// 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
}
// 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
}
// 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)
}
// 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
}
// 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
}