This MATLAB program models the pushover analysis of a triangular steel membrane subjected to lateral displacements. It uses finite element analysis to calculate the stiffness matrix and account for geometric and material nonlinearity under small strains. The program defines the geometry and material properties of the membrane, applies incremental lateral displacements, calculates the element stiffness matrices, and assembles the global stiffness matrix to solve for displacements at each step. The results of the MATLAB analysis are verified against a similar ABAQUS model.

1. >> IN THE NAME OF GOD <<
Pushover Analysis of Triangular Steel Membrane Element Subjected to Lateral Displacement with Effect of Geometric and
Material Nonlinearity and Small strain in MATLAB and ABAQUS (Displacement Control)
The MATLAB Program is Verified by ABAQUS v.6.10
This MATLAB program is written by Salar Delavar Ghashghaei - Date of Publication: March/23/2017
E-mail: salar.d.ghashghaei@gmail.com

2. Matlab Code:clear all;close all;clc
% Define Parameters in unit: mm,kN
P=[0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0;0]; % [kN]
D22=-.5;% [mm] Initial Displacement [DOF (22)] Incremental Displacement
D22max=500; % [mm] Maximum displacement [DOF (22)]
D24=-.5;% [mm] Initial Displacement [DOF (24)] Incremental Displacement
D24max=500; % [mm] Maximum displacement [DOF (24)]
XY1i=[50.6233 0]; % [x y] Point 1 Coordinate
XY2i=[0 0]; % [x y] Point 2 Coordinate
XY3i=[72.6173 138.8651]; % [x y] Point 3 Coordinate
XY4i=[24.4717 154.5085]; % [x y] Point 4 Coordinate
XY5i=[136.4466 264.137]; % [x y] Point 5 Coordinate
XY6i=[94.2101 291.3777]; % [x y] Point 6 Coordinate
XY7i=[235.863 363.5534]; % [x y] Point 7 Coordinate
XY8i=[204.1115 402.5126]; % [x y] Point 8 Coordinate
XY9i=[361.1349 427.3827]; % [x y] Point 9 Coordinate
XY10i=[346.0669 473.7574]; % [x y] Point 10 Coordinate
XY11i=[500 449.3767]; % [x y] Point 11 Coordinate
XY12i=[500 500]; % [x y] Point 12 Coordinate
T=10;% [mm] triangular membrane element thickness
E=200;% [kN/mm^2] Modulus of elasticity
V=.3;% Poisson's ratio
m = 348; % number of calculation
itermax = 15000;% maximum number of iterations
tolerance = 1e-12; % specified tolerance for convergence
%%% monitor cpu time
starttime = cputime;
%% Small Displacement Analysis
disp('###############################');
disp('# Small Displacement Analysis #');
disp('###############################');
u = zeros(16,1);% initial guess value
for i=1:m;
up22=D22*i;
up24=D24*i;
XY1=[XY1i(1) XY1i(2)]; % [x y] Point 1 Coordinate
XY2=[XY2i(1) XY2i(2)]; % [x y] Point 2 Coordinate
XY3=[XY3i(1) XY3i(2)]; % [x y] Point 3 Coordinate
XY4=[XY4i(1) XY4i(2)]; % [x y] Point 4 Coordinate
XY5=[XY5i(1) XY5i(2)]; % [x y] Point 5 Coordinate
XY6=[XY6i(1) XY6i(2)]; % [x y] Point 6 Coordinate
XY7=[XY7i(1) XY7i(2)]; % [x y] Point 7 Coordinate
XY8=[XY8i(1) XY8i(2)]; % [x y] Point 8 Coordinate
XY9=[XY9i(1) XY9i(2)]; % [x y] Point 9 Coordinate
XY10=[XY10i(1) XY10i(2)]; % [x y] Point 10 Coordinate
XY11=[XY11i(1) XY11i(2)]; % [x y] Point 11 Coordinate
XY12=[XY12i(1) XY12i(2)]; % [x y] Point 12 Coordinate
B1e1=XY2(2)-XY3(2);B2e1=XY3(2)-XY1(2);B3e1=XY1(2)-XY2(2);
G1e1=XY2(1)-XY3(1);G2e1=XY3(1)-XY1(1);G3e1=XY1(1)-XY2(1);
a1=.5*(XY1(1)*B1e1+XY2(1)*B2e1+XY3(1)*B3e1);a1=abs(a1);
B1=1/(2*a1)*[B1e1 0 B2e1 0 B3e1 0;
0 G1e1 0 G2e1 0 G3e1;
G1e1 B1e1 G2e1 B2e1 G3e1 B3e1];
B1e2=XY3(2)-XY4(2);B2e2=XY4(2)-XY2(2);B3e2=XY2(2)-XY3(2);
G1e2=XY3(1)-XY4(1);G2e2=XY4(1)-XY2(1);G3e2=XY2(1)-XY3(1);
a2=.5*(XY2(1)*B1e2+XY3(1)*B2e2+XY4(1)*B3e2);a2=abs(a2);
B2=1/(2*a2)*[B1e2 0 B2e2 0 B3e2 0;
0 G1e2 0 G2e2 0 G3e2;
G1e2 B1e2 G2e2 B2e2 G3e2 B3e2];
B1e3=XY4(2)-XY5(2);B2e3=XY5(2)-XY3(2);B3e3=XY3(2)-XY4(2);
G1e3=XY4(1)-XY5(1);G2e3=XY5(1)-XY3(1);G3e3=XY3(1)-XY4(1);
a3=.5*(XY3(1)*B1e3+XY4(1)*B2e3+XY5(1)*B3e3);a3=abs(a3);
B3=1/(2*a3)*[B1e3 0 B2e3 0 B3e3 0;
0 G1e3 0 G2e3 0 G3e3;
G1e3 B1e3 G2e3 B2e3 G3e1 B3e3];
B1e4=XY5(2)-XY6(2);B2e4=XY6(2)-XY4(2);B3e4=XY4(2)-XY5(2);
G1e4=XY5(1)-XY6(1);G2e4=XY6(1)-XY4(1);G3e4=XY4(1)-XY5(1);
a4=.5*(XY4(1)*B1e4+XY5(1)*B2e4+XY6(1)*B3e4);a4=abs(a4);
B4=1/(2*a4)*[B1e4 0 B2e4 0 B3e4 0;
0 G1e4 0 G2e4 0 G3e4;
G1e4 B1e4 G2e4 B2e4 G3e4 B3e4];
B1e5=XY6(2)-XY7(2);B2e5=XY7(2)-XY5(2);B3e5=XY5(2)-XY6(2);
G1e5=XY6(1)-XY7(1);G2e5=XY7(1)-XY5(1);G3e5=XY5(1)-XY6(1);
a5=.5*(XY5(1)*B1e5+XY6(1)*B2e5+XY7(1)*B3e5);a5=abs(a5);
B5=1/(2*a5)*[B1e5 0 B2e5 0 B3e5 0;
0 G1e5 0 G2e5 0 G3e5;
G1e5 B1e5 G2e5 B2e5 G3e5 B3e5];
B1e6=XY7(2)-XY8(2);B2e6=XY8(2)-XY6(2);B3e6=XY6(2)-XY7(2);
G1e6=XY7(1)-XY8(1);G2e6=XY8(1)-XY6(1);G3e6=XY6(1)-XY7(1);
a6=.5*(XY6(1)*B1e6+XY7(1)*B2e6+XY8(1)*B3e6);a6=abs(a6);
B6=1/(2*a6)*[B1e6 0 B2e6 0 B3e6 0;
0 G1e6 0 G2e6 0 G3e6;
G1e6 B1e6 G2e6 B2e6 G3e6 B3e6];
B1e7=XY8(2)-XY9(2);B2e7=XY9(2)-XY7(2);B3e7=XY7(2)-XY8(2);
G1e7=XY8(1)-XY9(1);G2e7=XY9(1)-XY7(1);G3e7=XY7(1)-XY8(1);
a7=.5*(XY7(1)*B1e7+XY8(1)*B2e7+XY9(1)*B3e7);a7=abs(a7);
B7=1/(2*a1)*[B1e7 0 B2e7 0 B3e7 0;
0 G1e7 0 G2e7 0 G3e7;
G1e7 B1e7 G2e7 B2e7 G3e7 B3e7];
B1e8=XY9(2)-XY10(2);B2e8=XY10(2)-XY8(2);B3e8=XY8(2)-XY9(2);
G1e8=XY9(1)-XY10(1);G2e8=XY10(1)-XY8(1);G3e8=XY8(1)-XY9(1);
a8=.5*(XY8(1)*B1e8+XY9(1)*B2e8+XY10(1)*B3e8);a8=abs(a8);
B8=1/(2*a8)*[B1e8 0 B2e8 0 B3e8 0;
0 G1e8 0 G2e8 0 G3e8;
G1e8 B1e8 G2e8 B2e8 G3e8 B3e8];
B1e9=XY10(2)-XY11(2);B2e9=XY11(2)-XY9(2);B3e9=XY9(2)-XY10(2);
G1e9=XY10(1)-XY11(1);G2e9=XY11(1)-XY9(1);G3e9=XY9(1)-XY10(1);
a9=.5*(XY9(1)*B1e9+XY10(1)*B2e9+XY11(1)*B3e9);a9=abs(a9);
B9=1/(2*a1)*[B1e9 0 B2e9 0 B3e9 0;
0 G1e9 0 G2e9 0 G3e9;
G1e9 B1e9 G2e9 B2e9 G3e9 B3e9];
B1e10=XY11(2)-XY12(2);B2e10=XY12(2)-XY10(2);B3e10=XY10(2)-XY11(2);
G1e10=XY11(1)-XY12(1);G2e10=XY12(1)-XY10(1);G3e10=XY10(1)-XY12(1);
a10=.5*(XY10(1)*B1e10+XY11(1)*B2e10+XY12(1)*B3e10);a10=abs(a10);
B10=1/(2*a10)*[B1e10 0 B2e10 0 B3e10 0;
0 G1e10 0 G2e10 0 G3e10;
G1e10 B1e10 G2e10 B2e10 G3e10 B3e10];
D=(E/(1-V^2))*[1 V 0;
V 1 0;
0 0 .5*(1-V)];
K1=B1'*D*a1*T*B1;
K2=B2'*D*a2*T*B2;
K3=B3'*D*a3*T*B3;
K4=B4'*D*a4*T*B4;
K5=B5'*D*a5*T*B5;
K6=B6'*D*a6*T*B6;
K7=B7'*D*a7*T*B7;
K8=B8'*D*a8*T*B8;
K9=B9'*D*a9*T*B9;
K10=B10'*D*a10*T*B10;
%% 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24
Kp=[K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0 0 0 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0 0 0 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6) 0 0 0 0;
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6) 0 0 0 0;
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4) K9(1,5) K9(1,6) 0 0;
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4) K9(2,5) K9(2,6) 0 0;
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2) K9(3,5)+K10(1,3) K9(3,6)+K10(1,4) K10(1,5) K10(1,6);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2) K9(4,5)+K10(2,3) K9(4,6)+K10(2,4) K10(2,5) K10(2,6);
0 0 0 0 0 0 0 0 0 0 0 0 K9(5,1) K9(5,2) K9(5,3)+K10(3,1) K9(5,4)+K10(3,2) K9(5,5)+K10(3,3) K9(5,6)+K10(3,4) K10(3,5) K10(3,6);
0 0 0 0 0 0 0 0 0 0 0 0 K9(6,1) K9(6,2) K9(6,3)+K10(4,1) K9(6,4)+K10(4,2) K9(6,5)+K10(4,3) K9(6,6)+K10(4,4) K10(4,5) K10(4,6);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 K10(5,1) K10(5,2) K10(5,3) K10(5,4) K10(5,5) K10(5,6);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 K10(6,1) K10(6,2) K10(6,3) K10(6,4) K10(6,5) K10(6,6)];
Fii=Kp(:,18)*up22+Kp(:,20)*up24;
Kini = [K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6);
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6);
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4);
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4);
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2)];
% Define the applied load
Fi = [P];
F=Fi-Fii;F=[F(1,1);F(2,1);F(3,1);F(4,1);F(5,1);F(6,1);F(7,1);F(8,1);F(9,1);F(10,1);F(11,1);F(12,1);F(13,1);F(14,1);F(15,1);F(16,1)];
it = 0; % initialize iteration count
residual = 100; % initialize residual
while (residual > tolerance)
XY1=[XY1i(1) XY1i(2)]; % [x y] Point 1 Coordinate
XY2=[XY2i(1) XY2i(2)]; % [x y] Point 2 Coordinate
XY3=[XY3i(1) XY3i(2)]; % [x y] Point 3 Coordinate
XY4=[XY4i(1) XY4i(2)]; % [x y] Point 4 Coordinate
XY5=[XY5i(1) XY5i(2)]; % [x y] Point 5 Coordinate
XY6=[XY6i(1) XY6i(2)]; % [x y] Point 6 Coordinate
XY7=[XY7i(1) XY7i(2)]; % [x y] Point 7 Coordinate
XY8=[XY8i(1) XY8i(2)]; % [x y] Point 8 Coordinate
XY9=[XY9i(1) XY9i(2)]; % [x y] Point 9 Coordinate
XY10=[XY10i(1) XY10i(2)]; % [x y] Point 10 Coordinate
XY11=[XY11i(1) XY11i(2)]; % [x y] Point 11 Coordinate
XY12=[XY12i(1) XY12i(2)]; % [x y] Point 12 Coordinate
B1e1=XY2(2)-XY3(2);B2e1=XY3(2)-XY1(2);B3e1=XY1(2)-XY2(2);
G1e1=XY2(1)-XY3(1);G2e1=XY3(1)-XY1(1);G3e1=XY1(1)-XY2(1);
a1=.5*(XY1(1)*B1e1+XY2(1)*B2e1+XY3(1)*B3e1);a1=abs(a1);
B1=1/(2*a1)*[B1e1 0 B2e1 0 B3e1 0;
0 G1e1 0 G2e1 0 G3e1;
G1e1 B1e1 G2e1 B2e1 G3e1 B3e1];
B1e2=XY3(2)-XY4(2);B2e2=XY4(2)-XY2(2);B3e2=XY2(2)-XY3(2);
G1e2=XY3(1)-XY4(1);G2e2=XY4(1)-XY2(1);G3e2=XY2(1)-XY3(1);
a2=.5*(XY2(1)*B1e2+XY3(1)*B2e2+XY4(1)*B3e2);a2=abs(a2);
B2=1/(2*a2)*[B1e2 0 B2e2 0 B3e2 0;
0 G1e2 0 G2e2 0 G3e2;
G1e2 B1e2 G2e2 B2e2 G3e2 B3e2];
B1e3=XY4(2)-XY5(2);B2e3=XY5(2)-XY3(2);B3e3=XY3(2)-XY4(2);
G1e3=XY4(1)-XY5(1);G2e3=XY5(1)-XY3(1);G3e3=XY3(1)-XY4(1);
a3=.5*(XY3(1)*B1e3+XY4(1)*B2e3+XY5(1)*B3e3);a3=abs(a3);
B3=1/(2*a3)*[B1e3 0 B2e3 0 B3e3 0;
0 G1e3 0 G2e3 0 G3e3;
G1e3 B1e3 G2e3 B2e3 G3e1 B3e3];
B1e4=XY5(2)-XY6(2);B2e4=XY6(2)-XY4(2);B3e4=XY4(2)-XY5(2);
G1e4=XY5(1)-XY6(1);G2e4=XY6(1)-XY4(1);G3e4=XY4(1)-XY5(1);
a4=.5*(XY4(1)*B1e4+XY5(1)*B2e4+XY6(1)*B3e4);a4=abs(a4);
B4=1/(2*a4)*[B1e4 0 B2e4 0 B3e4 0;

3. 0 G1e4 0 G2e4 0 G3e4;
G1e4 B1e4 G2e4 B2e4 G3e4 B3e4];
B1e5=XY6(2)-XY7(2);B2e5=XY7(2)-XY5(2);B3e5=XY5(2)-XY6(2);
G1e5=XY6(1)-XY7(1);G2e5=XY7(1)-XY5(1);G3e5=XY5(1)-XY6(1);
a5=.5*(XY5(1)*B1e5+XY6(1)*B2e5+XY7(1)*B3e5);a5=abs(a5);
B5=1/(2*a5)*[B1e5 0 B2e5 0 B3e5 0;
0 G1e5 0 G2e5 0 G3e5;
G1e5 B1e5 G2e5 B2e5 G3e5 B3e5];
B1e6=XY7(2)-XY8(2);B2e6=XY8(2)-XY6(2);B3e6=XY6(2)-XY7(2);
G1e6=XY7(1)-XY8(1);G2e6=XY8(1)-XY6(1);G3e6=XY6(1)-XY7(1);
a6=.5*(XY6(1)*B1e6+XY7(1)*B2e6+XY8(1)*B3e6);a6=abs(a6);
B6=1/(2*a6)*[B1e6 0 B2e6 0 B3e6 0;
0 G1e6 0 G2e6 0 G3e6;
G1e6 B1e6 G2e6 B2e6 G3e6 B3e6];
B1e7=XY8(2)-XY9(2);B2e7=XY9(2)-XY7(2);B3e7=XY7(2)-XY8(2);
G1e7=XY8(1)-XY9(1);G2e7=XY9(1)-XY7(1);G3e7=XY7(1)-XY8(1);
a7=.5*(XY7(1)*B1e7+XY8(1)*B2e7+XY9(1)*B3e7);a7=abs(a7);
B7=1/(2*a1)*[B1e7 0 B2e7 0 B3e7 0;
0 G1e7 0 G2e7 0 G3e7;
G1e7 B1e7 G2e7 B2e7 G3e7 B3e7];
B1e8=XY9(2)-XY10(2);B2e8=XY10(2)-XY8(2);B3e8=XY8(2)-XY9(2);
G1e8=XY9(1)-XY10(1);G2e8=XY10(1)-XY8(1);G3e8=XY8(1)-XY9(1);
a8=.5*(XY8(1)*B1e8+XY9(1)*B2e8+XY10(1)*B3e8);a8=abs(a8);
B8=1/(2*a8)*[B1e8 0 B2e8 0 B3e8 0;
0 G1e8 0 G2e8 0 G3e8;
G1e8 B1e8 G2e8 B2e8 G3e8 B3e8];
B1e9=XY10(2)-XY11(2);B2e9=XY11(2)-XY9(2);B3e9=XY9(2)-XY10(2);
G1e9=XY10(1)-XY11(1);G2e9=XY11(1)-XY9(1);G3e9=XY9(1)-XY10(1);
a9=.5*(XY9(1)*B1e9+XY10(1)*B2e9+XY11(1)*B3e9);a9=abs(a9);
B9=1/(2*a1)*[B1e9 0 B2e9 0 B3e9 0;
0 G1e9 0 G2e9 0 G3e9;
G1e9 B1e9 G2e9 B2e9 G3e9 B3e9];
B1e10=XY11(2)-XY12(2);B2e10=XY12(2)-XY10(2);B3e10=XY10(2)-XY11(2);
G1e10=XY11(1)-XY12(1);G2e10=XY12(1)-XY10(1);G3e10=XY10(1)-XY12(1);
a10=.5*(XY10(1)*B1e10+XY11(1)*B2e10+XY12(1)*B3e10);a10=abs(a10);
B10=1/(2*a10)*[B1e10 0 B2e10 0 B3e10 0;
0 G1e10 0 G2e10 0 G3e10;
G1e10 B1e10 G2e10 B2e10 G3e10 B3e10];
D=(E/(1-V^2))*[1 V 0;
V 1 0;
0 0 .5*(1-V)];
K1=B1'*D*a1*T*B1;
K2=B2'*D*a2*T*B2;
K3=B3'*D*a3*T*B3;
K4=B4'*D*a4*T*B4;
K5=B5'*D*a5*T*B5;
K6=B6'*D*a6*T*B6;
K7=B7'*D*a7*T*B7;
K8=B8'*D*a8*T*B8;
K9=B9'*D*a9*T*B9;
K10=B10'*D*a10*T*B10;
K = [K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6);
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6);
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4);
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4);
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2)];
f=K*u-F;
%calculate du1 & du2
du = Kini^-1 *(-f);
%Calculate the residual (internal-external force deviation)
residual = max(abs(du)); % evaluate residual
it = it + 1; % increment iteration count
if it == itermax
fprintf('(-)For increment %1.0f trail iterations reached to Ultimate %1.0fn',i,it)
disp(' ## The solution for this step is not converged ##');
break
end
u = u+du; % update u
end
% iteration control
if it < itermax
fprintf('(+)Increment %1.0f : It is converged in %1.0f iterationsn',i,it);
end
DU1(i)=residual;I1(i)=i;IT1(i)=it;
sU(:,i)=u;% Displacement of each node
sU22(i)=up22;sU24(i)=up24;
s1EleF(:,i)=K1*[0;0;0;0;u(1);u(2)];% Nodal force in element 1
s2EleF(:,i)=K2*[0;0;u(1);u(2);u(3);u(4)];% Nodal force in element 2
s3EleF(:,i)=K3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Nodal force in element 3
s4EleF(:,i)=K4*[u(3);u(4);u(5);u(6);u(7);u(8)];% Nodal force in element 4
s5EleF(:,i)=K5*[u(5);u(6);u(7);u(8);u(9);u(10)];% Nodal force in element 5
s6EleF(:,i)=K6*[u(7);u(8);u(9);u(10);u(11);u(12)];% Nodal force in element 6
s7EleF(:,i)=K7*[u(9);u(10);u(11);u(12);u(13);u(14)];% Nodal force in element 7
s8EleF(:,i)=K8*[u(11);u(12);u(13);u(14);u(15);u(16)];% Nodal force in element 8
s9EleF(:,i)=K9*[u(13);u(14);u(15);u(16);0;up22];% Nodal force in element 9
s10EleF(:,i)=K10*[u(15);u(16);0;up22;0;up24];% Nodal force in element 10
s1Strain(:,i)=B1*[0;0;0;0;u(1);u(2)];% Strain in element 1
s1Stress(:,i)=D*B1*[0;0;0;0;u(1);u(2)];% Stress in element 1
s2Strain(:,i)=B2*[0;0;u(1);u(2);u(3);u(4)];% Strain in element 2
s2Stress(:,i)=D*B2*[0;0;u(1);u(2);u(3);u(4)];% Stress in element 2
s3Strain(:,i)=B3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Strain in element 3
s3Stress(:,i)=D*B3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Stress in element 3
s4Strain(:,i)=B1*[u(3);u(4);u(5);u(6);u(7);u(8)];% Strain in element 4
s4Stress(:,i)=D*B1*[u(3);u(4);u(5);u(6);u(7);u(8)];% Stress in element 4
s5Strain(:,i)=B1*[u(5);u(6);u(7);u(8);u(9);u(10)];% Strain in element 5
s5Stress(:,i)=D*B1*[u(5);u(6);u(7);u(8);u(9);u(10)];% Stress in element 5
s6Strain(:,i)=B1*[u(7);u(8);u(9);u(10);u(11);u(12)];% Strain in element 6
s6Stress(:,i)=D*B1*[u(7);u(8);u(9);u(10);u(11);u(12)];% Stress in element 6
s7Strain(:,i)=B1*[u(9);u(10);u(11);u(12);u(13);u(14)];% Strain in element 7
s7Stress(:,i)=D*B1*[u(9);u(10);u(11);u(12);u(13);u(14)];% Stress in element 7
s8Strain(:,i)=B1*[u(11);u(12);u(13);u(14);u(15);u(16)];% Strain in element 8
s8Stress(:,i)=D*B1*[u(11);u(12);u(13);u(14);u(15);u(16)];% Stress in element 8
s9Strain(:,i)=B1*[u(13);u(14);u(15);u(16);0;up22];% Strain in element 9
s9Stress(:,i)=D*B1*[u(13);u(14);u(15);u(16);0;up22];% Stress in element 9
s10Strain(:,i)=B1*[u(15);u(16);0;up22;0;up24];% Strain in element 10
s10Stress(:,i)=D*B1*[u(15);u(16);0;up22;0;up24];% Stress in element 10
s1PriSt1(i)=.5*(s1Stress(1,i)+s1Stress(2,i))+((.5*(s1Stress(1,i)-s1Stress(2,i)))^2+s1Stress(3,i)^2)^.5; %Principal stress of 1
s1PriSt2(i)=.5*(s1Stress(1,i)+s1Stress(2,i))-((.5*(s1Stress(1,i)-s1Stress(2,i)))^2+s1Stress(3,i)^2)^.5; %Principal stress of 2
s1PriAng(i)=atan((2*s1Stress(3,i))/(s1Stress(1,i)-s1Stress(2,i))); % Principal angle of element 1
s1Von(i)=(1/(2)^.5)*(s1PriSt1(i)-s1PriSt2(i));% Maximum distortion energy (Von mises stress) of element 1
s2PriSt1(i)=.5*(s2Stress(1,i)+s2Stress(2,i))+((.5*(s2Stress(1,i)-s2Stress(2,i)))^2+s2Stress(3,i)^2)^.5; %Principal stress of 1
s2PriSt2(i)=.5*(s2Stress(1,i)+s2Stress(2,i))-((.5*(s2Stress(1,i)-s2Stress(2,i)))^2+s2Stress(3,i)^2)^.5; %Principal stress of 2
s2PriAng(i)=atan((2*s2Stress(3,i))/(s2Stress(1,i)-s2Stress(2,i))); % Principal angle of element 2
s2Von(i)=(1/(2)^.5)*(s2PriSt1(i)-s2PriSt2(i));% Maximum distortion energy (Von mises stress) of element 2
s3PriSt1(i)=.5*(s3Stress(1,i)+s3Stress(2,i))+((.5*(s3Stress(1,i)-s3Stress(2,i)))^2+s3Stress(3,i)^2)^.5; %Principal stress of 1
s3PriSt2(i)=.5*(s3Stress(1,i)+s3Stress(2,i))-((.5*(s3Stress(1,i)-s3Stress(2,i)))^2+s3Stress(3,i)^2)^.5; %Principal stress of 2
s3PriAng(i)=atan((2*s3Stress(3,i))/(s3Stress(1,i)-s3Stress(2,i))); % Principal angle of element 3
s3Von(i)=(1/(2)^.5)*(s3PriSt1(i)-s3PriSt2(i));% Maximum distortion energy (Von mises stress) of element 3
s4PriSt1(i)=.5*(s4Stress(1,i)+s4Stress(2,i))+((.5*(s4Stress(1,i)-s4Stress(2,i)))^2+s4Stress(3,i)^2)^.5; %Principal stress of 1
s4PriSt2(i)=.5*(s4Stress(1,i)+s4Stress(2,i))-((.5*(s4Stress(1,i)-s4Stress(2,i)))^2+s4Stress(3,i)^2)^.5; %Principal stress of 2
s4PriAng(i)=atan((2*s4Stress(3,i))/(s4Stress(1,i)-s4Stress(2,i))); % Principal angle of element 4
s4Von(i)=(1/(2)^.5)*(s4PriSt1(i)-s4PriSt2(i));% Maximum distortion energy (Von mises stress) of element 4
sBSH(i)=-[s1EleF(1,i)+s2EleF(1,i)+s1EleF(3,i)];% Base shear based of [DOF(1)+DOF(3)]
if abs(up22) >= D22max;disp(' ## Displacement at [DOF (22)] reached to Ultimate Displacement ##');break;end
end
%XXi10=[XY1i(1),XY2i(1),XY5i(1),XY4i(1),XY1i(1)];YYi10=[XY1i(2),XY2i(2),XY5i(2),XY4i(2),XY1i(2)];
%XXi11=[XY1i(1),XY2i(1)+sU(1,15),XY5i(1)+sU(2,.25*m),XY4i(1),XY1i(1)];YYi11=[XY1i(2),XY2i(2),XY5i(2)+sU10(.25*m),XY4i(2),XY1i(2)];
%XXi12=[XY1i(1),XY2i(1)+sU(1,30),XY5i(1)+sU(2,.5*m),XY4i(1),XY1i(1)];YYi12=[XY1i(2),XY2i(2),XY5i(2)+sU10(.5*m),XY4i(2),XY1i(2)];
%XXi13=[XY1i(1),XY2i(1)+sU(1,45),XY5i(1)+sU(2,.75*m),XY4i(1),XY1i(1)];YYi13=[XY1i(2),XY2i(2),XY5i(2)+sU10(.75*m),XY4i(2),XY1i(2)];
%XXi14=[XY1i(1),XY2i(1)+sU(1,60),XY5i(1)+sU(2,m),XY4i(1),XY1i(1)];YYi14=[XY1i(2),XY2i(2),XY5i(2)+sU10(m),XY4i(2),XY1i(2)];
XXi10=[XY1i(1),XY3i(1)+sU(1,1),XY5i(1)+sU(5,1),XY7i(1)+sU(9,1),XY9i(1)+sU(13,1),XY11i(1),XY12i(1),XY10i(1)+sU(15,1),XY8i(1)+sU(11,1),XY6i(1)+sU(7,1),XY4i(1)+sU(3,1),XY2i(1)];
YYi10=[XY1i(2),XY3i(2)+sU(2,1),XY5i(2)+sU(6,1),XY7i(2)+sU(10,1),XY9i(2)+sU(14,1),XY11i(2)+sU22(1),XY12i(2)+sU24(1),XY10i(2)+sU(16,1),XY8i(2)+sU(12,1),XY6i(2)+sU(8,1),XY4i(2)+sU(4,1),XY2i(2)];
XXi11=[XY1i(1),XY3i(1)+sU(1,.25*m),XY5i(1)+sU(5,.25*m),XY7i(1)+sU(9,.25*m),XY9i(1)+sU(13,.25*m),XY11i(1),XY12i(1),XY10i(1)+sU(15,.25*m),XY8i(1)+sU(11,.25*m),XY6i(1)+sU(7,.25*m),XY4i(1)+sU(3,.25*m),XY2i(1)];
YYi11=[XY1i(2),XY3i(2)+sU(2,.25*m),XY5i(2)+sU(6,.25*m),XY7i(2)+sU(10,.25*m),XY9i(2)+sU(14,.25*m),XY11i(2)+sU22(.25*m),XY12i(2)+sU24(.25*m),XY10i(2)+sU(16,.25*m),XY8i(2)+sU(12,.25*m),XY6i(2)+sU(8,.25*m),XY4i(2)+sU(4,.25*m),XY2i(2)];
XXi12=[XY1i(1),XY3i(1)+sU(1,.5*m),XY5i(1)+sU(5,.5*m),XY7i(1)+sU(9,.5*m),XY9i(1)+sU(13,.5*m),XY11i(1),XY12i(1),XY10i(1)+sU(15,.5*m),XY8i(1)+sU(11,.5*m),XY6i(1)+sU(7,.5*m),XY4i(1)+sU(3,.5*m),XY2i(1)];
YYi12=[XY1i(2),XY3i(2)+sU(2,.5*m),XY5i(2)+sU(6,.5*m),XY7i(2)+sU(10,.5*m),XY9i(2)+sU(14,.5*m),XY11i(2)+sU22(.5*m),XY12i(2)+sU24(.5*m),XY10i(2)+sU(16,.5*m),XY8i(2)+sU(12,.5*m),XY6i(2)+sU(8,.5*m),XY4i(2)+sU(4,.5*m),XY2i(2)];
XXi13=[XY1i(1),XY3i(1)+sU(1,.75*m),XY5i(1)+sU(5,.75*m),XY7i(1)+sU(9,.75*m),XY9i(1)+sU(13,.75*m),XY11i(1),XY12i(1),XY10i(1)+sU(15,.75*m),XY8i(1)+sU(11,.75*m),XY6i(1)+sU(7,.75*m),XY4i(1)+sU(3,.75*m),XY2i(1)];
YYi13=[XY1i(2),XY3i(2)+sU(2,.75*m),XY5i(2)+sU(6,.75*m),XY7i(2)+sU(10,.75*m),XY9i(2)+sU(14,.75*m),XY11i(2)+sU22(.75*m),XY12i(2)+sU24(.75*m),XY10i(2)+sU(16,.75*m),XY8i(2)+sU(12,.75*m),XY6i(2)+sU(8,.75*m),XY4i(2)+sU(4,.75*m),XY2i(2)];
XXi14=[XY1i(1),XY3i(1)+sU(1,m),XY5i(1)+sU(5,m),XY7i(1)+sU(9,m),XY9i(1)+sU(13,m),XY11i(1),XY12i(1),XY10i(1)+sU(15,m),XY8i(1)+sU(11,m),XY6i(1)+sU(7,m),XY4i(1)+sU(3,m),XY2i(1)];
YYi14=[XY1i(2),XY3i(2)+sU(2,m),XY5i(2)+sU(6,m),XY7i(2)+sU(10,m),XY9i(2)+sU(14,m),XY11i(2)+sU22(m),XY12i(2)+sU24(m),XY10i(2)+sU(16,m),XY8i(2)+sU(12,m),XY6i(2)+sU(8,m),XY4i(2)+sU(4,m),XY2i(2)];
%% Large Displacement Analysis
disp('###############################');
disp('# Large Displacement Analysis #');
disp('###############################');
u = zeros(16,1);% initial guess value
for i=1:m;
up22=D22*i;
up24=D24*i;
XY1=[XY1i(1) XY1i(2)]; % [x y] Point 1 Coordinate
XY2=[XY2i(1) XY2i(2)]; % [x y] Point 2 Coordinate
XY3=[XY3i(1)+u(1) XY3i(2)+u(2)]; % [x y] Point 3 Coordinate
XY4=[XY4i(1)+u(3) XY4i(2)+u(4)]; % [x y] Point 4 Coordinate
XY5=[XY5i(1)+u(5) XY5i(2)+u(6)]; % [x y] Point 5 Coordinate
XY6=[XY6i(1)+u(7) XY6i(2)+u(8)]; % [x y] Point 6 Coordinate
XY7=[XY7i(1)+u(9) XY7i(2)+u(10)]; % [x y] Point 7 Coordinate
XY8=[XY8i(1)+u(11) XY8i(2)+u(12)]; % [x y] Point 8 Coordinate
XY9=[XY9i(1)+u(13) XY9i(2)+u(14)]; % [x y] Point 9 Coordinate
XY10=[XY10i(1)+u(15) XY10i(2)+u(16)]; % [x y] Point 10 Coordinate
XY11=[XY11i(1) XY11i(2)+up22]; % [x y] Point 11 Coordinate
XY12=[XY12i(1) XY12i(2)+up24]; % [x y] Point 12 Coordinate
B1e1=XY2(2)-XY3(2);B2e1=XY3(2)-XY1(2);B3e1=XY1(2)-XY2(2);
G1e1=XY2(1)-XY3(1);G2e1=XY3(1)-XY1(1);G3e1=XY1(1)-XY2(1);
a1=.5*(XY1(1)*B1e1+XY2(1)*B2e1+XY3(1)*B3e1);a1=abs(a1);
B1=1/(2*a1)*[B1e1 0 B2e1 0 B3e1 0;
0 G1e1 0 G2e1 0 G3e1;
G1e1 B1e1 G2e1 B2e1 G3e1 B3e1];
B1e2=XY3(2)-XY4(2);B2e2=XY4(2)-XY2(2);B3e2=XY2(2)-XY3(2);
G1e2=XY3(1)-XY4(1);G2e2=XY4(1)-XY2(1);G3e2=XY2(1)-XY3(1);
a2=.5*(XY2(1)*B1e2+XY3(1)*B2e2+XY4(1)*B3e2);a2=abs(a2);
B2=1/(2*a2)*[B1e2 0 B2e2 0 B3e2 0;
0 G1e2 0 G2e2 0 G3e2;
G1e2 B1e2 G2e2 B2e2 G3e2 B3e2];
B1e3=XY4(2)-XY5(2);B2e3=XY5(2)-XY3(2);B3e3=XY3(2)-XY4(2);
G1e3=XY4(1)-XY5(1);G2e3=XY5(1)-XY3(1);G3e3=XY3(1)-XY4(1);
a3=.5*(XY3(1)*B1e3+XY4(1)*B2e3+XY5(1)*B3e3);a3=abs(a3);
B3=1/(2*a3)*[B1e3 0 B2e3 0 B3e3 0;
0 G1e3 0 G2e3 0 G3e3;
G1e3 B1e3 G2e3 B2e3 G3e1 B3e3];
B1e4=XY5(2)-XY6(2);B2e4=XY6(2)-XY4(2);B3e4=XY4(2)-XY5(2);
G1e4=XY5(1)-XY6(1);G2e4=XY6(1)-XY4(1);G3e4=XY4(1)-XY5(1);
a4=.5*(XY4(1)*B1e4+XY5(1)*B2e4+XY6(1)*B3e4);a4=abs(a4);
B4=1/(2*a4)*[B1e4 0 B2e4 0 B3e4 0;
0 G1e4 0 G2e4 0 G3e4;
G1e4 B1e4 G2e4 B2e4 G3e4 B3e4];
B1e5=XY6(2)-XY7(2);B2e5=XY7(2)-XY5(2);B3e5=XY5(2)-XY6(2);
G1e5=XY6(1)-XY7(1);G2e5=XY7(1)-XY5(1);G3e5=XY5(1)-XY6(1);
a5=.5*(XY5(1)*B1e5+XY6(1)*B2e5+XY7(1)*B3e5);a5=abs(a5);
B5=1/(2*a5)*[B1e5 0 B2e5 0 B3e5 0;
0 G1e5 0 G2e5 0 G3e5;
G1e5 B1e5 G2e5 B2e5 G3e5 B3e5];
B1e6=XY7(2)-XY8(2);B2e6=XY8(2)-XY6(2);B3e6=XY6(2)-XY7(2);
G1e6=XY7(1)-XY8(1);G2e6=XY8(1)-XY6(1);G3e6=XY6(1)-XY7(1);
a6=.5*(XY6(1)*B1e6+XY7(1)*B2e6+XY8(1)*B3e6);a6=abs(a6);
B6=1/(2*a6)*[B1e6 0 B2e6 0 B3e6 0;
0 G1e6 0 G2e6 0 G3e6;

4. G1e6 B1e6 G2e6 B2e6 G3e6 B3e6];
B1e7=XY8(2)-XY9(2);B2e7=XY9(2)-XY7(2);B3e7=XY7(2)-XY8(2);
G1e7=XY8(1)-XY9(1);G2e7=XY9(1)-XY7(1);G3e7=XY7(1)-XY8(1);
a7=.5*(XY7(1)*B1e7+XY8(1)*B2e7+XY9(1)*B3e7);a7=abs(a7);
B7=1/(2*a1)*[B1e7 0 B2e7 0 B3e7 0;
0 G1e7 0 G2e7 0 G3e7;
G1e7 B1e7 G2e7 B2e7 G3e7 B3e7];
B1e8=XY9(2)-XY10(2);B2e8=XY10(2)-XY8(2);B3e8=XY8(2)-XY9(2);
G1e8=XY9(1)-XY10(1);G2e8=XY10(1)-XY8(1);G3e8=XY8(1)-XY9(1);
a8=.5*(XY8(1)*B1e8+XY9(1)*B2e8+XY10(1)*B3e8);a8=abs(a8);
B8=1/(2*a8)*[B1e8 0 B2e8 0 B3e8 0;
0 G1e8 0 G2e8 0 G3e8;
G1e8 B1e8 G2e8 B2e8 G3e8 B3e8];
B1e9=XY10(2)-XY11(2);B2e9=XY11(2)-XY9(2);B3e9=XY9(2)-XY10(2);
G1e9=XY10(1)-XY11(1);G2e9=XY11(1)-XY9(1);G3e9=XY9(1)-XY10(1);
a9=.5*(XY9(1)*B1e9+XY10(1)*B2e9+XY11(1)*B3e9);a9=abs(a9);
B9=1/(2*a1)*[B1e9 0 B2e9 0 B3e9 0;
0 G1e9 0 G2e9 0 G3e9;
G1e9 B1e9 G2e9 B2e9 G3e9 B3e9];
B1e10=XY11(2)-XY12(2);B2e10=XY12(2)-XY10(2);B3e10=XY10(2)-XY11(2);
G1e10=XY11(1)-XY12(1);G2e10=XY12(1)-XY10(1);G3e10=XY10(1)-XY12(1);
a10=.5*(XY10(1)*B1e10+XY11(1)*B2e10+XY12(1)*B3e10);a10=abs(a10);
B10=1/(2*a10)*[B1e10 0 B2e10 0 B3e10 0;
0 G1e10 0 G2e10 0 G3e10;
G1e10 B1e10 G2e10 B2e10 G3e10 B3e10];
D=(E/(1-V^2))*[1 V 0;
V 1 0;
0 0 .5*(1-V)];
K1=B1'*D*a1*T*B1;
K2=B2'*D*a2*T*B2;
K3=B3'*D*a3*T*B3;
K4=B4'*D*a4*T*B4;
K5=B5'*D*a5*T*B5;
K6=B6'*D*a6*T*B6;
K7=B7'*D*a7*T*B7;
K8=B8'*D*a8*T*B8;
K9=B9'*D*a9*T*B9;
K10=B10'*D*a10*T*B10;
%% 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24
Kp=[K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0 0 0 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0 0 0 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6) 0 0 0 0;
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6) 0 0 0 0;
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4) K9(1,5) K9(1,6) 0 0;
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4) K9(2,5) K9(2,6) 0 0;
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2) K9(3,5)+K10(1,3) K9(3,6)+K10(1,4) K10(1,5) K10(1,6);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2) K9(4,5)+K10(2,3) K9(4,6)+K10(2,4) K10(2,5) K10(2,6);
0 0 0 0 0 0 0 0 0 0 0 0 K9(5,1) K9(5,2) K9(5,3)+K10(3,1) K9(5,4)+K10(3,2) K9(5,5)+K10(3,3) K9(5,6)+K10(3,4) K10(3,5) K10(3,6);
0 0 0 0 0 0 0 0 0 0 0 0 K9(6,1) K9(6,2) K9(6,3)+K10(4,1) K9(6,4)+K10(4,2) K9(6,5)+K10(4,3) K9(6,6)+K10(4,4) K10(4,5) K10(4,6);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 K10(5,1) K10(5,2) K10(5,3) K10(5,4) K10(5,5) K10(5,6);
0 0 0 0 0 0 0 0 0 0 0 0 0 0 K10(6,1) K10(6,2) K10(6,3) K10(6,4) K10(6,5) K10(6,6)];
Fii=Kp(:,18)*up22+Kp(:,20)*up24;
Kini = [K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6);
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6);
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4);
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4);
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2)];
% Define the applied load
Fi = [P];
F=Fi-Fii;F=[F(1,1);F(2,1);F(3,1);F(4,1);F(5,1);F(6,1);F(7,1);F(8,1);F(9,1);F(10,1);F(11,1);F(12,1);F(13,1);F(14,1);F(15,1);F(16,1)];
it = 0; % initialize iteration count
residual = 100; % initialize residual
while (residual > tolerance)
XY1=[XY1i(1) XY1i(2)]; % [x y] Point 1 Coordinate
XY2=[XY2i(1) XY2i(2)]; % [x y] Point 2 Coordinate
XY3=[XY3i(1)+u(1) XY3i(2)+u(2)]; % [x y] Point 3 Coordinate
XY4=[XY4i(1)+u(3) XY4i(2)+u(4)]; % [x y] Point 4 Coordinate
XY5=[XY5i(1)+u(5) XY5i(2)+u(6)]; % [x y] Point 5 Coordinate
XY6=[XY6i(1)+u(7) XY6i(2)+u(8)]; % [x y] Point 6 Coordinate
XY7=[XY7i(1)+u(9) XY7i(2)+u(10)]; % [x y] Point 7 Coordinate
XY8=[XY8i(1)+u(11) XY8i(2)+u(12)]; % [x y] Point 8 Coordinate
XY9=[XY9i(1)+u(13) XY9i(2)+u(14)]; % [x y] Point 9 Coordinate
XY10=[XY10i(1)+u(15) XY10i(2)+u(16)]; % [x y] Point 10 Coordinate
XY11=[XY11i(1) XY11i(2)+up22]; % [x y] Point 11 Coordinate
XY12=[XY12i(1) XY12i(2)+up24]; % [x y] Point 12 Coordinate
B1e1=XY2(2)-XY3(2);B2e1=XY3(2)-XY1(2);B3e1=XY1(2)-XY2(2);
G1e1=XY2(1)-XY3(1);G2e1=XY3(1)-XY1(1);G3e1=XY1(1)-XY2(1);
a1=.5*(XY1(1)*B1e1+XY2(1)*B2e1+XY3(1)*B3e1);a1=abs(a1);
B1=1/(2*a1)*[B1e1 0 B2e1 0 B3e1 0;
0 G1e1 0 G2e1 0 G3e1;
G1e1 B1e1 G2e1 B2e1 G3e1 B3e1];
B1e2=XY3(2)-XY4(2);B2e2=XY4(2)-XY2(2);B3e2=XY2(2)-XY3(2);
G1e2=XY3(1)-XY4(1);G2e2=XY4(1)-XY2(1);G3e2=XY2(1)-XY3(1);
a2=.5*(XY2(1)*B1e2+XY3(1)*B2e2+XY4(1)*B3e2);a2=abs(a2);
B2=1/(2*a2)*[B1e2 0 B2e2 0 B3e2 0;
0 G1e2 0 G2e2 0 G3e2;
G1e2 B1e2 G2e2 B2e2 G3e2 B3e2];
B1e3=XY4(2)-XY5(2);B2e3=XY5(2)-XY3(2);B3e3=XY3(2)-XY4(2);
G1e3=XY4(1)-XY5(1);G2e3=XY5(1)-XY3(1);G3e3=XY3(1)-XY4(1);
a3=.5*(XY3(1)*B1e3+XY4(1)*B2e3+XY5(1)*B3e3);a3=abs(a3);
B3=1/(2*a3)*[B1e3 0 B2e3 0 B3e3 0;
0 G1e3 0 G2e3 0 G3e3;
G1e3 B1e3 G2e3 B2e3 G3e1 B3e3];
B1e4=XY5(2)-XY6(2);B2e4=XY6(2)-XY4(2);B3e4=XY4(2)-XY5(2);
G1e4=XY5(1)-XY6(1);G2e4=XY6(1)-XY4(1);G3e4=XY4(1)-XY5(1);
a4=.5*(XY4(1)*B1e4+XY5(1)*B2e4+XY6(1)*B3e4);a4=abs(a4);
B4=1/(2*a4)*[B1e4 0 B2e4 0 B3e4 0;
0 G1e4 0 G2e4 0 G3e4;
G1e4 B1e4 G2e4 B2e4 G3e4 B3e4];
B1e5=XY6(2)-XY7(2);B2e5=XY7(2)-XY5(2);B3e5=XY5(2)-XY6(2);
G1e5=XY6(1)-XY7(1);G2e5=XY7(1)-XY5(1);G3e5=XY5(1)-XY6(1);
a5=.5*(XY5(1)*B1e5+XY6(1)*B2e5+XY7(1)*B3e5);a5=abs(a5);
B5=1/(2*a5)*[B1e5 0 B2e5 0 B3e5 0;
0 G1e5 0 G2e5 0 G3e5;
G1e5 B1e5 G2e5 B2e5 G3e5 B3e5];
B1e6=XY7(2)-XY8(2);B2e6=XY8(2)-XY6(2);B3e6=XY6(2)-XY7(2);
G1e6=XY7(1)-XY8(1);G2e6=XY8(1)-XY6(1);G3e6=XY6(1)-XY7(1);
a6=.5*(XY6(1)*B1e6+XY7(1)*B2e6+XY8(1)*B3e6);a6=abs(a6);
B6=1/(2*a6)*[B1e6 0 B2e6 0 B3e6 0;
0 G1e6 0 G2e6 0 G3e6;
G1e6 B1e6 G2e6 B2e6 G3e6 B3e6];
B1e7=XY8(2)-XY9(2);B2e7=XY9(2)-XY7(2);B3e7=XY7(2)-XY8(2);
G1e7=XY8(1)-XY9(1);G2e7=XY9(1)-XY7(1);G3e7=XY7(1)-XY8(1);
a7=.5*(XY7(1)*B1e7+XY8(1)*B2e7+XY9(1)*B3e7);a7=abs(a7);
B7=1/(2*a1)*[B1e7 0 B2e7 0 B3e7 0;
0 G1e7 0 G2e7 0 G3e7;
G1e7 B1e7 G2e7 B2e7 G3e7 B3e7];
B1e8=XY9(2)-XY10(2);B2e8=XY10(2)-XY8(2);B3e8=XY8(2)-XY9(2);
G1e8=XY9(1)-XY10(1);G2e8=XY10(1)-XY8(1);G3e8=XY8(1)-XY9(1);
a8=.5*(XY8(1)*B1e8+XY9(1)*B2e8+XY10(1)*B3e8);a8=abs(a8);
B8=1/(2*a8)*[B1e8 0 B2e8 0 B3e8 0;
0 G1e8 0 G2e8 0 G3e8;
G1e8 B1e8 G2e8 B2e8 G3e8 B3e8];
B1e9=XY10(2)-XY11(2);B2e9=XY11(2)-XY9(2);B3e9=XY9(2)-XY10(2);
G1e9=XY10(1)-XY11(1);G2e9=XY11(1)-XY9(1);G3e9=XY9(1)-XY10(1);
a9=.5*(XY9(1)*B1e9+XY10(1)*B2e9+XY11(1)*B3e9);a9=abs(a9);
B9=1/(2*a1)*[B1e9 0 B2e9 0 B3e9 0;
0 G1e9 0 G2e9 0 G3e9;
G1e9 B1e9 G2e9 B2e9 G3e9 B3e9];
B1e10=XY11(2)-XY12(2);B2e10=XY12(2)-XY10(2);B3e10=XY10(2)-XY11(2);
G1e10=XY11(1)-XY12(1);G2e10=XY12(1)-XY10(1);G3e10=XY10(1)-XY12(1);
a10=.5*(XY10(1)*B1e10+XY11(1)*B2e10+XY12(1)*B3e10);a10=abs(a10);
B10=1/(2*a10)*[B1e10 0 B2e10 0 B3e10 0;
0 G1e10 0 G2e10 0 G3e10;
G1e10 B1e10 G2e10 B2e10 G3e10 B3e10];
D=(E/(1-V^2))*[1 V 0;
V 1 0;
0 0 .5*(1-V)];
K1=B1'*D*a1*T*B1;
K2=B2'*D*a2*T*B2;
K3=B3'*D*a3*T*B3;
K4=B4'*D*a4*T*B4;
K5=B5'*D*a5*T*B5;
K6=B6'*D*a6*T*B6;
K7=B7'*D*a7*T*B7;
K8=B8'*D*a8*T*B8;
K9=B9'*D*a9*T*B9;
K10=B10'*D*a10*T*B10;
K = [K1(5,5)+K2(3,3)+K3(1,1) K1(5,6)+K2(3,4)+K3(1,2) K2(3,5)+K3(1,3) K2(3,6)+K3(1,4) K3(1,5) K3(1,6) 0 0 0 0 0 0 0 0 0 0;
K1(6,5)+K2(4,3)+K3(2,1) K1(6,6)+K2(4,4)+K3(2,2) K2(4,5)+K3(2,3) K2(4,6)+K3(2,4) K3(2,5) K3(2,6) 0 0 0 0 0 0 0 0 0 0;
K2(5,3)+K3(3,1) K2(5,4)+K3(3,2) K2(5,5)+K3(3,3)+K4(1,1) K2(5,6)+K3(3,4)+K4(1,2) K3(3,5)+K4(1,3) K3(3,6)+K4(1,4) K4(1,5) K4(1,6) 0 0 0 0 0 0 0 0;
K2(6,3)+K3(4,1) K2(6,4)+K3(4,2) K2(6,5)+K3(4,3)+K4(2,1) K2(6,6)+K3(4,4)+K4(2,2) K3(4,5)+K4(2,3) K3(4,6)+K4(2,4) K4(2,5) K4(2,6) 0 0 0 0 0 0 0 0;
K3(5,1) K3(5,2) K3(5,3)+K4(3,1) K3(5,4)+K4(3,2) K3(5,5)+K4(3,3)+K5(1,1) K3(5,6)+K4(3,4)+K5(1,2) K4(3,5)+K5(1,3) K4(3,6)+K5(1,4) K5(1,5) K5(1,6) 0 0 0 0 0 0;
K3(6,1) K3(6,2) K3(6,3)+K4(4,1) K3(6,4)+K4(4,2) K3(6,5)+K4(4,3)+K5(2,1) K3(6,6)+K4(4,4)+K5(2,2) K4(4,5)+K5(2,3) K4(4,6)+K5(2,4) K5(2,5) K5(2,6) 0 0 0 0 0 0;
0 0 K4(5,1) K4(5,2) K4(5,3)+K5(3,1) K4(5,4)+K5(3,2) K4(5,5)+K5(3,3)+K6(1,1) K4(5,6)+K5(3,4)+K6(1,2) K5(3,5)+K6(1,3) K5(3,6)+K6(1,4) K6(1,5) K6(1,6) 0 0 0 0;
0 0 K4(6,1) K4(6,2) K4(6,3)+K5(4,1) K4(6,4)+K5(4,2) K4(6,5)+K5(4,3)+K6(2,1) K4(6,6)+K5(4,4)+K6(2,2) K5(4,5)+K6(2,3) K5(4,6)+K6(2,4) K6(2,5) K6(2,6) 0 0 0 0;
0 0 0 0 K5(5,1) K5(5,2) K5(5,3)+K6(3,1) K5(5,4)+K6(3,2) K5(5,5)+K6(3,3)+K7(1,1) K5(5,6)+K6(3,4)+K7(1,2) K6(3,5)+K7(1,3) K6(3,6)+K7(1,4) K7(1,5) K7(1,6) 0 0;
0 0 0 0 K5(6,1) K5(6,2) K5(6,3)+K6(4,1) K5(6,4)+K6(4,2) K5(6,5)+K6(4,3)+K7(2,1) K5(6,6)+K6(4,4)+K7(2,2) K6(4,5)+K7(2,3) K6(4,6)+K7(2,4) K7(2,5) K7(2,6) 0 0;
0 0 0 0 0 0 K6(5,1) K6(5,2) K6(5,3)+K7(3,1) K6(5,4)+K7(3,2) K6(5,5)+K7(3,3)+K8(1,1) K6(5,6)+K7(3,4)+K8(1,2) K7(3,5)+K8(1,3) K7(3,6)+K8(1,4) K8(1,5) K8(1,6);
0 0 0 0 0 0 K6(6,1) K6(6,2) K6(6,3)+K7(4,1) K6(6,4)+K7(4,2) K6(6,5)+K7(4,3)+K8(2,1) K6(6,6)+K7(4,4)+K8(2,2) K7(4,5)+K8(2,3) K7(4,6)+K8(2,4) K8(2,5) K8(2,6);
0 0 0 0 0 0 0 0 K7(5,1) K7(5,2) K7(5,3)+K8(3,1) K7(5,4)+K8(3,2) K7(5,5)+K8(3,3)+K9(1,1) K7(5,6)+K8(3,4)+K9(1,2) K8(3,5)+K9(1,3) K8(3,6)+K9(1,4);
0 0 0 0 0 0 0 0 K7(6,1) K7(6,2) K7(6,3)+K8(4,1) K7(6,4)+K8(4,2) K7(6,5)+K8(4,3)+K9(2,1) K7(6,6)+K8(4,4)+K9(2,2) K8(4,5)+K9(2,3) K8(4,6)+K9(2,4);
0 0 0 0 0 0 0 0 0 0 K8(5,1) K8(5,2) K8(5,3)+K9(3,1) K8(5,4)+K9(3,2) K8(5,5)+K9(3,3)+K10(1,1) K8(5,6)+K9(3,4)+K10(1,2);
0 0 0 0 0 0 0 0 0 0 K8(6,1) K8(6,2) K8(6,3)+K9(4,1) K8(6,4)+K9(4,2) K8(6,5)+K9(4,3)+K10(2,1) K8(6,6)+K9(4,4)+K10(2,2)];
f=K*u-F;
%calculate du1 & du2
du = Kini^-1 *(-f);
%Calculate the residual (internal-external force deviation)
residual = max(abs(du)); % evaluate residual
it = it + 1; % increment iteration count
if it == itermax
fprintf('(-)For increment %1.0f trail iterations reached to Ultimate %1.0fn',i,it)
disp(' ## The solution for this step is not converged ##');
break
end
u = u+du; % update u
end
% iteration control
if it < itermax
fprintf('(+)Increment %1.0f : It is converged in %1.0f iterationsn',i,it);
end
DU2(i)=residual;I2(i)=i;IT2(i)=it;
lU(:,i)=u;% Displacement of each node
lU22(i)=up22;lU24(i)=up24;
l1EleF(:,i)=K1*[0;0;0;0;u(1);u(2)];% Nodal force in element 1
l2EleF(:,i)=K2*[0;0;u(1);u(2);u(3);u(4)];% Nodal force in element 2

5. l3EleF(:,i)=K3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Nodal force in element 3
l4EleF(:,i)=K4*[u(3);u(4);u(5);u(6);u(7);u(8)];% Nodal force in element 4
l5EleF(:,i)=K5*[u(5);u(6);u(7);u(8);u(9);u(10)];% Nodal force in element 5
l6EleF(:,i)=K6*[u(7);u(8);u(9);u(10);u(11);u(12)];% Nodal force in element 6
l7EleF(:,i)=K7*[u(9);u(10);u(11);u(12);u(13);u(14)];% Nodal force in element 7
l8EleF(:,i)=K8*[u(11);u(12);u(13);u(14);u(15);u(16)];% Nodal force in element 8
l9EleF(:,i)=K9*[u(13);u(14);u(15);u(16);0;up22];% Nodal force in element 9
l10EleF(:,i)=K10*[u(15);u(16);0;up22;0;up24];% Nodal force in element 10
l1Strain(:,i)=B1*[0;0;0;0;u(1);u(2)];% Strain in element 1
l1Stress(:,i)=D*B1*[0;0;0;0;u(1);u(2)];% Stress in element 1
l2Strain(:,i)=B2*[0;0;u(1);u(2);u(3);u(4)];% Strain in element 2
l2Stress(:,i)=D*B2*[0;0;u(1);u(2);u(3);u(4)];% Stress in element 2
l3Strain(:,i)=B3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Strain in element 3
l3Stress(:,i)=D*B3*[u(1);u(2);u(3);u(4);u(5);u(6)];% Stress in element 3
l4Strain(:,i)=B1*[u(3);u(4);u(5);u(6);u(7);u(8)];% Strain in element 4
l4Stress(:,i)=D*B1*[u(3);u(4);u(5);u(6);u(7);u(8)];% Stress in element 4
l5Strain(:,i)=B1*[u(5);u(6);u(7);u(8);u(9);u(10)];% Strain in element 5
l5Stress(:,i)=D*B1*[u(5);u(6);u(7);u(8);u(9);u(10)];% Stress in element 5
l6Strain(:,i)=B1*[u(7);u(8);u(9);u(10);u(11);u(12)];% Strain in element 6
l6Stress(:,i)=D*B1*[u(7);u(8);u(9);u(10);u(11);u(12)];% Stress in element 6
l7Strain(:,i)=B1*[u(9);u(10);u(11);u(12);u(13);u(14)];% Strain in element 7
l7Stress(:,i)=D*B1*[u(9);u(10);u(11);u(12);u(13);u(14)];% Stress in element 7
l8Strain(:,i)=B1*[u(11);u(12);u(13);u(14);u(15);u(16)];% Strain in element 8
l8Stress(:,i)=D*B1*[u(11);u(12);u(13);u(14);u(15);u(16)];% Stress in element 8
l9Strain(:,i)=B1*[u(13);u(14);u(15);u(16);0;up22];% Strain in element 9
l9Stress(:,i)=D*B1*[u(13);u(14);u(15);u(16);0;up22];% Stress in element 9
l10Strain(:,i)=B1*[u(15);u(16);0;up22;0;up24];% Strain in element 10
l10Stress(:,i)=D*B1*[u(15);u(16);0;up22;0;up24];% Stress in element 10
l1PriSt1(i)=.5*(s1Stress(1,i)+s1Stress(2,i))+((.5*(s1Stress(1,i)-s1Stress(2,i)))^2+s1Stress(3,i)^2)^.5; %Principal stress of 1
l1PriSt2(i)=.5*(s1Stress(1,i)+s1Stress(2,i))-((.5*(s1Stress(1,i)-s1Stress(2,i)))^2+s1Stress(3,i)^2)^.5; %Principal stress of 2
l1PriAng(i)=atan((2*s1Stress(3,i))/(s1Stress(1,i)-s1Stress(2,i))); % Principal angle of element 1
l1Von(i)=(1/(2)^.5)*(s1PriSt1(i)-s1PriSt2(i));% Maximum distortion energy (Von mises stress) of element 1
l2PriSt1(i)=.5*(s2Stress(1,i)+s2Stress(2,i))+((.5*(s2Stress(1,i)-s2Stress(2,i)))^2+s2Stress(3,i)^2)^.5; %Principal stress of 1
l2PriSt2(i)=.5*(s2Stress(1,i)+s2Stress(2,i))-((.5*(s2Stress(1,i)-s2Stress(2,i)))^2+s2Stress(3,i)^2)^.5; %Principal stress of 2
l2PriAng(i)=atan((2*s2Stress(3,i))/(s2Stress(1,i)-s2Stress(2,i))); % Principal angle of element 2
l2Von(i)=(1/(2)^.5)*(s2PriSt1(i)-s2PriSt2(i));% Maximum distortion energy (Von mises stress) of element 2
l3PriSt1(i)=.5*(s3Stress(1,i)+s3Stress(2,i))+((.5*(s3Stress(1,i)-s3Stress(2,i)))^2+s3Stress(3,i)^2)^.5; %Principal stress of 1
l3PriSt2(i)=.5*(s3Stress(1,i)+s3Stress(2,i))-((.5*(s3Stress(1,i)-s3Stress(2,i)))^2+s3Stress(3,i)^2)^.5; %Principal stress of 2
l3PriAng(i)=atan((2*s3Stress(3,i))/(s3Stress(1,i)-s3Stress(2,i))); % Principal angle of element 3
l3Von(i)=(1/(2)^.5)*(s3PriSt1(i)-s3PriSt2(i));% Maximum distortion energy (Von mises stress) of element 3
l4PriSt1(i)=.5*(s4Stress(1,i)+s4Stress(2,i))+((.5*(s4Stress(1,i)-s4Stress(2,i)))^2+s4Stress(3,i)^2)^.5; %Principal stress of 1
l4PriSt2(i)=.5*(s4Stress(1,i)+s4Stress(2,i))-((.5*(s4Stress(1,i)-s4Stress(2,i)))^2+s4Stress(3,i)^2)^.5; %Principal stress of 2
l4PriAng(i)=atan((2*s4Stress(3,i))/(s4Stress(1,i)-s4Stress(2,i))); % Principal angle of element 4
l4Von(i)=(1/(2)^.5)*(s4PriSt1(i)-s4PriSt2(i));% Maximum distortion energy (Von mises stress) of element 4
lBSH(i)=-[l1EleF(1,i)+l2EleF(1,i)+l1EleF(3,i)];% Base shear based of [DOF(1)+DOF(3)]
if abs(up22) >= D22max;disp(' ## Displacement at [DOF (22)] reached to Ultimate Displacement ##');break;end
end
XXi20=[XY1i(1),XY3i(1)+lU(1,1),XY5i(1)+lU(5,1),XY7i(1)+lU(9,1),XY9i(1)+lU(13,1),XY11i(1),XY12i(1),XY10i(1)+lU(15,1),XY8i(1)+lU(11,1),XY6i(1)+lU(7,1),XY4i(1)+lU(3,1),XY2i(1)];
YYi20=[XY1i(2),XY3i(2)+lU(2,1),XY5i(2)+lU(6,1),XY7i(2)+lU(10,1),XY9i(2)+lU(14,1),XY11i(2)+lU22(1),XY12i(2)+lU24(1),XY10i(2)+lU(16,1),XY8i(2)+lU(12,1),XY6i(2)+lU(8,1),XY4i(2)+lU(4,1),XY2i(2)];
XXi21=[XY1i(1),XY3i(1)+lU(1,.25*m),XY5i(1)+lU(5,.25*m),XY7i(1)+lU(9,.25*m),XY9i(1)+lU(13,.25*m),XY11i(1),XY12i(1),XY10i(1)+lU(15,.25*m),XY8i(1)+lU(11,.25*m),XY6i(1)+lU(7,.25*m),XY4i(1)+lU(3,.25*m),XY2i(1)];
YYi21=[XY1i(2),XY3i(2)+lU(2,.25*m),XY5i(2)+lU(6,.25*m),XY7i(2)+lU(10,.25*m),XY9i(2)+lU(14,.25*m),XY11i(2)+lU22(.25*m),XY12i(2)+lU24(.25*m),XY10i(2)+lU(16,.25*m),XY8i(2)+lU(12,.25*m),XY6i(2)+lU(8,.25*m),XY4i(2)+lU(4,.25*m),XY2i(2)];
XXi22=[XY1i(1),XY3i(1)+lU(1,.5*m),XY5i(1)+lU(5,.5*m),XY7i(1)+lU(9,.5*m),XY9i(1)+lU(13,.5*m),XY11i(1),XY12i(1),XY10i(1)+lU(15,.5*m),XY8i(1)+lU(11,.5*m),XY6i(1)+lU(7,.5*m),XY4i(1)+lU(3,.5*m),XY2i(1)];
YYi22=[XY1i(2),XY3i(2)+lU(2,.5*m),XY5i(2)+lU(6,.5*m),XY7i(2)+lU(10,.5*m),XY9i(2)+lU(14,.5*m),XY11i(2)+lU22(.5*m),XY12i(2)+lU24(.5*m),XY10i(2)+lU(16,.5*m),XY8i(2)+lU(12,.5*m),XY6i(2)+lU(8,.5*m),XY4i(2)+lU(4,.5*m),XY2i(2)];
XXi23=[XY1i(1),XY3i(1)+lU(1,.75*m),XY5i(1)+lU(5,.75*m),XY7i(1)+lU(9,.75*m),XY9i(1)+lU(13,.75*m),XY11i(1),XY12i(1),XY10i(1)+lU(15,.75*m),XY8i(1)+lU(11,.75*m),XY6i(1)+lU(7,.75*m),XY4i(1)+lU(3,.75*m),XY2i(1)];
YYi23=[XY1i(2),XY3i(2)+lU(2,.75*m),XY5i(2)+lU(6,.75*m),XY7i(2)+lU(10,.75*m),XY9i(2)+lU(14,.75*m),XY11i(2)+lU22(.75*m),XY12i(2)+lU24(.75*m),XY10i(2)+lU(16,.75*m),XY8i(2)+lU(12,.75*m),XY6i(2)+lU(8,.75*m),XY4i(2)+lU(4,.75*m),XY2i(2)];
XXi24=[XY1i(1),XY3i(1)+lU(1,m),XY5i(1)+lU(5,m),XY7i(1)+lU(9,m),XY9i(1)+lU(13,m),XY11i(1),XY12i(1),XY10i(1)+lU(15,m),XY8i(1)+lU(11,m),XY6i(1)+lU(7,m),XY4i(1)+lU(3,m),XY2i(1)];
YYi24=[XY1i(2),XY3i(2)+lU(2,m),XY5i(2)+lU(6,m),XY7i(2)+lU(10,m),XY9i(2)+lU(14,m),XY11i(2)+lU22(m),XY12i(2)+lU24(m),XY10i(2)+lU(16,m),XY8i(2)+lU(12,m),XY6i(2)+lU(8,m),XY4i(2)+lU(4,m),XY2i(2)];
%% SAP2000 OUTPUT
SapDisY=[];
SapRea=[];
%% ABAQUS OUTPUT
AbaDisY17=[0
-0.0147214
-0.0143727
-0.0143669
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0143668
-0.0214962
-0.0322323
-0.0483134
-0.0723828
-0.108367
-0.16207
-0.241989
-0.360385
-0.534476
-0.787313
-1.14685
-1.64127
-2.29211
-3.14679
-3.67655
-3.67621
-3.67621
-3.67621];
AbaDisY18=[0
-0.347777
-0.350591
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.350619
-0.524669
-0.787042
-1.18066
-1.77121
-2.65732
-3.98716
-5.98353
-8.98197
-13.4893
-20.275
-30.5193
-46.0648
-69.876
-106.909
-130.156
-130.156
-130.156
-130.156];
AbaDisY=[0 %dis dof 22
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.5
-0.748183
-1.12227
-1.68341
-2.52512
-3.78768
-5.68151
-8.52227
-12.7834
-19.1751
-28.7627
-43.144
-64.716
-97.074
-145.611
-175
-175
-175
-175];
AbaRea=[-0
16.627
16.9393
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431
16.9431

6. 16.9431
16.9431
16.9431
16.9431
16.9431
25.3524
38.0265
57.0347
85.5399
128.281
192.355
288.372
432.172
647.304
968.665
1446.99
2154.94
3192.2
4686.06
5554.03
5554
5554
5554];
%%% print time of computation
totaltime = cputime - starttime;
fprintf('nTotal time (s): %7.4f nn',totaltime)
%% imaging
figure(1)
IMAGE=imread('TriangleMembraneAnalysisdcL8eleMESHarc-image01.jpg');
image(IMAGE);axis image;axis off;
figure(2)
IMAGE=imread('TriangleMembraneAnalysisdcL8eleMESHarc-image02.jpg');
image(IMAGE);axis image;axis off;
figure(3)
IMAGE=imread('TriangleMembraneAnalysisdcL8eleMESHarc-image03.jpg');
image(IMAGE);axis image;axis off;
figure(4)
IMAGE=imread('TriangleMembraneAnalysisdcL8eleMESHarc-image04.jpg');
image(IMAGE);axis image;axis off;
figure(5)
IMAGE=imread('TriangleMembraneAnalysisdcL8eleMESHarc-image05.jpg');
image(IMAGE);axis image;axis off;
figure(6)
p1=plot(I1,DU1,'--blue',I2,DU2,'--r');grid on;set(p1,'LineWidth',2);
xlabel('increment');ylabel('Residual');
title('Residual-increment diagram','color','b');
legend('Small disp.','Large disp.','Location','NorthEastOutside');
figure(7)
p1=plot(I1,IT1,'--blue',I2,IT2,'--r');grid on;set(p1,'LineWidth',2);
xlabel('increment');ylabel('Iteration');
title('Iteration-increment diagram','color','b');
legend('Small disp.','Large disp.','Location','NorthEastOutside');
figure(8)
p1=plot(sU(15,:),sBSH,lU(15,:),lBSH,'--r',AbaDisY17,AbaRea,'--g');grid on;set(p1,'LineWidth',3);
xlabel('Displacement (mm) [DOF(17)]');ylabel('Base shear (kN) [DOF(1)+DOF(3)]');
title('Base Shear-Displacement of plate during the incremental displacement','color','b');
legend('Small disp.','Large disp.','ABAQUS','Location','NorthEastOutside');
figure(9)
p1=plot(sU(15,:),sU(15,:),lU(15,:),lU(16,:),'--r',AbaDisY17,AbaDisY18,'--g');grid on;set(p1,'LineWidth',3);
xlabel('Displacement (mm) [DOF(17)]');ylabel('Displacement (mm) [DOF(18)]');
title('Displacement of plate during the incremental displacement','color','b');
legend('Small disp.','Large disp.','ABAQUS','Location','NorthEastOutside');
figure(10)
p1=plot(sU22,sBSH,lU22,lBSH,'--r',AbaDisY,AbaRea,'g-.');grid on;set(p1,'LineWidth',3);
xlabel('Displacement (mm) [DOF(24)]');ylabel('Base shear (kN) [DOF(1)+DOF(3)]');
title('Base Shear-Displacement of plate during the incremental displacement','color','b');
legend('Small disp.','Large disp.','ABAQUS','Location','NorthEastOutside');
figure(11)
p1=plot(XXi10,YYi10,XXi11,YYi11,'--',XXi12,YYi12,'--',XXi13,YYi13,'--',XXi14,YYi14,'--');grid on;set(p1,'LineWidth',3);
xlabel('X-Diemention (mm)');ylabel('Y-Diemention (mm)');axis tight
title('Small displacement - Shape of plate during the incremental displacement [DOF(22)]','color','b');
legend('Not loading step [DOF(22)=0 mm]','[DOF(22)=250 mm]','[DOF(22)=500 mm]','[DOF(22)=750 mm]','Last step [DOF(22)=1000 mm]','Location','NorthEastOutside');
figure(12)
p1=plot(XXi20,YYi20,XXi21,YYi21,'--',XXi22,YYi22,'--',XXi23,YYi23,'--',XXi24,YYi24,'--');grid on;set(p1,'LineWidth',3);
xlabel('X-Diemention (mm)');ylabel('Y-Diemention (mm)');axis tight
title('Large displacement - Shape of plate during the incremental displacement [DOF(22)]','color','b');
legend('Not loading step [DOF(22)=0 mm]','[DOF(22)=250 mm]','[DOF(22)=500 mm]','[DOF(22)=750 mm]','Last step [DOF(22)=1000 mm]','Location','NorthEastOutside');
figure(13)
p1=plot(s1Strain(1,:),s1Stress(1,:),'--',s2Strain(1,:),s2Stress(1,:),'--',...
l1Strain(1,:),l1Stress(1,:),'--',l2Strain(1,:),l2Stress(1,:),'--');grid on;set(p1,'LineWidth',3);
xlabel('Strain (S11) [mm/mm]');ylabel('Stress (S11) [kN/mm^2]');
title('Starin-Stress of element diagram','color','b');
legend('Small disp-Ele.1','Small disp-Ele.2','Large disp.-Ele.1','Large disp.-Ele.2','Location','NorthEastOutside');
figure(14)
p1=plot(s1Strain(2,:),s1Stress(2,:),'--',s2Strain(2,:),s2Stress(2,:),'--',l1Strain(2,:),l1Stress(2,:),'--',l2Strain(2,:),l2Stress(2,:),'--');grid on;set(p1,'LineWidth',3);
xlabel('Strain (S22) [mm/mm]');ylabel('Stress (S22) [kN/mm^2]');
title('Starin-Stress of element diagram','color','b');
legend('Small disp-Ele.1','Small disp-Ele.2','Large disp.-Ele.1','Large disp.-Ele.2','Location','NorthEastOutside');
figure(15)
p1=plot(s1Strain(3,:),s1Stress(3,:),'--',s2Strain(3,:),s2Stress(3,:),'--',l1Strain(3,:),l1Stress(3,:),'--',l2Strain(3,:),l2Stress(3,:),'--');grid on;set(p1,'LineWidth',3);
xlabel('Strain (S12) [mm/mm]');ylabel('Stress (S12) [kN/mm^2]');
title('Starin-Stress of element diagram','color','b');
legend('Small disp-Ele.1','Small disp-Ele.2','Large disp.-Ele.1','Large disp.-Ele.2','Location','NorthEastOutside');
figure(16)
p1=plot(s1PriSt1,s1PriSt2,'--',s2PriSt1,s2PriSt2,'--',l1PriSt1,l1PriSt2,'--',l2PriSt1,l2PriSt2,'--');grid on;set(p1,'LineWidth',3);
xlabel('Principal stress (S11) [kN/mm^2]');ylabel('Principal stress (S22) [kN/mm^2]');
title('Principal stress of element diagram','color','b');
legend('Small disp-Ele.1','Small disp-Ele.2','Large disp.-Ele.1','Large disp.-Ele.2','Location','NorthEastOutside');
figure(17)
p1=plot(s1PriAng,s1Von,'--',s2PriAng,s2Von,'--',l1PriAng,l1Von,'--',l2PriAng,l2Von,'--');grid on;set(p1,'LineWidth',3);
xlabel('Principal angle [rad]');ylabel('Von mises stress [kN/mm^2]');
title('Principal angle-Von mises stress of element diagram','color','b');
legend('Small disp-Ele.1','Small disp-Ele.2','Large disp.-Ele.1','Large disp.-Ele.2','Location','NorthEastOutside');
Figure(1) Bilinear stress-Strain Relation for steel modelling in MATLAB and ABAQUS version 6.10
Analysis Report:
###########################
# Small Displacement Analysis #
###########################
(+)Increment 1 : It is converged in 2 iterations
(+)Increment 2 : It is converged in 2 iterations
(+)Increment 3 : It is converged in 2 iterations

7. (+)Increment 4 : It is converged in 2 iterations
(+)Increment 5 : It is converged in 2 iterations
(+)Increment 6 : It is converged in 2 iterations
(+)Increment 7 : It is converged in 2 iterations
(+)Increment 8 : It is converged in 2 iterations
(+)Increment 9 : It is converged in 2 iterations
(+)Increment 10 : It is converged in 2 iterations.
.
.
.
(+)Increment 791 : It is converged in 3 iterations
(+)Increment 792 : It is converged in 3 iterations
(+)Increment 793 : It is converged in 3 iterations
(+)Increment 794 : It is converged in 3 iterations
(+)Increment 795 : It is converged in 3 iterations
(+)Increment 796 : It is converged in 3 iterations
(+)Increment 797 : It is converged in 3 iterations
(+)Increment 798 : It is converged in 3 iterations
(+)Increment 799 : It is converged in 3 iterations
(+)Increment 800 : It is converged in 3 iterations
###########################
# Large Displacement Analysis #
###########################
(+)Increment 1 : It is converged in 2 iterations
(+)Increment 2 : It is converged in 2 iterations
(+)Increment 3 : It is converged in 2 iterations
(+)Increment 4 : It is converged in 2 iterations
(+)Increment 5 : It is converged in 2 iterations
(+)Increment 6 : It is converged in 2 iterations
(+)Increment 7 : It is converged in 2 iterations
(+)Increment 8 : It is converged in 2 iterations
(+)Increment 9 : It is converged in 2 iterations
(+)Increment 10 : It is converged in 2 iterations
.
.
.
(+)Increment 791 : It is converged in 3 iterations
(+)Increment 792 : It is converged in 3 iterations
(+)Increment 793 : It is converged in 3 iterations
(+)Increment 794 : It is converged in 3 iterations
(+)Increment 795 : It is converged in 3 iterations
(+)Increment 796 : It is converged in 3 iterations
(+)Increment 797 : It is converged in 3 iterations
(+)Increment 798 : It is converged in 3 iterations
(+)Increment 799 : It is converged in 3 iterations
(+)Increment 800 : It is converged in 3 iterations
Plot :

8. Figure(2) Residual-increment diagram

9. Figure(3) Force-Displacement of DOF(7) in MATLAB and ABAQUS

10. Figure(4) Small displacement – Shape of arc membrane element during the incremental displacement [DOF(22)]

11. Figure(5) Large displacement – Shape of arc membrane element during the incremental displacement [DOF(22)]

12. Figure(6) Large displacement – Shape of arc membrane element during the incremental displacement [DOF(22)] in ABAQUS