├─Plate_FEM_explicit_3_SURFplot
│  ├─cores
│  │  ├─functions
│  │  ├─solver
│  │  └─ToolBoxes
│  └─save
│      └─fig
└─Plate_FEM_implicit_0
    ├─cores
    │  ├─functions
    │  ├─solver
    │  └─ToolBoxes
    └─save
        └─fig

• Influence of the aspect ratio of the sheet for an electric generator utilizing the rotation of a flapping sheet, Mechanical Engineering Journal, Vol. 8, No. 1 (2021).
  https://doi.org/10.1299/mej.20-00459

@article{Akio YAMANO202120-00459,
    title={Influence of the aspect ratio of the sheet for an electric generator utilizing the rotation of a flapping sheet},
    author={Akio YAMANO and Hiroshi IJIMA and Atsuhiko SHINTANI and Chihiro NAKAGAWA and Tomohiro ITO},
    journal={Mechanical Engineering Journal},
    volume={8},
    number={1},
    pages={20-00459-20-00459},
    year={2021},
    doi={10.1299/mej.20-00459}
}

• Flow-induced vibration and energy-harvesting performance analysis for parallelized two flutter-mills considering span-wise plate deformation with geometrical nonlinearity and three-dimensional flow, International Journal of Structural Stability and Dynamics, Vol. 22, No. 14, (2022).
  https://doi.org/10.1142/S0219455422501632

@article{doi:10.1142/S0219455422501632,
    author = {Yamano, Akio and Chiba, Masakatsu},
    title = {Flow-Induced Vibration and Energy-Harvesting Performance Analysis for Parallelized Two Flutter-Mills Considering Span-Wise Plate Deformation with Geometrical Nonlinearity and Three-Dimensional Flow},
    journal = {International Journal of Structural Stability and Dynamics},
    volume = {22},
    number = {14},
    pages = {2250163},
    year = {2022},
    doi = {10.1142/S0219455422501632}
}

• Influence of boundary conditions on a flutter-mill, Journal of Sound and Vibration, Vol. 478, No. 21 (2020).
  https://doi.org/10.1016/j.jsv.2020.115359

@article{YAMANO2020115359,
    title = {Influence of boundary conditions on a flutter-mill},
    journal = {Journal of Sound and Vibration},
    volume = {478},
    pages = {115359},
    year = {2020},
    doi = {https://doi.org/10.1016/j.jsv.2020.115359},
    author = {A. Yamano and A. Shintani and T. Ito and C. Nakagawa and H. Ijima}
}

[Step 1] Install the ToolBoxes

The following ToolBoxes in “./XXXX/cores/ToolBoxes/” are required,

For numerical analysis:

• “Meshing a plate using four noded elements” by KSSV:

https://jp.mathworks.com/matlabcentral/fileexchange/33731-meshing-a-plate-using-four-noded-elements

• “Sparse sub access” by Bruno Luong:

https://jp.mathworks.com/matlabcentral/fileexchange/23488-sparse-sub-access

• “Vectorized Multi-Dimensional Matrix Multiplication” by Darin Koblick:

https://jp.mathworks.com/matlabcentral/fileexchange/47092-vectorized-multi-dimensional-matrix-multiplication?s_tid=prof_contriblnk

For plotting results:

• “mmwrite” by Micah Richert:

https://jp.mathworks.com/matlabcentral/fileexchange/15881-mmwrite

• “mpgwrite” by David Foti:

https://jp.mathworks.com/matlabcentral/fileexchange/309-mpgwrite?s_tid=srchtitle

• “mmread” by Micah Richert:

https://jp.mathworks.com/matlabcentral/fileexchange/8028-mmread

[Step 1.2] Add path to installed ToolBoxes

Modify "add_pathes.m" to add path to abovementined installed ToolBoxes as follows,

addpath ./cores/ToolBoxes/XX;

where XX is the name of folder of the installed ToolBox.

[Step 2] Start GUI form

Open the “GUI.fig” from MATLAB.

[Step 2.1] Pre-setting

Push the "Parameters" button and edit parameters.

[Step 3] Start analysis

Push the “exe” button and wait until the finish of the analysis.

[Step 4] Plot results

Push the “plot” button.

[Step 5] View plotted results

Results (figures and movie) plotted by [Step 4] are in "./save" directory.

Analytical condisions are in "./save/param_setting.m"

End_Time = 1.0;             %% Analytical time [s]
d_t = 1e-4;                 %% step time [s]
core_num = 6;               %% The number of CPUs for computing [-]
movie_format = 'mpeg';      %% movie format [-]
% movie_format = 'avi';
speed_check = 0;            %% 

%% Plate
rho_m = 1000;           	%% density [kg/m^3]
Eelastic = 1e+3;        	%% Young's modulus [Pa]
nu = 0.3;                   %% Poiison ratio [-]

Length = 100e-3;          	%% Length [m]
Width = 100e-3;             %% Width [m]
thick = 10e-3;           	%% Thickness [m]
Nx = 8;                   	%% The number of x-directional elements [-]
Ny = 8;                   	%% The number of y-directional elements [-]
N_gauss = 5;                %% Gauss-Legendre [-]

g = 9.81;                   %% gravity acc. [m/s^2]
F_in = -rho_m*g*[ 0 0 1].';	%% gravity [N/m^3]

and boundary conditions for nodes on the plate;

%% Boundary conditions
node_r_0 = [ 1];          	%% Node number for fixed node [-]
node_dxr_0 = [ ];        	%% Node number for fixed x-directional gradient [-]
node_dyr_0 = [ ];       	%% Node number for fixed y-directional gradient [-]

Then, boundary conditions for a plate are written as,

• Pinned at the corner of the plate

%% Boundary conditions
node_r_0 = [ 1];          	%% Node number for fixed node [-]
node_dxr_0 = [ ];        	%% Node number for fixed x-directional gradient [-]
node_dyr_0 = [ ];       	%% Node number for fixed y-directional gradient [-]

• Clamped at the leading-edge

%% Boundary conditions
node_r_0 = [ 1:Ny+1 ];       %% Node number giving the displacement constraint [-]
node_dxr_0 = [ 1:Ny+1 ];     %% Node number giving x-directional gradient constraint [-]
node_dyr_0 = [ 1:Ny+1 ];     %% Node number giving y-directional gradient constraint [-]

• Pinned at the leading-edge

%% Boundary conditions
node_r_0 = [ 1:Ny+1 ];     %% Node number giving the displacement constraint [-]
node_dxr_0 = [ ];          %% Node number giving x-directional gradient constraint [-]
node_dyr_0 = [ 1:Ny+1 ];   %% Node number giving y-directional gradient constraint [

where index in vector shows the node index around a plate element to apply boundary conditions.