords for every point.
  • One can just set initial Z coords of all 0 by
    aaa.set_init_z()
  • If you need some points having different z coords, just insert
    aaa.set_init_z([0, 0, 0], [2, 4, 1]) # optional for additional z coords
    > It's meaningless to assign initial z coords to joints not constrained...
• Set connections
  aaa.set_connectivities()
  • This must be done.
• Set frame force densities
  aaa.set_force_density(10000)
  • "10000" is to set all frames force densities of 10000 kN/m
  • When it's positive, means the frame is in tension.
  • For special values, just use
    aaa.set_force_density(default_rou, [frameID1, rou1], [frameID2, rou2], ..)
• Run
  aaa.force_density("g", True, "China", "JTG", "JTGD62 fpk1470", 7, 0.06)
  • 1st argument, what's to return.
    • "g" means to return a Matplotlib graph.
    • "w" returns all coords after form-finding instead.
  • 2nd argument, to bake to SAP2000
    • True means to return a SAP2000 model.
      > SAP2000 must be opened first.
      > The rest parameters are for frame properties in SAP2000.
    • If it is False, no material properties needed.
      aaa.force_density("g", False)

2. Initate a model from SAP2000

Notes
a), To start, copy an example SAP2000 model from here and the relative py.
b), All nodes and frame elements will be used in form finding.
c), The model unit MUST be KN.m.C.

1. Open the model in SAP2000
2. In Python
   • Initiate the instance
     a = TwoDShapeFinding(1, 3, 1, init_fr_sap=True)

     The first 3 arguments here is not functional.

   • Read data from the SAP2000 model
     a.init_fr_sap2000("Pre_loading", "China", "JTG", "JTGD62 fpk1470", 7, 0.3, 2000)
     • 1st argument, a pre-defined load pattern in SAP2000.

       Only point loads are allowed, nevertheless the pattern name can be anything. See bullet point 3 if you want to do form-finding under self-weight.

     • 2nd to 5th arguments, SAP2000 material library parameters.

       Refer to SAP2000 OAPI manual SapModel.PropMaterial.SetMaterial part.

     • 6th arguments, section diameter of the frame object.

       Use a circular rod to simulate everything for now...

     • 7th argument, the frame force density.
       • Since SAP2000 is involved, material properties thus are mandatory.
       • By using group definition in SAP2000, different materials/force densities are supported. Put group name and other special material properties in a [] and adding it after the default args.
         a.init_fr_sap2000("Pre_loading","China", "JTG", "JTGD62 fpk1470", 7, 0.3, 2000, ["group_name", "China", "JTG", "JTGD62 fpk1470", 7, 0.3, 1500],...)

         You can define as many group as you want, however using conceptional design and only add extra groups when necessary.

   • Run ll1 = a.force_density("w", False, tolerance=1e-9, remove=False)
     • The first 2 arguments is not functional.
     • If remove=False, tolerance can actually be larger, like 1e-4.

       The idea behind "remove" is a joint only affects joints nearby. If the location between the current iterative step and the previous step is less than the tolerance, then this joint can be removed from the next step. It can improve the speed but needs carefully reviewing the form found.

     • FYI, this method can return frame lengths.
3. If you want to do form-finding under structure self-weight,
   • just replace "Pre_loading" by mass_assign(a.SapModel, "Pre_loading").