Solution | Arch js library API

The object which is returned after calling Forward.run, or created given a Model and the computed Burger's vectors on the discontinuities making the Model.

example

solver.run()
const solution = new arch.Solution(model)

const displOnSurfaces = solution.burgers(true, true) // locally and at triangle centers

const pos = [] ;
for (let i=0; i<10; ++i) pos.push(4*(Math.random()-0.5), 4*(Math.random()-0.5), 0)

const displ   = solution.displ (pos)
const strain  = solution.strain(pos)
const stress  = solution.stress(pos)

Hierarchy

Solution

Index

Constructors

constructor

Methods

Constructors

constructor

new Solution(): Solution

Returns Solution

Methods

burgers

burgers(local: boolean, atTriangles: boolean): FlatVectors[]

brief
Get the computed displacement vectors on surface discontinuities, also known as Burger's vectors. For a given triangle, the Burger's vector, b, can be written as the difference between b(+), the displacment on the positive side of the triangle, and b(-), the displacment on the negtive side of the triangle. That is to say: b = b(+) - b(-), with b provided by burgers, b(+) provided by burgersPlus and b(-) provided by burgersMinus.

warning
The returned array comprises all Surface. This is why the return type is an array of FlatVectors (one entry for each Surface) and not a FlatVectors. The order of the corresponding surface is the same as the addition in the model.

warning
If you want to display iso-contours of a component of the Burger's vectors, you have to use local = false and atTriangles = false, as OpenGL uses values at nodes and because interpolation from triangles to nodes have to be done in the global coordinate systems (we cannot add vectors from differents coordinate systems, i.e., local coordinate system of the triangles).

Parameters
- local: boolean
  
  Local or global coordinate system
- atTriangles: boolean
  
  Compute at triangle center, at vertices otherwise
Returns FlatVectors[]
An array of flat vectors. Each entry corresponds to the burger vectors of a Surface.

burgersMinus

burgersMinus(local: boolean, atTriangles: boolean): FlatVectors[]

brief
Get the computed displacement discontinuity on the negative side of the triangles. If you do the substraction of burgersPlus and burgersMinus, you should retrieve burgers

warning
The returned array comprises all Surface. This is why the return type is an array of FlatVectors (one entry for each Surface) and not a FlatVectors. The order of the corresponding surface is the same as the addition in the model.

warning
If you want to display iso-contours of a component of the Burger's vectors, you have to use local = false and atTriangles = false, as OpenGL uses values at nodes and because interpolation from triangles to nodes have to be done in the global coordinate systems (we cannot add vectors from differents coordinate systems, i.e., local coordinate system of the triangles).

see
[[delta]]

Parameters
- local: boolean
  
  Local or global coordinate system
- atTriangles: boolean
  
  Compute at triangle center, at vertices otherwise
Returns FlatVectors[]
An array of flat vectors. Each entry corresponds to a Surface.

burgersPlus

burgersPlus(local: boolean, atTriangles: boolean): FlatVectors[]

brief
Get the computed displacement discontinuity on the positive side of the triangles. If you do the substraction of burgersPlus and burgersMinus, you should retrieve burgers

warning
The returned array comprises all Surface. This is why the return type is an array of FlatVectors (one entry for each Surface) and not a FlatVectors. The order of the corresponding surface is the same as the addition in the model.

warning
If you want to display iso-contours of a component of the Burger's vectors, you have to use local = false and atTriangles = false, as OpenGL uses values at nodes and because interpolation from triangles to nodes have to be done in the global coordinate systems (we cannot add vectors from differents coordinate systems, i.e., local coordinate system of the triangles).

see
[[delta]]

Parameters
- local: boolean
  
  Local or global coordinate system
- atTriangles: boolean
  
  Compute at triangle center, at vertices otherwise
Returns FlatVectors[]
An array of flat vectors. Each entry corresponds to a Surface.

displ

displ(position: FlatVectors): FlatVectors

brief
Compute the displacement field at points given in the flat array position.

Parameters
- position: FlatVectors
Returns FlatVectors
The array of displacement in flat array

displAt

displAt(x: number, y: number, z: number): Vector

brief
Get the displacement at one observation point

Parameters
- x: number
- y: number
- z: number
Returns Vector

onEnd

onEnd(cb: Function): void

Triggered when a post-process (displ, strain or stress) is done or stopped.

Parameters
- cb: Function
  
  Callback of type cb(): void
Returns void

onMessage

onMessage(cb: Function): void

Notification when a message is sent by this class

Parameters
- cb: Function
  
  Signature is cb(msg: string): void
Returns void

onProgress

onProgress(cb: SolutionProgressCB): void

Set the callback function to call to notify the advance of the post-process.

example

solver.run()
const solution = new arch.Solution(model)
solution.onProgress( (i,p) => {
  console.log(`nb-pts so far: ${i}, realized: ${p.toFixed(0)}%`))
}
solution.displ(positions)

will display

nb-pts so far:    0, realized:  0%
nb-pts so far: 2000, realized:  5%
nb-pts so far: 4000, realized: 10%
nb-pts so far: 6000, realized: 15%
...

Parameters

cb: SolutionProgressCB

Returns void

residualTractions

residualTractions(): FlatVectors[]

brief
Get the residual tractions after computing the Burger's vectors. For a model without any inequality constraints, the residual should be zero. However, for example for frictional model, residual tractions are different from zero.

warning
The returned array comprises all Surface. This is why the return type is an array of FlatVectors (one entry for each Surface) and not a FlatVectors. The order of the corresponding surface is the same as the addition in the model.

example
Display the resisual traction vectors for the first Surface
```
...
solver.run()
const solution = new arch.Solution(model)

const resT = solution.residualTractions()[0] // first surface

const it = new arch.VectorIt(resT)
it.forEach( t => console.log(t) )
```
Returns FlatVectors[]
An array of flat vectors. Each entry corresponds to the residual traction vectors of a Surface.

setDelta

setDelta(d: number): any

brief
This threshold is used to compute the D+ and D- on each side of each triangle. Typically, it is used to shift by a small amount along the normal, the center of the triangle in order to avoid numerical instabilities. Depending on the model sizes, it can be judicious to increase or decrease its value.

More info can be found in the following paper:

Maerten, F., Maerten, L., & Pollard, D. D. (2014). iBem3D, a three-dimensional iterative boundary element method using angular dislocations for modeling geologic structures. Computers & Geosciences, 72, 1-17., Appendix A.2.2. Corrective displacement for triangular elements, Eq. 27

And an application is here:

Maerten, F., & Maerten, L. (2008). Iterative 3d bem solver on complex faults geometry using angular dislocation approach in heterogeneous, isotropic elastic whole or halfspace. Brebbia, editor, Boundary Elements and other Mesh Reduction Methods, 30, 201-208.

default
1e-8

see
burgersMinus

see
burgersPlus

Parameters
- d: number
Returns any

setNbCores

setNbCores(n: number): any

brief
Set the number of threads to use for computing displacement, strain or stress at observation points. It is understood that this procedure applies only for multiple observation points, i.e., when calling displ, strain or stress only.

default
1

Parameters
- n: number
Returns any

stopRequested

stopRequested(cb: Function): void

Set the callback function to call to khnow if the user want to stop the computation.

Parameters
- cb: Function
  
  The callback to pass with signature cb(): boolean
Returns void

strain

strain(position: FlatVectors): FlatTensors

brief
Compute the strain field at points given in the flat array position.

Parameters
- position: FlatVectors
Returns FlatTensors
The array of strains in flat array

strainAt

strainAt(x: number, y: number, z: number): Tensor

brief
Get the strain at one observation point

Parameters
- x: number
- y: number
- z: number
Returns Tensor

stress

stress(position: FlatVectors): FlatTensors

brief
Compute the stress field at points given in the flat array position.

Parameters
- position: FlatVectors
Returns FlatTensors
The array of strains in flat array

stressAt

stressAt(x: number, y: number, z: number): Tensor

brief
Get the stress at one observation point

Parameters
- x: number
- y: number
- z: number
Returns Tensor

Static create

create(model: Model, burgers: FlatVectors[]): Solution

Create a Solution given a model and the computed burgers vectors for each discontinuities.

example

...
const burgers = solution.burgers(true, true)

// In a web-worker
const sol = arch.Solution.create(model, burgers)

sol.onProgress( (i,p) => console.log(`nb-pts so far: ${i},\trealized: ${p.toFixed(0)}%`))
sol.onMessage( m => console.log('arch-Message :', m) )

const U = sol.displ (pos)
const S = sol.stress(pos)

Will display

arch-Message : performing displacement post-process
nb-pts so far: 0,       realized: 0%
nb-pts so far: 12500,   realized: 5%
nb-pts so far: 25000,   realized: 10%
...
arch-Message : performing stress post-process
nb-pts so far: 0,       realized: 0%
nb-pts so far: 12500,   realized: 5%
nb-pts so far: 25000,   realized: 10%
...

Parameters

model: Model
burgers: FlatVectors[]

An array of FlatVectors, where each entry of the array represents the burger's vector of a surface discontinuity in the model.

Hierarchy

Index

Constructors

Methods

Constructors

constructor

Returns Solution

Methods

burgers

Parameters

local: boolean

atTriangles: boolean

Returns FlatVectors[]

burgersMinus

Parameters

local: boolean

atTriangles: boolean

Returns FlatVectors[]

burgersPlus

Parameters

local: boolean

atTriangles: boolean

Returns FlatVectors[]

displ

Parameters

position: FlatVectors

Returns FlatVectors

displAt

Parameters

x: number

y: number

z: number

Returns Vector

onEnd

Parameters

cb: Function

Returns void

onMessage

Parameters

cb: Function

Returns void

onProgress

Parameters

cb: SolutionProgressCB

Returns void

residualTractions

Returns FlatVectors[]

setDelta

Parameters

d: number

Returns any

setNbCores

Parameters

n: number

Returns any

stopRequested

Parameters

cb: Function

Returns void

strain

Parameters

position: FlatVectors

Returns FlatTensors

strainAt

Parameters

x: number

y: number

z: number

Returns Tensor

stress

Parameters

position: FlatVectors

Returns FlatTensors

stressAt

Parameters

x: number

y: number

z: number

Returns Tensor

Static create