// register element
func init() {
// information allocator
infogetters["beam"] = func(cellType string, faceConds []*FaceCond) *Info {
// new info
var info Info
// solution variables
ykeys := []string{"ux", "uy", "rz"}
if Global.Ndim == 3 {
ykeys = []string{"ux", "uy", "uz", "rx", "ry", "rz"}
}
info.Dofs = make([][]string, 2)
for m := 0; m < 2; m++ {
info.Dofs[m] = ykeys
}
// maps
info.Y2F = map[string]string{"ux": "fx", "uy": "fy", "uz": "fz", "rx": "mx", "ry": "my", "rz": "mz"}
// t1 and t2 variables
info.T2vars = ykeys
return &info
}
// element allocator
eallocators["beam"] = func(cellType string, faceConds []*FaceCond, cid int, edat *inp.ElemData, x [][]float64) Elem {
// check
if LogErrCond(Global.Ndim == 3, "beam is not implemented for 3D yet") {
return nil
}
// basic data
var o Beam
o.Cid = cid
o.X = x
ndim := Global.Ndim
ndof := 3 * (ndim - 1)
o.Nu = ndof * ndim
// parameters
matname := edat.Mat
matdata := Global.Sim.Mdb.Get(edat.Mat)
if LogErrCond(matdata == nil, "materials database failed on getting %q material\n", matname) {
return nil
}
for _, p := range matdata.Prms {
switch p.N {
case "E":
o.E = p.V
case "A":
o.A = p.V
case "Izz":
o.Izz = p.V
case "rho":
o.Rho = p.V
}
}
// vectors and matrices
o.T = la.MatAlloc(o.Nu, o.Nu)
o.Kl = la.MatAlloc(o.Nu, o.Nu)
o.K = la.MatAlloc(o.Nu, o.Nu)
o.Ml = la.MatAlloc(o.Nu, o.Nu)
o.M = la.MatAlloc(o.Nu, o.Nu)
o.ue = make([]float64, o.Nu)
o.ζe = make([]float64, o.Nu)
o.fxl = make([]float64, o.Nu)
o.Rus = make([]float64, o.Nu)
// T
dx := o.X[0][1] - o.X[0][0]
dy := o.X[1][1] - o.X[1][0]
l := math.Sqrt(dx*dx + dy*dy)
c := dx / l
s := dy / l
o.T[0][0] = c
o.T[0][1] = s
o.T[1][0] = -s
o.T[1][1] = c
o.T[2][2] = 1
o.T[3][3] = c
o.T[3][4] = s
o.T[4][3] = -s
o.T[4][4] = c
o.T[5][5] = 1
// aux vars
ll := l * l
m := o.E * o.A / l
n := o.E * o.Izz / (ll * l)
// K
o.Kl[0][0] = m
o.Kl[0][3] = -m
o.Kl[1][1] = 12 * n
o.Kl[1][2] = 6 * l * n
o.Kl[1][4] = -12 * n
o.Kl[1][5] = 6 * l * n
o.Kl[2][1] = 6 * l * n
o.Kl[2][2] = 4 * ll * n
o.Kl[2][4] = -6 * l * n
o.Kl[2][5] = 2 * ll * n
o.Kl[3][0] = -m
o.Kl[3][3] = m
o.Kl[4][1] = -12 * n
o.Kl[4][2] = -6 * l * n
o.Kl[4][4] = 12 * n
o.Kl[4][5] = -6 * l * n
o.Kl[5][1] = 6 * l * n
o.Kl[5][2] = 2 * ll * n
o.Kl[5][4] = -6 * l * n
o.Kl[5][5] = 4 * ll * n
la.MatTrMul3(o.K, 1, o.T, o.Kl, o.T) // K := 1 * trans(T) * Kl * T
// M
m = o.Rho * o.A * l / 420.0
o.Ml[0][0] = 140.0 * m
o.Ml[0][3] = 70.0 * m
o.Ml[1][1] = 156.0 * m
o.Ml[1][2] = 22.0 * l * m
o.Ml[1][4] = 54.0 * m
o.Ml[1][5] = -13.0 * l * m
o.Ml[2][1] = 22.0 * l * m
o.Ml[2][2] = 4.0 * ll * m
o.Ml[2][4] = 13.0 * l * m
o.Ml[2][5] = -3.0 * ll * m
o.Ml[3][0] = 70.0 * m
o.Ml[3][3] = 140.0 * m
o.Ml[4][1] = 54.0 * m
o.Ml[4][2] = 13.0 * l * m
o.Ml[4][4] = 156.0 * m
o.Ml[4][5] = -22.0 * l * m
o.Ml[5][1] = -13.0 * l * m
o.Ml[5][2] = -3.0 * ll * m
o.Ml[5][4] = -22.0 * l * m
o.Ml[5][5] = 4.0 * ll * m
la.MatTrMul3(o.M, 1, o.T, o.Ml, o.T) // M := 1 * trans(T) * Ml * T
// scratchpad. computed @ each ip
o.grav = make([]float64, Global.Ndim)
o.fi = make([]float64, o.Nu)
// return new element
return &o
}
}
// Recompute re-compute matrices after dimensions or parameters are externally changed
func (o *Beam) Recompute(withM bool) {
// T
dx := o.X[0][1] - o.X[0][0]
dy := o.X[1][1] - o.X[1][0]
l := math.Sqrt(dx*dx + dy*dy)
o.L = l
c := dx / l
s := dy / l
o.T[0][0] = c
o.T[0][1] = s
o.T[1][0] = -s
o.T[1][1] = c
o.T[2][2] = 1
o.T[3][3] = c
o.T[3][4] = s
o.T[4][3] = -s
o.T[4][4] = c
o.T[5][5] = 1
// aux vars
ll := l * l
m := o.E * o.A / l
n := o.E * o.Izz / (ll * l)
// K
o.Kl[0][0] = m
o.Kl[0][3] = -m
o.Kl[1][1] = 12 * n
o.Kl[1][2] = 6 * l * n
o.Kl[1][4] = -12 * n
o.Kl[1][5] = 6 * l * n
o.Kl[2][1] = 6 * l * n
o.Kl[2][2] = 4 * ll * n
o.Kl[2][4] = -6 * l * n
o.Kl[2][5] = 2 * ll * n
o.Kl[3][0] = -m
o.Kl[3][3] = m
o.Kl[4][1] = -12 * n
o.Kl[4][2] = -6 * l * n
o.Kl[4][4] = 12 * n
o.Kl[4][5] = -6 * l * n
o.Kl[5][1] = 6 * l * n
o.Kl[5][2] = 2 * ll * n
o.Kl[5][4] = -6 * l * n
o.Kl[5][5] = 4 * ll * n
la.MatTrMul3(o.K, 1, o.T, o.Kl, o.T) // K := 1 * trans(T) * Kl * T
// M
if withM {
m = o.Rho * o.A * l / 420.0
o.Ml[0][0] = 140.0 * m
o.Ml[0][3] = 70.0 * m
o.Ml[1][1] = 156.0 * m
o.Ml[1][2] = 22.0 * l * m
o.Ml[1][4] = 54.0 * m
o.Ml[1][5] = -13.0 * l * m
o.Ml[2][1] = 22.0 * l * m
o.Ml[2][2] = 4.0 * ll * m
o.Ml[2][4] = 13.0 * l * m
o.Ml[2][5] = -3.0 * ll * m
o.Ml[3][0] = 70.0 * m
o.Ml[3][3] = 140.0 * m
o.Ml[4][1] = 54.0 * m
o.Ml[4][2] = 13.0 * l * m
o.Ml[4][4] = 156.0 * m
o.Ml[4][5] = -22.0 * l * m
o.Ml[5][1] = -13.0 * l * m
o.Ml[5][2] = -3.0 * ll * m
o.Ml[5][4] = -22.0 * l * m
o.Ml[5][5] = 4.0 * ll * m
la.MatTrMul3(o.M, 1, o.T, o.Ml, o.T) // M := 1 * trans(T) * Ml * T
}
}