FEA with general material models on beam elements

AbstractAlgorithm

Abstract type to define numerical method algorithms.

BoundaryConds

Contains the boundary conditions of the structure.
Includes the support definition and the external forces.
Fields:

• suppMatrix::Matrix: Matrix whose i-th row contains the fixed degrees of freedom of the fixed i-th node according to the structure: [Nodeᵢ uz θy].
• nodalForceMatrix::Matrix: Matrix whose i-th row contains the external nodal forces applied to the loaded i-th node according the structure: [Nodeᵢ Fz My].

IsotropicBiLinear

Isotropic BiLinear constitutive model i.e. Linear softening or Linear Hardening.
Stress is proportional to strain given by either the Elasticity Modulus E and the Elastoplastic tangent modulus C.
Change in proportionality occurs after the stress reaches a given value σY0.

Fields:

• E::Float64: Young Elasticity modulus.
• σY0::Float64: Initial yield stress.
• K::Float64: Slope of the hardening function.
• ne::Int64: Gauss integration points along the element length.
• ns::Int64: Gauss integration points along the section height.

IterPArams

Store the criterion stop at each load increment.

LinearElastic

Isotropic Linear elastic constitutive model.
Stress is proportional to strain given by Elasticity Modulus E.

Fields:

• E::Float64: Young Elasticity modulus.
• ne::Int64: Gauss integration points along the element length.
• ns::Int64: Gauss integration points along the section height.

MaterialModel

Abstract type to define material constitutive model.

Mesh

Contains the mesh node coordinates and conectivity matrix.

Fields:

• nodesMat::Matrix{Float64}: Matrix containing the (xᵢ,zᵢ) coordinates of the i-th node.
• conecMat::Matrix: Matrix whose i-th row contains the information of the i-th element according the structure: [Material, Section, (nodeᵢ, nodeⱼ)].

ModelSol

Stores the solution of the problem.

Rectangle

Rectangular section.

Fields:

• b::Float64: Section width.
• h::Float64: Section height.
• A::Float64: Section area.
• Iy::Float64: Second moment of inertia.

Note:
A and Iy are computed internally, only provide fields b and h.

Section

Abstract type to define element sections.

StressArraySets

Struct that defines settings to compute the stress array.

UserModel

User defined constitutive model.
The user shall use import materialNonLinearity: constitutive_model and define the function constitutive_model as follows.

function constitutive_model(ElemMaterialModel::UserModel, εₖ)
    ...
    return σ, ∂σ∂ε
end

Fields:

• ne::Int64: Gauss integration points along the element length.
• ns::Int64: Gauss integration points along the section height.