5. Procedures

There are several procedures available to handle structural analysis in the finite element framework. The most general procedure is the continuum theory, which solves the momentum equation over a three dimensional body. However, the computational cost of this can be high which led to the development of specialised beam and shell theory. These reduced models alleviate the burden of a three-dimensional simulation with some restrictions.

In this section, an outline of specialised theory in neon is documented along with the modelling assumption the theory contains.

5.1. Beam

When approximating the structural member with beam theory, additional information regarding the cross-sectional area and the second moment of area must be given in order find an approximate solution. This is accomplished for all beam theories by specifying a profile and the orientation of this profile in space for every finite element.

Each element group with the same profile is grouped together inside a mesh object in the input file

"meshes" : [{
    ...
    "section" : [{
        "name" : "<name of element group in mesh file>",
        "profile" : "<name of profile definition>",
        "tangent" : [0.0, 1.0, 0.0],
        "normal" : [1.0, 0.0, 0.0]
    },
    ...
    ],
}]

5.1.1. Linear (C0)

In order to avoid the requirement of higher order shape functions (see Beam Theory (C1)), a reduced form of the momentum equation is solved rather than discretising the Euler-Bernoulli fourth order differential equation. This involves the computation of four separate stiffness matrices; axial, torsional, bending and shear. A specialised integration scheme is automatically applied to this analysis to avoid shear locking through under integration of selected stiffness matrices.

5.1.2. Euler-Bernoulli (C1)

If the Euler-Bernoulli beam theory is directly formulated in the finite element method, the resulting shape functions are required to be C1 continuous, resulting in a higher order interpolation. This theory will be implemented after the C0 theory.

5.2. Continuum

The evaluation of the integrals in the finite element method use numerical quadrature rules specialised for each element. For computational efficiency reasons, these could be under-integrated or fully-integrated. However, in the current state reduced integration rules produce a rank-deficient element stiffness matrix and are therefore not recommended for use until stabilisation is applied. For each mesh type, the element options can be specified

"element_options" : {
    "quadrature" : "full"
}

with reduced integration selected when "quadrature" : "reduced".