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https://github.com/soypat/go-fem
Go packages for finite element analysis/methods.
https://github.com/soypat/go-fem
fem finite-element-analysis finite-element-methods go golang matrix-assembly rigidity-matrix stiffness-matrix stiffness-matrix-assembly
Last synced: about 1 month ago
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Go packages for finite element analysis/methods.
- Host: GitHub
- URL: https://github.com/soypat/go-fem
- Owner: soypat
- License: mit
- Created: 2022-06-12T06:08:21.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2023-07-09T19:28:01.000Z (over 1 year ago)
- Last Synced: 2024-10-12T09:11:26.891Z (2 months ago)
- Topics: fem, finite-element-analysis, finite-element-methods, go, golang, matrix-assembly, rigidity-matrix, stiffness-matrix, stiffness-matrix-assembly
- Language: Go
- Homepage:
- Size: 168 KB
- Stars: 1
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# go-fem
Extremely clean API toolkit for finite element analysis/methods.
#### Roadmap
* ~~3D Isoparametric element assembly.~~
* ~~Better sparse assembler~~ As fast as high performance libraries.
* ~~2D Isoparametric element assembly.~~
* ~~Arbitrary Isoparametric element assembly.~~
* Stress extraction from displacements.
* Shell and plate element assembly.
* Better define Element3 API.
* Add constraints assembly.
- Lagrange Multipliers or Penalty method.
* Stiffness matrix utility functions for better conditioning and troubleshooting.
#### Axisymmetric assembly example
```go
package main
import (
"fmt"
"log"
"github.com/soypat/go-fem"
"github.com/soypat/go-fem/constitution/solids"
"github.com/soypat/go-fem/elements"
"github.com/soypat/lap"
"gonum.org/v1/gonum/spatial/r3"
)
func main() {
// We assemble a single 2D axisymmetric element.
// With a young modulus of 1000 and a poisson ratio of 0.33.
// The units are undefined. If using SI, E would be 1kPa and node positions
// would be in meters.
material := solids.Isotropic{E: 1000, Poisson: 0.33}
nodes := []r3.Vec{
{X: 20, Y: 0},
{X: 30, Y: 0},
{X: 30, Y: 1},
{X: 20, Y: 1},
}
elems := [][4]int{
{0, 1, 2, 3},
}
elemType := elements.Quad4{}
ga := fem.NewGeneralAssembler(nodes, elemType.Dofs())
err := ga.AddIsoparametric(elemType, material.Axisymmetric(), 1, func(i int) (elem []int, xC, yC r3.Vec) {
return elems[i][:], r3.Vec{}, r3.Vec{}
})
if err != nil {
log.Fatal(err)
}
fmt.Printf("K=\n%.3g\n", lap.Formatted(ga.Ksolid()))
}
```
**Output:**
```
K=
⎡ 2.93e+04 5.23e+03 1.45e+04 2.06e+03 -1.63e+04 -6.45e+03 -2.77e+04 -848⎤
⎢ 5.23e+03 1.11e+05 -2.36e+03 6.14e+04 -7.37e+03 -6.19e+04 848 -1.11e+05⎥
⎢ 1.45e+04 -2.36e+03 3.6e+04 -8.59e+03 -3.37e+04 3.58e+03 -1.63e+04 7.37e+03⎥
⎢ 2.06e+03 6.14e+04 -8.59e+03 1.36e+05 -3.58e+03 -1.36e+05 6.45e+03 -6.19e+04⎥
⎢-1.63e+04 -7.37e+03 -3.37e+04 -3.58e+03 3.6e+04 8.59e+03 1.45e+04 2.36e+03⎥
⎢-6.45e+03 -6.19e+04 3.58e+03 -1.36e+05 8.59e+03 1.36e+05 -2.06e+03 6.14e+04⎥
⎢-2.77e+04 848 -1.63e+04 6.45e+03 1.45e+04 -2.06e+03 2.93e+04 -5.23e+03⎥
⎣ -848 -1.11e+05 7.37e+03 -6.19e+04 2.36e+03 6.14e+04 -5.23e+03 1.11e+05⎦
```
#### Benchmarks
Takes ~33s to assemble 680k dofs for 1.3 million 4 node 3D tetrahedrons on a low end AMD Zen2 CPU:
```
$ go test -bench=. -benchmem .
goos: linux
goarch: amd64
pkg: github.com/soypat/go-fem
cpu: AMD Ryzen 5 3400G with Radeon Vega Graphics
BenchmarkTetra4Assembly/105_dofs,_48_elems-8 1218 932708 ns/op 155646 B/op 744 allocs/op
BenchmarkTetra4Assembly/3723_dofs,_5376_elems-8 10 109067373 ns/op 10928022 B/op 74500 allocs/op
BenchmarkTetra4Assembly/27027_dofs,_46080_elems-8 1 1023632489 ns/op 88685256 B/op 634443 allocs/op
BenchmarkTetra4Assembly/206115_dofs,_380928_elems-8 1 8849933029 ns/op 717490648 B/op 5229747 allocs/op
BenchmarkTetra4Assembly/684723_dofs,_1299456_elems-8 1 32997698741 ns/op 2742313160 B/op 17888792 allocs/op
```