// 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)
}
// Update perform (tangent) update
func (o *Rjoint) Update(sol *Solution) (err error) {
// auxiliary
nsig := 2 * o.Ndim
rodH := o.Rod.Cell.Shp
rodS := rodH.S
rodNn := rodH.Nverts
sldH := o.Sld.Cell.Shp
sldNn := sldH.Nverts
// extrapolate stresses at integration points of solid element to its nodes
if o.Coulomb {
la.MatFill(o.σNo, 0)
for idx, _ := range o.Sld.IpsElem {
σ := o.Sld.States[idx].Sig
for i := 0; i < nsig; i++ {
for m := 0; m < sldNn; m++ {
o.σNo[m][i] += o.Emat[m][idx] * σ[i]
}
}
}
}
// interpolate Δu of solid to find ΔuC @ rod node; Eq (30)
var r, I int
for m := 0; m < rodNn; m++ {
for i := 0; i < o.Ndim; i++ {
o.ΔuC[m][i] = 0
for n := 0; n < sldNn; n++ {
r = i + n*o.Ndim
I = o.Sld.Umap[r]
o.ΔuC[m][i] += o.Nmat[n][m] * sol.ΔY[I] // Eq (30)
}
}
}
// loop over ips of rod
var Δwb0, Δwb1, Δwb2, σc float64
for idx, ip := range o.Rod.IpsElem {
// auxiliary
e0, e1, e2 := o.e0[idx], o.e1[idx], o.e2[idx]
// interpolation functions and gradients
err = rodH.CalcAtIp(o.Rod.X, ip, true)
if err != nil {
return
}
// interpolated relative displacements @ ip of join; Eqs (31) and (32)
for i := 0; i < o.Ndim; i++ {
o.Δw[i] = 0
for m := 0; m < rodNn; m++ {
r = i + m*o.Ndim
I = o.Rod.Umap[r]
o.Δw[i] += rodS[m] * (o.ΔuC[m][i] - sol.ΔY[I]) // Eq (31) and (32)
}
}
// relative displacents in the coratational system
Δwb0, Δwb1, Δwb2 = 0, 0, 0
for i := 0; i < o.Ndim; i++ {
Δwb0 += e0[i] * o.Δw[i]
Δwb1 += e1[i] * o.Δw[i]
Δwb2 += e2[i] * o.Δw[i]
}
// new confining stress
σc = 0.0
if o.Coulomb {
// calculate σIp
for j := 0; j < nsig; j++ {
o.σIp[j] = 0
for n := 0; n < sldNn; n++ {
o.σIp[j] += o.Pmat[n][idx] * o.σNo[n][j]
}
}
// calculate t1 and t2
for i := 0; i < o.Ndim; i++ {
o.t1[i], o.t2[i] = 0, 0
for j := 0; j < o.Ndim; j++ {
o.t1[i] += tsr.M2T(o.σIp, i, j) * e1[j]
o.t2[i] += tsr.M2T(o.σIp, i, j) * e2[j]
}
}
// calculate p1, p2 and σcNew
p1, p2 := 0.0, 0.0
for i := 0; i < o.Ndim; i++ {
p1 += o.t1[i] * e1[i]
p2 += o.t2[i] * e2[i]
}
// σcNew
σc = -(p1 + p2) / 2.0
}
// update model
err = o.Mdl.Update(o.States[idx], σc, Δwb0)
if err != nil {
return
}
o.States[idx].Phi[0] += o.k1 * Δwb1 // qn1
o.States[idx].Phi[1] += o.k2 * Δwb2 // qn2
// debugging
//if true {
if false {
o.debug_update(idx, Δwb0, Δwb1, Δwb2, σc)
}
}
return
}
// 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
}