Elements

The examples below reuse steel, wshape (a frame section), and bar (an axial-only section) from Materials and sections.

Frame elements

3D Euler-Bernoulli beam-columns carrying axial force, biaxial bending, shear, and torsion. rollangle is the section roll angle about the member axis (default π/2).

na = Node([0.0, 0.0, 0.0], :fixed)
nb = Node([4.0, 0.0, 0.0], :free)

girder = FrameElement(na, nb, wshape, :girder)
rolled = FrameElement(na, nb, wshape; rollangle = 0.0)
girder

FrameElement :girder
  from [0.0, 0.0, 0.0] to [4.0, 0.0, 0.0]
  length = 4.0  [length]
  rollangle = 1.5707963267948966  [rad]  (section roll about the element axis)
  connections :fixedfixed
  section rigidities:
    EA  = 2.0e6, EIx = 16000.000000000002,
    EIy = 6000.0, GJ = 38.5

End releases and semi-rigid connections

Connections are end springs in the element's local axes. The classical releases are exact limits (Inf = rigid, 0 = released), and any finite value is a semi-rigid connection:

hinged = FrameElement(na, nb, wshape; release = :fixedfree)   # hinge at far end
# available: :fixedfixed (default), :fixedfree, :freefixed, :freefree, :joist

# semi-rigid: e.g. a bolted end plate with finite rotational stiffness
semi = FrameElement(na, nb, wshape,
    EndConditions(EndSprings(Inf, Inf, 5e4, 5e4), rigid_end()), :connection)

FrameElement :connection
  from [0.0, 0.0, 0.0] to [4.0, 0.0, 0.0]
  length = 4.0  [length]
  rollangle = 1.5707963267948966  [rad]  (section roll about the element axis)
  semi-rigid connections
  section rigidities:
    EA  = 2.0e6, EIx = 16000.000000000002,
    EIy = 6000.0, GJ = 38.5

Connection stiffness is ordinary data — it can be a design variable in gradient-based optimization, and everything downstream (fixed-end forces, force recovery) handles it with no special cases.

Truss elements — and mixing them with frames

Axial-only two-force members. They coexist freely with frame elements in one model; a truss element simply never touches rotational DOFs:

n1 = Node([0.0, 0.0, 0.0], :fixed)
n2 = Node([3.0, 0.0, 0.0], :free)
n3 = Node([3.0, 0.0, 3.0], :fixed)                # an anchor above

beam = FrameElement(n1, n2, wshape, :beam)
tie  = TrussElement(n2, n3, bar, :tie)

model = Model([n1, n2, n3],
    AbstractElement{Float64}[beam, tie],          # mixed vector: type it explicitly
    AbstractLoad{Float64}[NodeForce(n2, [0.0, 0.0, -100.0])])
solve!(model)
axial_force(model.results, tie)                   # tension-positive

99.46949602122015

Variable elements (varying cross-section)

One user-facing member whose section varies along its length as a chain of prismatic segments — for haunched girders, stepped columns, or optimization results. Interior joints become internal DOFs: the model is never mutated, no phantom nodes appear, and you query the member as a single piece:

deep    = Section(steel, 2e-2, 4e-4, 1e-4, 2e-6)
mid     = Section(steel, 1.5e-2, 2e-4, 6e-5, 1e-6)
shallow = wshape

v1 = Node([0.0, 0.0, 0.0], :fixed)
v2 = Node([8.0, 0.0, 0.0], :free)
haunched = VariableElement(v1, v2,
    AbstractSection{Float64}[deep, mid, shallow],   # one section per segment
    [0.25, 0.6])                                    # interior break fractions

vmodel = Model([v1, v2], AbstractElement{Float64}[haunched],
    AbstractLoad{Float64}[LineLoad(haunched, [0.0, 0.0, -2.0])])
solve!(vmodel)
moment_z(vmodel, haunched, 0.5)                 # resolves to the right segment

-15.999999999999908

element_forces(vmodel.results, haunched, 2)     # or reach a specific segment

12-element Vector{Float64}:
   0.0
  11.999999999999993
   7.347880794884084e-16
   0.0
  -2.204364238465206e-15
  35.99999999999989
   0.0
  -6.399999999999993
  -3.918869757271496e-16
   0.0
   6.27019161163433e-16
 -10.239999999999949

SelfWeight on a VariableElement automatically varies with each segment's ρA:

push!(vmodel.loads, SelfWeight(haunched; g = [0.0, 0.0, -9.81]))
solve!(vmodel)
moment_z(vmodel, haunched, 0.5)

-22.403967999999885