PUPM

stiffness matrix for orthotropic

function to apply nodal forces to external force vector in 3D

apply_nodal_force_3d!(grid, node_set_name, load_vector, f_ext)

Function for the local stiffness matrix(element stiffness matrix)

assemble_cell!(ke, cell_values, E, ν)

function to assemble the local stiffness matrix for 3D

assemble_cell_3d!(ke, cell_values, E, ν)

Function for external forces from surface tractions

assemble_external_forces!(f_ext, dh, facetset, facet_values, traction)

function to assemble external forces from surface tractions in 3D

assemble_external_forces_3d!(f_ext, dh, facetset, facet_values, traction)

Function for external forces from pressure

assemble_external_pressure!(f_ext, dh, facetset, facet_values, pressure)

function to assemble external forces from pressure in 3D

assemble_external_pressure_3d!(f_ext, dh, facetset, facet_values, pressure)

Function for the global stiffness matrix

assemble_global!(K, dh, cell_values, E, ν)

function to assemble the global stiffness matrix for 3D

assemble_global_3d!(K, dh, cell_values, E, ν)

Function to calculate parameter H

calculate_H(grid, dh, cv, u, E, ν)

function to calculate parameter H in 3D

calculate_H_3d(grid, dh, cv, u, E, ν)

Function to calculate the average strain energy

calculate_average_strain_energy(grid, dh, cv, u, E, ν)

Function to calculate the cell volume

calculate_cell_volume(cv)

Function to calculate element strain energy

calculate_strain_energy(grid, dh, cv, u, E, ν)

function to calculate element strain energy in 3D

calculate_strain_energy_3d(grid, dh, cv, u, E, ν)

Function to calculate strains

calculate_strains(grid, dh, cv, u)

function to calculate strains in 3D

calculate_strains_3d(grid, dh, cv, u)

Function to calculate stresses

calculate_stresses(grid, dh, cv, u, E, ν)

function to calculate stresses in 3D

calculate_stresses_3d(grid, dh, cv, u, E, ν)

Main finite element solver for two dimension

fem_solver(par::DynamicParams)

Main finite element solver for 3D

fem_solver_3d(par::DynamicParams)

function to apply volume fraction

example:

ρnew = rand(Float64, 8)
nx, ny , nz = 2 , 2 , 2
vf = 0.5
η = π/4

ρ =  filter_density_to_vf!(ρnew, vf, nx, ny, nz, η)

Get the material matrix C

get_material_matrix(E, ν)

function to get the material matrix for 3D

get_material_matrix_3d(E, ν)

Function to calculate the derivative of the strain energy with respect to the Young's modulus

get_material_matrix_derivative_wrt_E(E, ν)

function to get the derivative of the material matrix with respect to the Young's modulus in 3D

get_material_matrix_derivative_wrt_E_3d(E::Vector{Float64,1}, ν)

function to remove vtu file

remove_vtk_files(directory::String)

function to perform topology optimization using UPM approach (2D case)

top_upm(par::DynamicParams, name_of_file::String, directory::String)

function to perform topology optimization using UPM approach (3D case)

top_upm_3d(par::DynamicParams, name_of_file::String, directory::String)

function to convert Young's modulus to density E = E0(rho/rho0)^gamma

Example:

Enew = rand(Float64, 5)
E0 = 1.0
ρ0 = 1.0
γ = 1
ρ = transfer_to_density(Enew, E0, ρ0, γ)

function to transfer density to young modulus example: ρnew = rand(Float64, 4) E0 = 1.0 ρ0 = 1.0 γ = 1 Emin = 1e-4 Emax = 1.0

transfertoyoung(ρnew , E0, ρ0, γ, Emin , Emax)

function for update Young's modulus based on UPM approach

Example:

k = 1
E = rand(Float64, 5)
H = rand(Float64, 5)
Emax = 1.0
Emin = 1e-4
# test code
Enew = update_upm!(k, E, H,Emax,Emin)

Function to apply nodal forces to external force vector

apply_nodal_force!(grid, node_set_name, load_vector, f_ext)