Пример #1
0
// adds -R to global residual vector fb
func (o Beam) AddToRhs(fb []float64, sol *Solution) (ok bool) {

	// node displacements
	for i, I := range o.Umap {
		o.ue[i] = sol.Y[I]
	}

	// steady/dynamics
	if Global.Sim.Data.Steady {
		la.MatVecMul(o.fi, 1, o.K, o.ue)
	} else {
		dc := Global.DynCoefs
		for i := 0; i < o.Nu; i++ {
			o.fi[i] = 0
			for j := 0; j < o.Nu; j++ {
				o.fi[i] += o.M[i][j]*(dc.α1*o.ue[j]-o.ζe[j]) + o.K[i][j]*o.ue[j]
			}
		}
	}

	// distributed loads
	if o.Hasq {
		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)
		qnL := o.QnL.F(sol.T, nil)
		qnR := o.QnR.F(sol.T, nil)
		qt := o.Qt.F(sol.T, nil)
		o.fxl[0] = qt * l / 2.0
		o.fxl[1] = l * (7.0*qnL + 3.0*qnR) / 20.0
		o.fxl[2] = l * l * (3.0*qnL + 2.0*qnR) / 60.0
		o.fxl[3] = qt * l / 2.0
		o.fxl[4] = l * (3.0*qnL + 7.0*qnR) / 20.0
		o.fxl[5] = -l * l * (2.0*qnL + 3.0*qnR) / 60.0
		la.MatTrVecMulAdd(o.fi, -1.0, o.T, o.fxl) // Rus -= fx; fx = trans(T) * fxl
	}

	// add to fb
	for i, I := range o.Umap {
		fb[I] -= o.fi[i]
	}
	return true
}
Пример #2
0
// adds -R to global residual vector fb
func (o *Beam) AddToRhs(fb []float64, sol *Solution) (err error) {

	// node displacements
	for i, I := range o.Umap {
		o.ue[i] = sol.Y[I]
	}

	// steady/dynamics
	if sol.Steady {
		la.MatVecMul(o.fi, 1, o.K, o.ue)
	} else {
		α1 := sol.DynCfs.α1
		for i := 0; i < o.Nu; i++ {
			o.fi[i] = 0
			for j := 0; j < o.Nu; j++ {
				o.fi[i] += o.M[i][j]*(α1*o.ue[j]-o.ζe[j]) + o.K[i][j]*o.ue[j]
			}
		}
	}

	// distributed loads
	if o.Hasq {
		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)
		qnL, qnR, qt := o.calc_loads(sol.T)
		o.fxl[0] = qt * l / 2.0
		o.fxl[1] = l * (7.0*qnL + 3.0*qnR) / 20.0
		o.fxl[2] = l * l * (3.0*qnL + 2.0*qnR) / 60.0
		o.fxl[3] = qt * l / 2.0
		o.fxl[4] = l * (3.0*qnL + 7.0*qnR) / 20.0
		o.fxl[5] = -l * l * (2.0*qnL + 3.0*qnR) / 60.0
		la.MatTrVecMulAdd(o.fi, -1.0, o.T, o.fxl) // Rus -= fx; fx = trans(T) * fxl
	}

	// add to fb
	for i, I := range o.Umap {
		fb[I] -= o.fi[i]
	}
	return
}
Пример #3
0
// AddToRhs adds -R to global residual vector fb
func (o *ElemU) AddToRhs(fb []float64, sol *Solution) (ok bool) {

	// clear fi vector if using B matrix
	if o.UseB {
		la.VecFill(o.fi, 0)
	}

	// for each integration point
	dc := Global.DynCoefs
	ndim := Global.Ndim
	nverts := o.Shp.Nverts
	for idx, ip := range o.IpsElem {

		// interpolation functions, gradients and variables @ ip
		if !o.ipvars(idx, sol) {
			return
		}

		// auxiliary
		coef := o.Shp.J * ip.W * o.Thickness
		S := o.Shp.S
		G := o.Shp.G

		// add internal forces to fb
		if o.UseB {
			radius := 1.0
			if Global.Sim.Data.Axisym {
				radius = o.Shp.AxisymGetRadius(o.X)
				coef *= radius
			}
			IpBmatrix(o.B, ndim, nverts, G, radius, S)
			la.MatTrVecMulAdd(o.fi, coef, o.B, o.States[idx].Sig) // fi += coef * tr(B) * σ
		} else {
			for m := 0; m < nverts; m++ {
				for i := 0; i < ndim; i++ {
					r := o.Umap[i+m*ndim]
					for j := 0; j < ndim; j++ {
						fb[r] -= coef * tsr.M2T(o.States[idx].Sig, i, j) * G[m][j] // -fi
					}
				}
			}
		}

		// dynamic term
		if !Global.Sim.Data.Steady {
			for m := 0; m < nverts; m++ {
				for i := 0; i < ndim; i++ {
					r := o.Umap[i+m*ndim]
					fb[r] -= coef * S[m] * (o.Rho*(dc.α1*o.us[i]-o.ζs[idx][i]-o.grav[i]) + o.Cdam*(dc.α4*o.us[i]-o.χs[idx][i])) // -RuBar
				}
			}
		}
	}

	// assemble fb if using B matrix
	if o.UseB {
		for i, I := range o.Umap {
			fb[I] -= o.fi[i]
		}
	}

	// external forces
	return o.add_surfloads_to_rhs(fb, sol)
}
Пример #4
0
// adds -R to global residual vector fb
func (o ElemUP) AddToRhs(fb []float64, sol *Solution) (ok bool) {

	// clear variables
	if o.P.DoExtrap {
		la.VecFill(o.P.ρl_ex, 0)
	}
	if o.U.UseB {
		la.VecFill(o.U.fi, 0)
	}

	// for each integration point
	dc := Global.DynCoefs
	ndim := Global.Ndim
	u_nverts := o.U.Shp.Nverts
	p_nverts := o.P.Shp.Nverts
	var coef, plt, klr, ρl, ρ, p, Cpl, Cvs, divvs float64
	var r int
	for idx, ip := range o.U.IpsElem {

		// interpolation functions, gradients and variables @ ip
		if !o.ipvars(idx, sol) {
			return
		}
		coef = o.U.Shp.J * ip.W
		S := o.U.Shp.S
		G := o.U.Shp.G
		Sb := o.P.Shp.S
		Gb := o.P.Shp.G

		// axisymmetric case
		radius := 1.0
		if Global.Sim.Data.Axisym {
			radius = o.U.Shp.AxisymGetRadius(o.U.X)
			coef *= radius
		}

		// auxiliary
		σe := o.U.States[idx].Sig
		divvs = dc.α4*o.divus - o.U.divχs[idx] // divergence of Eq. (35a) [1]

		// tpm variables
		plt = dc.β1*o.P.pl - o.P.ψl[idx] // Eq. (35c) [1]
		klr = o.P.Mdl.Cnd.Klr(o.P.States[idx].A_sl)
		if LogErr(o.P.Mdl.CalcLs(o.P.res, o.P.States[idx], o.P.pl, o.divus, false), "AddToRhs") {
			return
		}
		ρl = o.P.res.A_ρl
		ρ = o.P.res.A_ρ
		p = o.P.res.A_p
		Cpl = o.P.res.Cpl
		Cvs = o.P.res.Cvs

		// compute ρwl. see Eq (34b) and (35) of [1]
		for i := 0; i < ndim; i++ {
			o.P.ρwl[i] = 0
			for j := 0; j < ndim; j++ {
				o.P.ρwl[i] += klr * o.P.Mdl.Klsat[i][j] * o.hl[j]
			}
		}

		// p: add negative of residual term to fb; see Eqs. (38a) and (45a) of [1]
		for m := 0; m < p_nverts; m++ {
			r = o.P.Pmap[m]
			fb[r] -= coef * Sb[m] * (Cpl*plt + Cvs*divvs)
			for i := 0; i < ndim; i++ {
				fb[r] += coef * Gb[m][i] * o.P.ρwl[i] // += coef * div(ρl*wl)
			}
			if o.P.DoExtrap { // Eq. (19) of [2]
				o.P.ρl_ex[m] += o.P.Emat[m][idx] * ρl
			}
		}

		// u: add negative of residual term to fb; see Eqs. (38b) and (45b) [1]
		if o.U.UseB {
			IpBmatrix(o.U.B, ndim, u_nverts, G, radius, S)
			la.MatTrVecMulAdd(o.U.fi, coef, o.U.B, σe) // fi += coef * tr(B) * σ
			for m := 0; m < u_nverts; m++ {
				for i := 0; i < ndim; i++ {
					r = o.U.Umap[i+m*ndim]
					fb[r] -= coef * S[m] * ρ * o.bs[i]
					fb[r] += coef * p * G[m][i]
				}
			}
		} else {
			for m := 0; m < u_nverts; m++ {
				for i := 0; i < ndim; i++ {
					r = o.U.Umap[i+m*ndim]
					fb[r] -= coef * S[m] * ρ * o.bs[i]
					for j := 0; j < ndim; j++ {
						fb[r] -= coef * tsr.M2T(σe, i, j) * G[m][j]
					}
					fb[r] += coef * p * G[m][i]
				}
			}
		}
	}

	// add fi term to fb, if using B matrix
	if o.U.UseB {
		for i, I := range o.U.Umap {
			fb[I] -= o.U.fi[i]
		}
	}

	// external forces
	if len(o.U.NatBcs) > 0 {
		if !o.U.add_surfloads_to_rhs(fb, sol) {
			return
		}
	}

	// contribution from natural boundary conditions
	if len(o.P.NatBcs) > 0 {
		return o.P.add_natbcs_to_rhs(fb, sol)
	}
	return true
}
Пример #5
0
// AddToRhs adds -R to global residual vector fb
func (o *ElemU) AddToRhs(fb []float64, sol *Solution) (err error) {

	// clear fi vector if using B matrix
	if o.UseB {
		la.VecFill(o.fi, 0)
	}

	// for each integration point
	nverts := o.Cell.Shp.Nverts
	for idx, ip := range o.IpsElem {

		// interpolation functions, gradients and variables @ ip
		err = o.ipvars(idx, sol)
		if err != nil {
			return
		}

		// auxiliary
		coef := o.Cell.Shp.J * ip[3] * o.Thickness
		S := o.Cell.Shp.S
		G := o.Cell.Shp.G

		// add internal forces to fb
		if o.UseB {
			radius := 1.0
			if sol.Axisym {
				radius = o.Cell.Shp.AxisymGetRadius(o.X)
				coef *= radius
			}
			IpBmatrix(o.B, o.Ndim, nverts, G, radius, S, sol.Axisym)
			la.MatTrVecMulAdd(o.fi, coef, o.B, o.States[idx].Sig) // fi += coef * tr(B) * σ
		} else {
			for m := 0; m < nverts; m++ {
				for i := 0; i < o.Ndim; i++ {
					r := o.Umap[i+m*o.Ndim]
					for j := 0; j < o.Ndim; j++ {
						fb[r] -= coef * tsr.M2T(o.States[idx].Sig, i, j) * G[m][j] // -fi
					}
				}
			}
		}

		// dynamic term
		if !sol.Steady {
			α1 := sol.DynCfs.α1
			α4 := sol.DynCfs.α4
			for m := 0; m < nverts; m++ {
				for i := 0; i < o.Ndim; i++ {
					r := o.Umap[i+m*o.Ndim]
					fb[r] -= coef * S[m] * (o.Rho*(α1*o.us[i]-o.ζs[idx][i]-o.grav[i]) + o.Cdam*(α4*o.us[i]-o.χs[idx][i])) // -RuBar
				}
			}
		}
	}

	// assemble fb if using B matrix
	if o.UseB {
		for i, I := range o.Umap {
			fb[I] -= o.fi[i]
		}
	}

	// external forces
	err = o.add_surfloads_to_rhs(fb, sol)
	if err != nil {
		return
	}

	// contact: additional term to fb
	err = o.contact_add_to_rhs(fb, sol)

	// xfem: additional term to fb
	err = o.xfem_add_to_rhs(fb, sol)
	return
}