forked from mallano/gofem
/
auxsolid.go
232 lines (218 loc) · 9.51 KB
/
auxsolid.go
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// Copyright 2015 Dorival Pedroso and Raul Durand. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be fndim in the LICENSE file.
package fem
import (
"math"
"github.com/cpmech/gosl/la"
"github.com/cpmech/gosl/tsr"
)
const SQ2 = math.Sqrt2
func IpAddToKt(Kt [][]float64, nne, ndim int, coef float64, G, D [][]float64) {
if ndim == 3 {
for m := 0; m < nne; m++ {
for n := 0; n < nne; n++ {
Kt[0+m*3][0+n*3] += coef * (G[m][2]*G[n][2]*D[5][5] + G[m][2]*G[n][1]*D[5][3] + SQ2*G[m][2]*G[n][0]*D[5][0] + G[m][1]*G[n][2]*D[3][5] + G[m][1]*G[n][1]*D[3][3] + SQ2*G[m][1]*G[n][0]*D[3][0] + SQ2*G[m][0]*G[n][2]*D[0][5] + SQ2*G[m][0]*G[n][1]*D[0][3] + 2.0*G[m][0]*G[n][0]*D[0][0]) / 2.0
Kt[0+m*3][1+n*3] += coef * (G[m][2]*G[n][2]*D[5][4] + G[m][2]*G[n][0]*D[5][3] + SQ2*G[m][2]*G[n][1]*D[5][1] + G[m][1]*G[n][2]*D[3][4] + G[m][1]*G[n][0]*D[3][3] + SQ2*G[m][1]*G[n][1]*D[3][1] + SQ2*G[m][0]*G[n][2]*D[0][4] + SQ2*G[m][0]*G[n][0]*D[0][3] + 2.0*G[m][0]*G[n][1]*D[0][1]) / 2.0
Kt[0+m*3][2+n*3] += coef * (G[m][2]*G[n][0]*D[5][5] + G[m][2]*G[n][1]*D[5][4] + SQ2*G[m][2]*G[n][2]*D[5][2] + G[m][1]*G[n][0]*D[3][5] + G[m][1]*G[n][1]*D[3][4] + SQ2*G[m][1]*G[n][2]*D[3][2] + SQ2*G[m][0]*G[n][0]*D[0][5] + SQ2*G[m][0]*G[n][1]*D[0][4] + 2.0*G[m][0]*G[n][2]*D[0][2]) / 2.0
Kt[1+m*3][0+n*3] += coef * (G[m][2]*G[n][2]*D[4][5] + G[m][2]*G[n][1]*D[4][3] + SQ2*G[m][2]*G[n][0]*D[4][0] + G[m][0]*G[n][2]*D[3][5] + G[m][0]*G[n][1]*D[3][3] + SQ2*G[m][0]*G[n][0]*D[3][0] + SQ2*G[m][1]*G[n][2]*D[1][5] + SQ2*G[m][1]*G[n][1]*D[1][3] + 2.0*G[m][1]*G[n][0]*D[1][0]) / 2.0
Kt[1+m*3][1+n*3] += coef * (G[m][2]*G[n][2]*D[4][4] + G[m][2]*G[n][0]*D[4][3] + SQ2*G[m][2]*G[n][1]*D[4][1] + G[m][0]*G[n][2]*D[3][4] + G[m][0]*G[n][0]*D[3][3] + SQ2*G[m][0]*G[n][1]*D[3][1] + SQ2*G[m][1]*G[n][2]*D[1][4] + SQ2*G[m][1]*G[n][0]*D[1][3] + 2.0*G[m][1]*G[n][1]*D[1][1]) / 2.0
Kt[1+m*3][2+n*3] += coef * (G[m][2]*G[n][0]*D[4][5] + G[m][2]*G[n][1]*D[4][4] + SQ2*G[m][2]*G[n][2]*D[4][2] + G[m][0]*G[n][0]*D[3][5] + G[m][0]*G[n][1]*D[3][4] + SQ2*G[m][0]*G[n][2]*D[3][2] + SQ2*G[m][1]*G[n][0]*D[1][5] + SQ2*G[m][1]*G[n][1]*D[1][4] + 2.0*G[m][1]*G[n][2]*D[1][2]) / 2.0
Kt[2+m*3][0+n*3] += coef * (G[m][0]*G[n][2]*D[5][5] + G[m][0]*G[n][1]*D[5][3] + SQ2*G[m][0]*G[n][0]*D[5][0] + G[m][1]*G[n][2]*D[4][5] + G[m][1]*G[n][1]*D[4][3] + SQ2*G[m][1]*G[n][0]*D[4][0] + SQ2*G[m][2]*G[n][2]*D[2][5] + SQ2*G[m][2]*G[n][1]*D[2][3] + 2.0*G[m][2]*G[n][0]*D[2][0]) / 2.0
Kt[2+m*3][1+n*3] += coef * (G[m][0]*G[n][2]*D[5][4] + G[m][0]*G[n][0]*D[5][3] + SQ2*G[m][0]*G[n][1]*D[5][1] + G[m][1]*G[n][2]*D[4][4] + G[m][1]*G[n][0]*D[4][3] + SQ2*G[m][1]*G[n][1]*D[4][1] + SQ2*G[m][2]*G[n][2]*D[2][4] + SQ2*G[m][2]*G[n][0]*D[2][3] + 2.0*G[m][2]*G[n][1]*D[2][1]) / 2.0
Kt[2+m*3][2+n*3] += coef * (G[m][0]*G[n][0]*D[5][5] + G[m][0]*G[n][1]*D[5][4] + SQ2*G[m][0]*G[n][2]*D[5][2] + G[m][1]*G[n][0]*D[4][5] + G[m][1]*G[n][1]*D[4][4] + SQ2*G[m][1]*G[n][2]*D[4][2] + SQ2*G[m][2]*G[n][0]*D[2][5] + SQ2*G[m][2]*G[n][1]*D[2][4] + 2.0*G[m][2]*G[n][2]*D[2][2]) / 2.0
}
}
} else {
for m := 0; m < nne; m++ {
for n := 0; n < nne; n++ {
Kt[0+m*2][0+n*2] += coef * (G[m][1]*G[n][1]*D[3][3] + SQ2*G[m][1]*G[n][0]*D[3][0] + SQ2*G[m][0]*G[n][1]*D[0][3] + 2.0*G[m][0]*G[n][0]*D[0][0]) / 2.0
Kt[0+m*2][1+n*2] += coef * (G[m][1]*G[n][0]*D[3][3] + SQ2*G[m][1]*G[n][1]*D[3][1] + SQ2*G[m][0]*G[n][0]*D[0][3] + 2.0*G[m][0]*G[n][1]*D[0][1]) / 2.0
Kt[1+m*2][0+n*2] += coef * (G[m][0]*G[n][1]*D[3][3] + SQ2*G[m][0]*G[n][0]*D[3][0] + SQ2*G[m][1]*G[n][1]*D[1][3] + 2.0*G[m][1]*G[n][0]*D[1][0]) / 2.0
Kt[1+m*2][1+n*2] += coef * (G[m][0]*G[n][0]*D[3][3] + SQ2*G[m][0]*G[n][1]*D[3][1] + SQ2*G[m][1]*G[n][0]*D[1][3] + 2.0*G[m][1]*G[n][1]*D[1][1]) / 2.0
}
}
}
}
func IpStrains(εs []float64, nne, ndim int, u []float64, Umap []int, G [][]float64) {
var r, c int
var εsij float64
for i := 0; i < ndim; i++ {
for j := i; j < ndim; j++ { // note: j := i => only diagonal and above
εsij = 0
for m := 0; m < nne; m++ {
r, c = i+m*ndim, j+m*ndim
εsij += (u[Umap[r]]*G[m][j] + u[Umap[c]]*G[m][i]) / 2.0
}
if i != j {
εsij *= SQ2
}
εs[tsr.T2MI[i][j]] = εsij
}
}
}
func IpStrainsAndInc(εs, Δεs []float64, nne, ndim int, u, Δu []float64, Umap []int, G [][]float64) {
var r, c int
var εsij, Δεsij float64
for i := 0; i < ndim; i++ {
for j := i; j < ndim; j++ { // note: j := i => only diagonal and above
εsij, Δεsij = 0, 0
for m := 0; m < nne; m++ {
r, c = i+m*ndim, j+m*ndim
εsij += (u[Umap[r]]*G[m][j] + u[Umap[c]]*G[m][i]) / 2.0
Δεsij += (Δu[Umap[r]]*G[m][j] + Δu[Umap[c]]*G[m][i]) / 2.0
}
if i != j {
εsij *= SQ2
Δεsij *= SQ2
}
εs[tsr.T2MI[i][j]] = εsij
Δεs[tsr.T2MI[i][j]] = Δεsij
}
}
}
// DerivSig returns the derivative of σ (Mandel) with respect to displacement at nodes
// Note: DσDun = ∂σ/∂un [nσ][ndim]
func DerivSig(DσDun [][]float64, n, ndim int, G, D [][]float64) {
if ndim == 3 {
DσDun[0][0] = (G[n][2]*D[0][5]*SQ2 + G[n][1]*D[0][3]*SQ2 + 2.0*G[n][0]*D[0][0]) / 2.0
DσDun[0][1] = (G[n][2]*D[0][4]*SQ2 + G[n][0]*D[0][3]*SQ2 + 2.0*G[n][1]*D[0][1]) / 2.0
DσDun[0][2] = (G[n][0]*D[0][5]*SQ2 + G[n][1]*D[0][4]*SQ2 + 2.0*G[n][2]*D[0][2]) / 2.0
DσDun[1][0] = (G[n][2]*D[1][5]*SQ2 + G[n][1]*D[1][3]*SQ2 + 2.0*G[n][0]*D[1][0]) / 2.0
DσDun[1][1] = (G[n][2]*D[1][4]*SQ2 + G[n][0]*D[1][3]*SQ2 + 2.0*G[n][1]*D[1][1]) / 2.0
DσDun[1][2] = (G[n][0]*D[1][5]*SQ2 + G[n][1]*D[1][4]*SQ2 + 2.0*G[n][2]*D[1][2]) / 2.0
DσDun[2][0] = (G[n][2]*D[2][5]*SQ2 + G[n][1]*D[2][3]*SQ2 + 2.0*G[n][0]*D[2][0]) / 2.0
DσDun[2][1] = (G[n][2]*D[2][4]*SQ2 + G[n][0]*D[2][3]*SQ2 + 2.0*G[n][1]*D[2][1]) / 2.0
DσDun[2][2] = (G[n][0]*D[2][5]*SQ2 + G[n][1]*D[2][4]*SQ2 + 2.0*G[n][2]*D[2][2]) / 2.0
DσDun[3][0] = (G[n][0]*D[3][0]*SQ2 + G[n][2]*D[3][5] + G[n][1]*D[3][3]) / SQ2
DσDun[3][1] = (G[n][1]*D[3][1]*SQ2 + G[n][2]*D[3][4] + G[n][0]*D[3][3]) / SQ2
DσDun[3][2] = (G[n][2]*D[3][2]*SQ2 + G[n][0]*D[3][5] + G[n][1]*D[3][4]) / SQ2
DσDun[4][0] = (G[n][0]*D[4][0]*SQ2 + G[n][2]*D[4][5] + G[n][1]*D[4][3]) / SQ2
DσDun[4][1] = (G[n][1]*D[4][1]*SQ2 + G[n][2]*D[4][4] + G[n][0]*D[4][3]) / SQ2
DσDun[4][2] = (G[n][2]*D[4][2]*SQ2 + G[n][0]*D[4][5] + G[n][1]*D[4][4]) / SQ2
DσDun[5][0] = (G[n][0]*D[5][0]*SQ2 + G[n][2]*D[5][5] + G[n][1]*D[5][3]) / SQ2
DσDun[5][1] = (G[n][1]*D[5][1]*SQ2 + G[n][2]*D[5][4] + G[n][0]*D[5][3]) / SQ2
DσDun[5][2] = (G[n][2]*D[5][2]*SQ2 + G[n][0]*D[5][5] + G[n][1]*D[5][4]) / SQ2
} else {
DσDun[0][0] = (G[n][0]*D[0][0]*SQ2 + G[n][1]*D[0][3]) / SQ2
DσDun[0][1] = (G[n][1]*D[0][1]*SQ2 + G[n][0]*D[0][3]) / SQ2
DσDun[1][0] = (G[n][0]*D[1][0]*SQ2 + G[n][1]*D[1][3]) / SQ2
DσDun[1][1] = (G[n][1]*D[1][1]*SQ2 + G[n][0]*D[1][3]) / SQ2
DσDun[2][0] = (G[n][0]*D[2][0]*SQ2 + G[n][1]*D[2][3]) / SQ2
DσDun[2][1] = (G[n][1]*D[2][1]*SQ2 + G[n][0]*D[2][3]) / SQ2
DσDun[3][0] = (G[n][0]*D[3][0]*SQ2 + G[n][1]*D[3][3]) / SQ2
DσDun[3][1] = (G[n][1]*D[3][1]*SQ2 + G[n][0]*D[3][3]) / SQ2
}
}
func IpBmatrix(B [][]float64, ndim, nne int, G [][]float64, radius float64, S []float64) {
if ndim == 3 {
for i := 0; i < nne; i++ {
B[0][0+i*3] = G[i][0]
B[1][1+i*3] = G[i][1]
B[2][2+i*3] = G[i][2]
B[3][0+i*3] = G[i][1] / SQ2
B[4][1+i*3] = G[i][2] / SQ2
B[5][2+i*3] = G[i][0] / SQ2
B[3][1+i*3] = G[i][0] / SQ2
B[4][2+i*3] = G[i][1] / SQ2
B[5][0+i*3] = G[i][2] / SQ2
}
return
}
if Global.Sim.Data.Axisym {
for i := 0; i < nne; i++ {
B[0][0+i*2] = G[i][0]
B[1][1+i*2] = G[i][1]
B[2][0+i*2] = S[i] / radius
B[3][0+i*2] = G[i][1] / SQ2
B[3][1+i*2] = G[i][0] / SQ2
}
return
}
for i := 0; i < nne; i++ {
B[0][0+i*2] = G[i][0]
B[1][1+i*2] = G[i][1]
B[3][0+i*2] = G[i][1] / SQ2
B[3][1+i*2] = G[i][0] / SQ2
}
}
func IpStrainsAndIncB(εs, Δεs []float64, nσ, nu int, B [][]float64, u, Δu []float64, Umap []int) {
for i := 0; i < nσ; i++ {
εs[i], Δεs[i] = 0, 0
for j := 0; j < nu; j++ {
εs[i] += B[i][j] * u[Umap[j]]
Δεs[i] += B[i][j] * Δu[Umap[j]]
}
}
}
func IpBmatrix_sparse(B *la.Triplet, ndim, nne int, G [][]float64, radius float64, S []float64) {
B.Start()
if ndim == 3 {
for i := 0; i < nne; i++ {
B.Put(0, 0+i*3, G[i][0])
B.Put(1, 1+i*3, G[i][1])
B.Put(2, 2+i*3, G[i][2])
B.Put(3, 0+i*3, G[i][1]/SQ2)
B.Put(4, 1+i*3, G[i][2]/SQ2)
B.Put(5, 2+i*3, G[i][0]/SQ2)
B.Put(3, 1+i*3, G[i][0]/SQ2)
B.Put(4, 2+i*3, G[i][1]/SQ2)
B.Put(5, 0+i*3, G[i][2]/SQ2)
}
return
}
if Global.Sim.Data.Axisym {
for i := 0; i < nne; i++ {
B.Put(0, 0+i*2, G[i][0])
B.Put(1, 1+i*2, G[i][1])
B.Put(2, 0+i*2, S[i]/radius)
B.Put(3, 0+i*2, G[i][1]/SQ2)
B.Put(3, 1+i*2, G[i][0]/SQ2)
}
return
}
for i := 0; i < nne; i++ {
B.Put(0, 0+i*2, G[i][0])
B.Put(1, 1+i*2, G[i][1])
B.Put(3, 0+i*2, G[i][1]/SQ2)
B.Put(3, 1+i*2, G[i][0]/SQ2)
}
}
// Ivs2sigmas converts ivs map to σ values [nsig]
// σ -- [ndim] stresses
// i -- index of integration point
func Ivs2sigmas(σ []float64, i int, ivs map[string][]float64) {
for key, vals := range ivs {
switch key {
case "sx":
σ[0] = vals[i]
case "sy":
σ[1] = vals[i]
case "sz":
σ[2] = vals[i]
case "sxy":
σ[3] = vals[i]
case "syz":
if len(σ) > 4 {
σ[4] = vals[i]
}
case "szx":
if len(σ) > 5 {
σ[5] = vals[i]
}
}
}
}
func StressKeys() []string {
if Global.Ndim == 2 {
return []string{"sx", "sy", "sz", "sxy"}
}
return []string{"sx", "sy", "sz", "sxy", "syz", "szx"}
}
func FlowKeys() []string {
// nwl == nl・wl == filter velocity
if Global.Ndim == 2 {
return []string{"nwlx", "nwly"}
}
return []string{"nwlx", "nwly", "nwlz"}
}