Finite Element pre-processing of Unit Cell

This Julia module contains methods capable of creating Finite Element model which should be ready for solving. Though, we are trying to write the FE pre-processing code as generic as possible the primary motivation for this module is for Unit Cell Homogenization. This is inevitable, given the vast applications of Finite element analysis.

Installation

From Julia REPL, execute the following,

julia> using Pkg
julia> Pkg.add("https://github.com/338rajesh/FEPreProcessing.jl#main")

Documentation

This module exports the following single function.

julia> using FEPreProcessing
julia> uc_fea_model = make_unit_cell_FEA_model(ntags, ncoor, phases_data; <kwargs>)

where,

• ntags::Vector{Int}, Node Tags

• ncoor::Matrix{Float64}, Nodal Coordinates matrix. Here each column of ncoor should corresponds to a finite element node.

• phases_data::Dict, data corresponding to each phase of the unit cell can be given supplied as the following key-value pairs.

  • key: phase finite element set ID.
  • value: A tuple of the folloing two values
    • phase finite element connectivity, of Matrix{Int} type where each column corresponds to a finite element. In each of these columns, first element is finite element tag and the remaining are finite element node tags.
    • Material,

• kwargs, Keyword Arguments

  • ϵ::Float64 = 1e-06, small parameter/tolerance to be used in the modelling process.
  • numIP::Int = 4, Number of integration points to be used.
  • gqOrder::Int = 2, Gass quadrature order

• returns, UnitCellFEModel:: Dict{String, Any}

  • all_node_set
  • element_sets
  • pc_node_tags
  • constraing_ntag

Analysis Types

• AbstractFEAnalysis
  • FEA_3Danalysis
    • Elastic_3DFEA
    • Piezo_Electric_3DFEA
    • Piezo_Magnetic_3DFEA
    • Magneto_Electro_Elastic_3DFEA
    • Thermal_Conductivity_3DFEA
    • Thermo_Elastic_3DFEA
    • Thermo_Piezo_Electric_3DFEA
    • Thermo_Piezo_Magnetic_3DFEA
    • Thermo_Magneto_Electro_Elastic_3DFEA
  • FEA_2Danalysis
    • Elastic_2DFEA
      • PlaneStress_2DFEA
      • PlaneStrain_2DFEA

Usage

• Nodal degrees of freedom for an ananlysis can be obtained using,

julia> using FEPreProcessing
julia> FEPreProcessing.get_nodal_dof(Elastic_3DFEA)
(:ux, :uy, :uz)
julia> FEPreProcessing.get_nodal_dof(Thermal_Conductivity_3DFEA)
(:T,)

• node pairs of the unit cells, assuming model has periodic mesh, can be obtained using make_rve_node_pairs method. It takes node tags of Vector{Int} type and node coordinates of Matrix{Float64} type. Note that, each column of node coordinates matrix corresponds to a node.

julia> using FEPreProcessing
julia> node_pairs = FEPreProcessing.make_rve_node_pairs(all_node_tags, all_node_coor)
julia> pc_node_tags = [(i.n1, i.n2) for i in node_pairs]

Adding a new analysis type

• In FEPrepBase.jl,
  • Define its structure using sturct
  • Update get_nodal_dof() and get_material_matrix_size()
• In prepare_material_data.jl,
  • Update get_material_tensors() method and its dependencies like get_elastic_tensor()
• In assembly.jl
  • Update get_B_matrix() method

Code (dependency) structure

• unit_cell_FEModel
  • make_rve_node_pairs()
    • get_rve_node_groups()
    • node_pairs(::Dict{String,Matrix{IF64}}, ::NTuple{6,Float64})
      • node_pairs(::Matrix{IF64}, ::Matrix{IF64}, ::NTuple{3,Float64}, ::String; ::Float64)
  • make_fe_node_set()
  • get_felement_sets()