problem(field_name, X, time)

Interpolate field from a set of elements defined in problem. Here, X is the location inside domain described by elements.

Internally, function loops through all the elements, finding the one containing the point X. After that, using inverse isoparametric mapping, first find dimensionless coordinates (ξ,η,ζ) of that element corresponding to the location of point X and after that interpolate the values of field under investigation. Algorithm can be expected to be somewhat slow for big models, but for tests models the performance is good.

Examples

Having a problem called body, one can query the field displacement at position X = (1.0, 2.0, 3.0) and time t = 1.0, with the command

X = (1.0, 2.0, 3.0)
time = 1.0
u = body("displacement", X, time)

Elasticity equations.

Field equation is:

m∂²u/∂t² = ∇⋅σ - b

Weak form is: find u∈U such that ∀v in V

δW := ∫ρ₀∂²u/∂t²⋅δu dV₀ + ∫S:δE dV₀ - ∫b₀⋅δu dV₀ - ∫t₀⋅δu dA₀ = 0

where

ρ₀ = density
b₀ = displacement load
t₀ = displacement traction

Formulations

plane stress, plane strain, 3D

References

https://en.wikipedia.org/wiki/Linearelasticity https://en.wikipedia.org/wiki/Finitestraintheory https://en.wikipedia.org/wiki/Stressmeasures https://en.wikipedia.org/wiki/Mooney%E2%80%93Rivlinsolid https://en.wikipedia.org/wiki/Strainenergydensityfunction https://en.wikipedia.org/wiki/Planestress https://en.wikipedia.org/wiki/Hooke'slaw