Exemplo n.º 1
0
// 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
	}
}
Exemplo n.º 2
0
// 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
	}
}