# Assembly prescribed Stress using JuAFEM

**URL:** https://discourse.julialang.org/t/assembly-prescribed-stress-using-juafem/52178
**Category:** General Usage
**Tags:** juafem
**Created:** [December 21, 2020, 3:00pm UTC](https://discourse.julialang.org/t/assembly-prescribed-stress-using-juafem/52178 "2020-12-21T15:00:35Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![FrootLoops](https://avatars.discourse-cdn.com/v4/letter/f/c4cdca/32.png) [@FrootLoops](https://discourse.julialang.org/u/FrootLoops)
#### Post date: [December 21, 2020, 3:00pm UTC](https://discourse.julialang.org/t/assembly-prescribed-stress-using-juafem/52178/1 "2020-12-21T15:00:35Z")

</div>

Checking the example [incompressible\_elasticity](https://kristofferc.github.io/JuAFEM.jl/latest/examples/incompressible_elasticity/), it is solving the equation Ku = f based on the following assemble code:

```julia
function doassemble(cellvalues_u::CellVectorValues{dim}, cellvalues_p::CellScalarValues{dim},
                    facevalues_u::FaceVectorValues{dim}, K::SparseMatrixCSC, grid::Grid,
                    dh::DofHandler, mp::LinearElasticity) where {dim}

    f = zeros(ndofs(dh))
    assembler = start_assemble(K, f)
    nu = getnbasefunctions(cellvalues_u)
    np = getnbasefunctions(cellvalues_p)

    fe = PseudoBlockArray(zeros(nu + np), [nu, np]) # local force vector
    ke = PseudoBlockArray(zeros(nu + np, nu + np), [nu, np], [nu, np]) # local stiffness matrix

    # traction vector
    t = Vec{2}((0.0, 1/16))
    # cache ɛdev outside the element routine to avoid some unnecessary allocations
    ɛdev = [zero(SymmetricTensor{2, dim}) for i in 1:getnbasefunctions(cellvalues_u)]

    for cell in CellIterator(dh)
        fill!(ke, 0)
        fill!(fe, 0)
        assemble_up!(ke, fe, cell, cellvalues_u, cellvalues_p, facevalues_u, grid, mp, ɛdev, t)
        assemble!(assembler, celldofs(cell), fe, ke)
    end

    return K, f
end;

```

And after applying boundary conditions by `apply!(K, f, dbc)` one can solve the system.

My question is, what is the best way to solve the system Ku = f -g, where g is a vector describing predescribed stress. My first was, was to create a vector g\_e and subtract it from the vector f\_e such that f = Assemble(f\_e -g\_e). The problem is, that the command `apply!(K, f, dbc)` would apply boundary conditions on g too. And I am not sure if this is the correct way.

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<div class="post-metadata">

### Author: ![koehlerson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/koehlerson/32/13108_2.png) [@koehlerson](https://discourse.julialang.org/u/koehlerson)
#### Post date: [December 21, 2020, 3:20pm UTC](https://discourse.julialang.org/t/assembly-prescribed-stress-using-juafem/52178/2 "2020-12-21T15:20:02Z")

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Heyho,

IIRC neumann and dirichlet boundary do not intersect. Therefore, I don’t think that `apply!(K,f,dbc)` does anything wrong for you, since g\_e should be 0 anyways at the dirichlet boundary. You can test this with: [https://github.com/KristofferC/JuAFEM.jl/pull/304](https://github.com/KristofferC/JuAFEM.jl/pull/304)