MATLAB code

This MATLAB code is documented with Sphinx using the matlabdomain extension.

src

src module contains the following source code files:

src.main()

main function

An electromechanically coupled beam, Dengpeng Huang @ LTD-FAU, August 2022.

Reference: Huang and Leyendecker. Computational Mechanics, 69(2022)(3):805-824.


src.a_ini

set initial configuration, material parameters and boundary conditions


src.b_dEL_AD

derive discrete Euler-Lagrange equations and tangents using automatic differentiation

Parameters:

param – initial conditions, boundary conditions, material parameter

Returns:

symbolic functions of residual and tangent


src.c_NR

Newton-Raphson scheme to solve the discrete Euler-Lagrange equations

Parameters:

  • param – initial conditions, boundary conditions, material parameter

  • fns – symbolic functions of residual and tangent

Returns:

discrete trajectory of the beam

src/integrator

src.integrator.constraints

constraints

Parameters:

  • q – current configuraiton

  • q_ref – reference configuraiton

  • param – parameters

Returns:

constraints


src.integrator.elmass01

(consistent) mass matrix for beam element

Parameters:

  • eref – eref = […, phi^A, (d1)^A, (d2)^A, (d3)^A, … ](0); A=1,2

  • inertia – inertia = (rho*A, M_1, M_2)

Returns:

Me, consistent elemental mass matrix (15*2 x 15*2)


src.integrator.exp_operator

exponential map


src.integrator.ext_constraints

external constraints

Parameters:

  • q – current configuraiton

  • q_ref – reference configuraiton

  • param – parameters

Returns:

external constraints


src.integrator.ext_potEn

external potential energy

Parameters:

  • q – current configuraiton

  • _ref – reference configuraiton

Returns:

external potential energy


src.integrator.hat_vec

skew-symmetric matrix with axial vector a


src.integrator.int_constraints

internal constraints

Parameters:

  • q – current configuration

  • param – parameters

Returns:

internal constraints


src.integrator.int_potEn_bm_w

evaluate terms in the strain energy function


src.integrator.int_potEn_bm

strain energy computed from beam kinematics

Parameters:

  • eref – nodal configuraitons of beam element in reference configuraiton

  • eq – nodal configuraitons of beam element in current configuraiton

  • param – parameters

Returns:

strain energy


src.integrator.int_potEn_cm

strain energy computed from kinematics in contunuum mechanics

Parameters:

  • eref – nodal configuraitons of beam element in reference configuraiton

  • eq – nodal configuraitons of beam element in current configuraiton

  • param – parameters

Returns:

strain energy


src.integrator.int_potEn

internal potential energy

Parameters:

  • q – current configuraiton

  • q_ref – reference configuraiton

  • param – parameters

Returns:

internal potential energy


src.integrator.kinEnergy_new

kinetic energy

Parameters:

  • q_dot – velocity

  • param – parameters

Returns:

kinetic energy


src.integrator.LagrangeEqu

discrete Lagrange

Parameters:

  • q_n – configuraiton at step n

  • q_np1 – configuraiton at step n+1

  • q_ref – configuraiton in reference configuraiton

  • param – parameters

Returns:

discrete Lagrange


src.integrator.null_space_matrix

null space matrix

Parameters:

  • q_bm – current configuraiton

  • param – parameters

Returns:

null space matrix P


src.integrator.RK

evaluate residual and tangent for step n

Parameters:

  • X – configuraiton at step n+1

  • q_nm1 – configuraiton at step n-1

  • q_n – configuraiton at step n

  • param – parameters

  • fns – symbolic functions

Returns:

residual and tangent


src.integrator.RK0

evaluate residual and tangent for step 1

Parameters:

  • X – configuraiton at step n+1

  • q_n – configuraiton at step n

  • param – parameters

  • fns – symbolic functions

Returns:

residual and tangent


src.integrator.update

nodal reparametrization

Parameters:

  • dx – generalized configuration

  • q – redandent configuraiton

  • param – parameters

Returns:

updated redandent configuraiton


src.integrator.viscos_force_PF

1st Piola-Kirchhoff stress (Kelvin–Voigt viscosity model) and deformation gradient F in element j

Parameters:

  • eref – nodal configuraitons of beam element in reference configuraiton

  • eq – nodal configuraitons of beam element in current configuraiton

  • e_dot – nodal velocity of beam element in current configuraiton

  • XY – coordinates of integration point in cross section

  • param – parameters

Returns:

1st Piola-Kirchhoff stress and deformation gradient F


src.integrator.viscos_force

viscosity force vector as external forces

Parameters:

  • q_n – configuraiton at step n

  • q_np1 – configuraiton at step n+1

  • q_ref – reference configuraiton

  • param – parameters

Returns:

viscosity force vector

src/pre_post_processing

src.pre_post_processing.Energy

plot internal potential energy and kinetic energy


src.pre_post_processing.Hami_Energy_red

reduced Kinetic energy: p*invM*p/2


src.pre_post_processing.Hami_Energy

kinetic energy: p*invM*p/2


src.pre_post_processing.Hamilton

plot discrete Hamiltonian


src.pre_post_processing.Hd_red

plot reduced discrete Hamiltonian


src.pre_post_processing.path_s

generating initial configutaiton q for straight beam with length L


src.pre_post_processing.plot_FE_mov

creates a movie from Q and colors the beam if strain results are provided, saved to code folder under sim_vid


src.pre_post_processing.plot_FE

plot configuration of the beam


src.pre_post_processing.plot_theta

plot rotation angle of the end node


src.pre_post_processing.plot_u

plot position or displacement of the end node