%% *3D Solid Cantilever Beam (Brick element)*
% This example presents a three-dimensional cantilever beam modeled using solid 
% (continuum) elements. The objective is to verify the accuracy of displacement 
% and stress predictions obtained from OpenSeesMatlab by comparing them with classical 
% beam theory solutions.
% 
% 
% 
% A rectangular beam of length \( L \), width \( b \), and height \( h \) is 
% fixed at one end and subjected to a vertical load at the free end. The beam 
% is modeled using 3D solid elements, and both displacement and stress responses 
% are evaluated.
% 
% 

clear; clc;

opsMAT = OpenSeesMatlab();
ops = opsMAT.opensees;
%% 
% 


ops.wipe();
ops.model('basic', '-ndm', 3, '-ndf', 3);

%% Parameters
L  = 3.0;
b  = 0.2;
h  = 0.3;
E  = 30e9;
nu = 0.25;
P  = 1.0e4;   % 10 kN

nx = 40;
ny = 4;
nz = 5;

dx = L / nx;
dy = b / ny;
dz = h / nz;

%% Material
matTag = 1;
ops.nDMaterial('ElasticIsotropic', matTag, E, nu);

%% Node generation
nodeTag = 0;
nodeId = zeros(nx+1, ny+1, nz+1);

for i = 0:nx
    x = i * dx;
    for j = 0:ny
        y = -b/2 + j * dy;
        for k = 0:nz
            z = -h/2 + k * dz;
            nodeTag = nodeTag + 1;
            nodeId(i+1,j+1,k+1) = nodeTag;
            ops.node(nodeTag, x, y, z);
        end
    end
end

%% Element generation
eleTag = 0;
for i = 1:nx
    for j = 1:ny
        for k = 1:nz
            n1 = nodeId(i  ,j  ,k  );
            n2 = nodeId(i+1,j  ,k  );
            n3 = nodeId(i+1,j+1,k  );
            n4 = nodeId(i  ,j+1,k  );
            n5 = nodeId(i  ,j  ,k+1);
            n6 = nodeId(i+1,j  ,k+1);
            n7 = nodeId(i+1,j+1,k+1);
            n8 = nodeId(i  ,j+1,k+1);

            eleTag = eleTag + 1;
            ops.element('stdBrick', eleTag, ...
                n1,n2,n3,n4,n5,n6,n7,n8, ...
                matTag, 0.0, 0.0, 0.0);
        end
    end
end

%% Boundary conditions at x = 0
for j = 1:(ny+1)
    for k = 1:(nz+1)
        nd = nodeId(1,j,k);
        ops.fix(nd, 1, 1, 1);
    end
end

%% Load at free end x = L
tipFaceNodes = [];
for j = 1:(ny+1)
    for k = 1:(nz+1)
        tipFaceNodes(end+1) = nodeId(nx+1,j,k);
    end
end

fz = -P / numel(tipFaceNodes);

ops.timeSeries('Linear', 1);
ops.pattern('Plain', 1, 1);

for ii = 1:numel(tipFaceNodes)
    ops.load(tipFaceNodes(ii), 0.0, 0.0, fz);
end
%% 
% 
% 
% 
% 
% 

opts = opsMAT.vis.defaultPlotModelOptions;
opts.nodes.showLabels = false;
opts.elements.showLabels = false;
opts.loads.showNodal = true;
opsMAT.vis.plotModel(opts=opts);
grid off
%% 

Nsteps = 1;
ops.constraints('Plain');
ops.numberer('RCM');
ops.system('BandGeneral');
ops.test('NormDispIncr', 1e-10, 50);
ops.algorithm('Newton');
ops.integrator('LoadControl', 1.0/Nsteps);
ops.analysis('Static');
%% 
% 

ODB = opsMAT.post.createODB("myODB", projectGaussToNodes="extrapolation");  % create ODB
for i = 1:Nsteps
    ok = ops.analyze(1);
    ODB.fetchResponseStep();
end
ODB.saveResponse();
%% 
% 

nodeResp = opsMAT.post.getNodalResponse("myODB");

opts = opsMAT.vis.defaultPlotNodalResponseOptions;
opts.fixed.show = false;
opts.surf.showEdges = false;
opts.deform.showUndeformed = true;

opsMAT.vis.plotNodalResponse(nodeResp, respType="disp", stepIdx="absMax", respComponent="UZ", opts=opts);
colormap("jet")
axis off
view([0 0]);
%% 
% 
% 
% 

%% Theoretical solution
I = b*h^3/12;
w_theory = P*L^3/(3*E*I);

%% By OpenSeesMatlab
uz = nodeResp.disp.uz;
w_fe = min(uz(:));


fprintf("Maximal deflection in the z-direction:\n" + ...
        "  OpenSeesMatlab:  %g \n" + ...
        "  Theoretical:     %g \n", ...
        w_fe, -w_theory);
solidResp = opsMAT.post.getElementResponse("myODB", eleType="Solid");

opts = opsMAT.vis.defaultPlotContinuumResponseOptions;
opts.fixed.show = false;
opts.surf.showEdges = false;

opsMAT.vis.plotContinuumResponse(solidResp, ...
    respType="StressAtNode", respComponent="sxx", opts=opts);
axis off
view([0 0]);

sigma_theory = P*L*(h/2)/I;
sxx = solidResp.StressAtNode.sxx;
sxx_fe = max(sxx(:));
fprintf("Maximal sxx stress:\n" + ...
        "  OpenSeesMatlab: %g \n" + ...
        "  Theoretical   : %g \n", ...
        sxx_fe, sigma_theory);
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