diff options
author | blendoit <blendoit@gmail.com> | 2019-09-30 18:47:15 -0700 |
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committer | blendoit <blendoit@gmail.com> | 2019-09-30 18:47:15 -0700 |
commit | 4fbe70cf817d2e31cbae5aae264d0ef1a3821afc (patch) | |
tree | 1de77be1bf764b80342cd78f730b316aa9658429 | |
parent | 588c34a3d595fcad5e93b8d4893f1098ce64d046 (diff) |
Delete MATLAB scripts
-rw-r--r-- | README.org | 6 | ||||
-rw-r--r-- | wing_scripts/eye_beam_example.m | 70 | ||||
-rw-r--r-- | wing_scripts/get_dp.m | 4 | ||||
-rw-r--r-- | wing_scripts/get_ds.m | 20 | ||||
-rw-r--r-- | wing_scripts/get_int.m | 35 | ||||
-rw-r--r-- | wing_scripts/get_z.m | 34 | ||||
-rw-r--r-- | wing_scripts/my_progress.m | 459 | ||||
-rw-r--r-- | wing_scripts/stringersBeamExample.m | 47 | ||||
-rw-r--r-- | wing_scripts/wingAnalysis_190422.m | 579 |
9 files changed, 4 insertions, 1250 deletions
@@ -1,7 +1,9 @@ -#+TITLE: UCLA MAE 154B -#+SUBTITLE: Spring 2019 Final Project +#+TITLE: Aircraft Studio +#+AUTHOR: Marius Peter This program enables the creation of NACA airfoils; the analysis of the airfoil's structural properties; the optimization via genetic algorithm of a population of airfoils; With the final objective of designing a lightweight FAR 23 compliant airfoil. + +I adapted it from my own code for the UCLA MAE 154B final project (Spring 2019). diff --git a/wing_scripts/eye_beam_example.m b/wing_scripts/eye_beam_example.m deleted file mode 100644 index 70b4d92..0000000 --- a/wing_scripts/eye_beam_example.m +++ /dev/null @@ -1,70 +0,0 @@ -% Bending/Shear stress example -close all; - -length = 20; % in -force = 10000; %lbs - -%eye-beam dimensions - -max_width = 4; % in -min_width = 1; % in -y_max = 4; % in -center_y = 2; % in - - -%max bending moment at the root... - -M = force*length; - -I = min_width*(2*center_y)^3/12 + 2*( max_width*(y_max-center_y)^3/12 + ... - max_width*(y_max-center_y)*((y_max+center_y)/2)^2); - -sigma_max = M * y_max / I; - - -% solve for shear stress distribution -% V / (I * t) * int(y*da) - -% Point 1: evaluated at location just before thickness changes from 4 to 1 in -tempCoeff = force / (I * max_width); -int_y_da = ((y_max+center_y)/2) * max_width*(y_max-center_y); -shear_1 = tempCoeff*int_y_da; - -% Point 2: evaluated at location just after thickness changes from 4 to 1 in -tempCoeff = force / (I * min_width); -shear_2 = tempCoeff*int_y_da; - - -% Point 3: evaluated at center of beam -tempCoeff = force / (I * min_width); -int_y_da = (center_y/2) * min_width*center_y; -shear_3 = shear_2+tempCoeff*int_y_da; - -%evaluating continous integral for width of 4.. -int_y_da_4 = force / (I * max_width)*4*(y_max^2/2 - (center_y:.1:y_max).^2/2); - -%evaluating continous integral for width of 1.. -int_y_da_1 = shear_2 + force / (I * min_width)*1*(center_y^2/2 - (0:.1:center_y).^2/2); - -figure; grid on; hold on;set(gcf,'color',[1 1 1]); -plot(int_y_da_4,center_y:.1:y_max,'linewidth',2) -plot(int_y_da_1,0:.1:center_y,'linewidth',2) -plot(int_y_da_1,0:-.1:-center_y,'linewidth',2) -plot(int_y_da_4,-center_y:-.1:-y_max,'linewidth',2) -plot([shear_1 shear_2],[center_y center_y],'linewidth',2) -plot([shear_1 shear_2],[-center_y -center_y],'linewidth',2) - -plot(shear_1,center_y,'o') -plot(shear_2,center_y,'o') -plot(shear_3,0,'o') -plot(shear_2,-center_y,'o') -plot(shear_1,-center_y,'o') - -xlabel('shear stress (lb/in^2)','fontsize',16,'fontweight','bold');ylabel('Distance from Center (in)','fontsize',16,'fontweight','bold') -set(gca,'FontSize',16,'fontweight','bold'); - - -figure; grid on; hold on;set(gcf,'color',[1 1 1]); -plot([0 4 4 2.5 2.5 4 4 0 0 1.5 1.5 0 0],[4 4 2 2 -2 -2 -4 -4 -2 -2 2 2 4],'linewidth',2) - - diff --git a/wing_scripts/get_dp.m b/wing_scripts/get_dp.m deleted file mode 100644 index 2a3281d..0000000 --- a/wing_scripts/get_dp.m +++ /dev/null @@ -1,4 +0,0 @@ -function z = get_dp(xDist,zDist,Vx,Vz,Ix,Iz,Ixz,A) - -denom = (Ix*Iz-Ixz^2); -z = -A*xDist*(Ix*Vx-Ixz*Vz)/denom - A*zDist*(Iz*Vz-Ixz*Vx)/denom; diff --git a/wing_scripts/get_ds.m b/wing_scripts/get_ds.m deleted file mode 100644 index 2f0eb9d..0000000 --- a/wing_scripts/get_ds.m +++ /dev/null @@ -1,20 +0,0 @@ -function ds = get_ds(xi,xf,u) - -dist = 0; -numSteps = 10; -dx = (xf-xi)/numSteps; -z0 = get_z(xi,u); -x0 = xi; -for i=1:10 - tempX = x0+dx; - if tempX > 0 - tempZ = get_z(tempX,u); - else - tempZ = 0; - end - dist = dist + (dx^2+(tempZ-z0)^2)^.5; - z0 = tempZ; - x0 = tempX; -end - -ds =dist;
\ No newline at end of file diff --git a/wing_scripts/get_int.m b/wing_scripts/get_int.m deleted file mode 100644 index edbfda3..0000000 --- a/wing_scripts/get_int.m +++ /dev/null @@ -1,35 +0,0 @@ -function z = get_int(xi,xf,u) - -M = 0.02; -P = 0.4; -T = 0.12; -a0 = 0.2969; -a1 = -0.126; -a2 = -0.3516; -a3 = 0.2843; -a4 = -0.1015; - - -%evaluate the integral of camber line, depending on xi and xf related to P - -if xf <P - intCamb = M/P^2*(2*P*xf^2/2 - xf^3/3) - M/P^2*(2*P*xi^2/2 - xi^3/3); -elseif xi<P - intCamb = (M/(1-P)^2)*((1 - 2*P)*xf +2*P*xf^2/2 - xf^3/3) - (M/(1-P)^2)*((1 - 2*P)*P +2*P*P^2/2 - P^3/3); - intCamb = intCamb + M/P^2*(2*P*P^2/2 - P^3/3) - M/P^2*(2*P*xi^2/2 - xi^3/3); -else - intCamb = (M/(1-P)^2)*((1 - 2*P)*xf +2*P*xf^2/2 - xf^3/3) - (M/(1-P)^2)*((1 - 2*P)*xi +2*P*xi^2/2 - xi^3/3); -end - -% do integral on thickness line -%z_thickness = (T/0.2)*(a0*x^.5+a1*x+a2*x^2+a3*x^3+a4*x^4); - -intThickness = (T/0.2)*(a0*xf^1.5/1.5 + a1*xf^2/2 + a2*xf^3/3 + a3*xf^4/4 +a4*xf^5/5); -intThickness = intThickness - (T/0.2)*(a0*xi^1.5/1.5 + a1*xi^2/2 + a2*xi^3/3 + a3*xi^4/4 +a4*xi^5/5); - -% combine both integral results to get total integral -if u == 1 - z = intCamb + intThickness; -else - z = abs(intCamb - intThickness); -end
\ No newline at end of file diff --git a/wing_scripts/get_z.m b/wing_scripts/get_z.m deleted file mode 100644 index 5387b52..0000000 --- a/wing_scripts/get_z.m +++ /dev/null @@ -1,34 +0,0 @@ -function z = get_z(x,u) - - - -if (x < 0 ) - disp('invalid X') -end - -M = 0.02; -P = 0.4; -T = 0.12; -a0 = 0.2969; -a1 = -0.126; -a2 = -0.3516; -a3 = 0.2843; -a4 = -0.1015; - -if x <P - z_camber = M/P^2*(2*P*x - x^2); -else - z_camber = (M/(1-P)^2)*(1 - 2*P +2*P*x - x^2); -end - -%z_camber = M/P^2*(2*P*x - x^2); -z_thickness = (T/0.2)*(a0*x^.5+a1*x+a2*x^2+a3*x^3+a4*x^4); - -if u==1 - z = z_camber + z_thickness; -else - z = z_camber - z_thickness; -end - - - diff --git a/wing_scripts/my_progress.m b/wing_scripts/my_progress.m deleted file mode 100644 index e87ef23..0000000 --- a/wing_scripts/my_progress.m +++ /dev/null @@ -1,459 +0,0 @@ -%wing shear flow -clear all; -close all; - -Vx = 1; Vz = 1; My = 1; %test loads will be applied individually - - -%Ixz = -Ixz; - -%define webs - -%% web cell 1 - -%upper webs -numStringers = numTopStringers; -stringerGap = upperStringerGap; -webThickness = t_upper; -tempStringers = topStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(1).posX + stringerGap*(i-1); - web(i).xEnd = sparCaps(1).posX + stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,1)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord; - if i==1 - web(i).dp_area = sparCaps(1).area; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = 0; - web(i).qPrime_Z = 0; - else - web(i).dp_area = tempStringers(i-1).area; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); %just Vx - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); %just Vz - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2; %integral of airfoil function - triangle1 = abs( (web(i).xStart - sparCaps(1).posX)*web(i).zStart/2); - triangle2 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); -end -webTop = web; -web = []; - -%rear spar -i=1; -web(i).xStart = sparCaps(3).posX; -web(i).xEnd = sparCaps(4).posX; -web(i).thickness = t_rearSpar; -web(i).zStart = sparCaps(3).posZ; -web(i).zEnd = sparCaps(4).posZ; -web(i).dp_area = sparCaps(3).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webTop(numTopStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webTop(numTopStringers+1).qPrime_Z - web(i).dP_Z; - -web(i).Area = (sparCaps(3).posX-sparCaps(1).posX)*sparCaps(3).posZ/2 + ... - abs((sparCaps(3).posX-sparCaps(1).posX)*sparCaps(4).posZ/2); -web(i).ds = abs(sparCaps(3).posZ - sparCaps(4).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; - -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webRearSpar = web; -web = []; - - -%lower webs -numStringers = numBottomStringers; -stringerGap = lowerStringerGap; -webThickness = t_lower; -tempStringers = bottomStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(4).posX - stringerGap*(i-1); - web(i).xEnd = sparCaps(4).posX - stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,0)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - if i==1 - web(i).dp_area = sparCaps(4).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = webRearSpar.qPrime_X - web(i).dP_X; - web(i).qPrime_Z = webRearSpar.qPrime_Z - web(i).dP_Z; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz, Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz, 0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - - tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2; %integral of airfoil function - triangle2 = abs((web(i).xStart - sparCaps(1).posX)*web(i).zStart/2); - triangle1 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X*(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z*(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X*(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z*(web(i).zEnd-web(i).zStart); - - %web(i).radCurv = ... Example: get_curve(web(i).xStart,web(i).xEnd,1) -end -webBottom = web; -web = []; - -%front Spar -i=1; -web(i).xStart = sparCaps(2).posX; -web(i).xEnd = sparCaps(1).posX; -web(i).thickness = t_frontSpar; -web(i).zStart = sparCaps(2).posZ; -web(i).zEnd = sparCaps(1).posZ; -web(i).dp_area = sparCaps(2).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webBottom(numBottomStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webBottom(numBottomStringers+1).qPrime_Z - web(i).dP_Z; -web(i).Area = 0; -web(i).ds = abs(sparCaps(2).posZ - sparCaps(1).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; - -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webFrontSpar = web; -web = []; - - - - -%% web cell 2 - -%lower nose webs -numStringers = numNoseBottomStringers; -stringerGap = lowerNoseStringerGap; -webThickness = t_lower_front; -tempStringers = noseBottomStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(2).posX - stringerGap*(i-1); - web(i).xEnd = sparCaps(2).posX - stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,0)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - - if i==1 - web(i).dp_area = sparCaps(2).area; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = 0; - web(i).qPrime_Z = 0; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2; %integral of airfoil function - triangle1 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2); - triangle2 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - - %web(i).radCurv = ... Example: get_curve(web(i).xStart,web(i).xEnd,1) -end -webLowerNose = web; -web = []; - -%upper nose webs -numStringers = numNoseTopStringers; -stringerGap = upperNoseStringerGap; -webThickness = t_upper_front; -tempStringers = noseTopStringers; - -for i=1:(numStringers+1) - web(i).xStart = stringerGap*(i-1); - web(i).xEnd = stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,1)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - if i==1 - web(i).dp_area = 0; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = webLowerNose(numNoseBottomStringers+1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = webLowerNose(numNoseBottomStringers+1).qPrime_Z - web(i).dP_Z; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2; %integral of airfoil function - triangle2 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2); - triangle1 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -end -webUpperNose = web; -web = []; - - -%front Spar -i=1; -web(i).xStart = sparCaps(1).posX; -web(i).xEnd = sparCaps(2).posX; -web(i).thickness = t_frontSpar; -web(i).zStart = sparCaps(1).posZ; -web(i).zEnd = sparCaps(2).posZ; -web(i).dp_area = sparCaps(1).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webUpperNose(numNoseTopStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webUpperNose(numNoseTopStringers+1).qPrime_Z - web(i).dP_Z; -web(i).Area = 0; -web(i).ds = abs(sparCaps(1).posZ - sparCaps(2).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webFrontSparCell2 = web; -web = []; - - -%check that q'*dx sums up to Vx - -Fx = sum([webTop.qp_dx_X])+webRearSpar.qp_dx_X+ sum([webBottom.qp_dx_X])+webFrontSpar.qp_dx_X; %cell 1 -Fx = Fx + sum([webLowerNose.qp_dx_X])+ sum([webUpperNose.qp_dx_X]); %cell 2 -Fx -Fz = sum([webTop.qp_dz_X])+webRearSpar.qp_dz_X+ sum([webBottom.qp_dz_X])+webFrontSpar.qp_dz_X; %cell 1 -Fz = Fz + sum([webLowerNose.qp_dz_X])+ sum([webUpperNose.qp_dz_X]); %cell 2 -Fz - -%check that q'*dz sums up to Vz - - -Fx = sum([webTop.qp_dx_Z])+webRearSpar.qp_dx_Z+ sum([webBottom.qp_dx_Z])+webFrontSpar.qp_dx_Z; %cell 1 -Fx = Fx + sum([webLowerNose.qp_dx_Z])+ sum([webUpperNose.qp_dx_Z]); %cell 2 -Fx -Fz = sum([webTop.qp_dz_Z])+webRearSpar.qp_dz_Z+ sum([webBottom.qp_dz_Z])+webFrontSpar.qp_dz_Z; %cell 1 -Fz = Fz + sum([webLowerNose.qp_dz_Z])+ sum([webUpperNose.qp_dz_Z]); %cell 2 -Fz - -%% - -% sum up the ds/t and q*ds/t to solve 2 equations, 2 unknowns - -% [A]*[q1s q2s] = B - -A11 = sum([webTop.dS_over_t])+webRearSpar.dS_over_t+ sum([webBottom.dS_over_t])+webFrontSpar.dS_over_t; -A22 = sum([webLowerNose.dS_over_t])+ sum([webUpperNose.dS_over_t])+webFrontSparCell2.dS_over_t; -A12 = -webFrontSpar.dS_over_t; -A21 = -webFrontSparCell2.dS_over_t; - -B1_X = sum([webTop.q_dS_over_t_X])+webRearSpar.q_dS_over_t_X+ sum([webBottom.q_dS_over_t_X])+webFrontSpar.q_dS_over_t_X; -B2_X = sum([webLowerNose.q_dS_over_t_X])+ sum([webUpperNose.q_dS_over_t_X])+webFrontSparCell2.q_dS_over_t_X; -B1_Z = sum([webTop.q_dS_over_t_Z])+webRearSpar.q_dS_over_t_Z+ sum([webBottom.q_dS_over_t_Z])+webFrontSpar.q_dS_over_t_Z; -B2_Z = sum([webLowerNose.q_dS_over_t_Z])+ sum([webUpperNose.q_dS_over_t_Z])+webFrontSparCell2.q_dS_over_t_Z; - -Amat = [A11 A12; A21 A22]; -Bmat_X = -[B1_X;B2_X]; -Bmat_Z = -[B1_Z;B2_Z]; - -qs_X = inv(Amat)*Bmat_X; -qs_Z = inv(Amat)*Bmat_Z; - - - -sum_2_a_q_X = sum([webTop.two_A_qprime_X])+webRearSpar.two_A_qprime_X+ sum([webBottom.two_A_qprime_X]); %cell 1 qprimes -sum_2_a_q_X = sum_2_a_q_X + sum([webLowerNose.two_A_qprime_X])+ sum([webUpperNose.two_A_qprime_X]); %cell 2 qprimes -sum_2_a_q_X = sum_2_a_q_X + 2*qs_X(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area])); -sum_2_a_q_X = sum_2_a_q_X + 2*qs_X(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area])); - -sum_2_a_q_Z = sum([webTop.two_A_qprime_Z])+webRearSpar.two_A_qprime_Z+ sum([webBottom.two_A_qprime_Z]); %cell 1 qprimes -sum_2_a_q_Z = sum_2_a_q_Z + sum([webLowerNose.two_A_qprime_Z])+ sum([webUpperNose.two_A_qprime_Z]); %cell 2 qprimes -sum_2_a_q_Z = sum_2_a_q_Z + 2*qs_Z(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area])); -sum_2_a_q_Z = sum_2_a_q_Z + 2*qs_Z(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area])); - -%shear center -sc.posX = sum_2_a_q_Z / Vz + frontSpar*chord; -sc.posZ = - sum_2_a_q_X / Vx; - - -% now consider the torque representing shifting the load from the quarter -% chord to the SC (need to check signs on these moments) - -torque_Z = Vz*(sc.posX - 0.25*chord); -torque_X = -Vx*sc.posZ; - - -Area1 = sum([webTop.Area]) + webRearSpar.Area + sum([webBottom.Area]); -%check area -Area1_check = get_int(frontSpar,backSpar,1)*chord^2 + get_int(frontSpar,backSpar,0)*chord^2; - -Area2 = sum([webLowerNose.Area]) + sum([webUpperNose.Area]); -Area2_check = get_int(0,frontSpar,1)*chord^2 + get_int(0,frontSpar,0)*chord^2; - - -%for twist equation (see excel spreadsheet example) - -q1t_over_q2t = (A22/Area2 + webFrontSpar.dS_over_t/Area1)/(A11/Area1 + webFrontSpar.dS_over_t/Area2); - -q2t = torque_X/(2*Area1*q1t_over_q2t + 2*Area2); -q1t = q2t*q1t_over_q2t; -qt_X = [q1t;q2t]; - -q2t = torque_Z/(2*Area1*q1t_over_q2t + 2*Area2); -q1t = q2t*q1t_over_q2t; -qt_Z = [q1t;q2t]; - - - -% --- - add up all shear flows: qtot = (qPrime + qs) + qt - - - - -%--- insert force balance to check total shear flows --- - -% --- -- - - -%end - -sc - - -%plotting airfoil cross-section - -xChord = 0:.01:1; -xChord = xChord*chord; -upperSurface = zeros(1,length(xChord)); -lowerSurface = zeros(1,length(xChord)); - -for i=1:length(xChord) - upperSurface(i) = get_z(xChord(i)/chord,1)*chord; - lowerSurface(i) = get_z(xChord(i)/chord,0)*chord; -end - -figure; hold on; axis equal; grid on; -%plot(xChord,z_camber,'-') -plot(xChord,upperSurface,'-k','linewidth',2) -plot(xChord,lowerSurface,'-k','linewidth',2) -plot([0 1],[0 0],'--k','linewidth',1) - - -for i = 1:length(webTop) - vecX = [frontSpar*chord webTop(i).xStart webTop(i).xEnd]; - vecZ = [0 webTop(i).zStart webTop(i).zEnd]; - fill(vecX,vecZ,[0.9 0.9 0.9]) -end - -for i = 1:length(webBottom) - vecX = [frontSpar*chord webBottom(i).xStart webBottom(i).xEnd]; - vecZ = [0 webBottom(i).zStart webBottom(i).zEnd]; - fill(vecX,vecZ,[0.9 0.9 0.9]) -end - -for i = 1:length(webUpperNose) - vecX = [frontSpar*chord webUpperNose(i).xStart webUpperNose(i).xEnd]; - vecZ = [0 webUpperNose(i).zStart webUpperNose(i).zEnd]; - fill(vecX,vecZ,[0.7 0.9 1.0]) -end - -for i = 1:length(webLowerNose) - vecX = [frontSpar*chord webLowerNose(i).xStart webLowerNose(i).xEnd]; - vecZ = [0 webLowerNose(i).zStart webLowerNose(i).zEnd]; - fill(vecX,vecZ,[0.7 0.9 1.0]) -end - - vecX = [frontSpar*chord sparCaps(3).posX sparCaps(4).posX]; - vecZ = [0 sparCaps(3).posZ sparCaps(4).posZ]; - fill(vecX,vecZ,[0.9 0.9 0.9]) - - -sparCapSize = 18; -stringerSize = 18; -plot([sparCaps(1).posX sparCaps(2).posX],[sparCaps(1).posZ sparCaps(2).posZ],'-k','linewidth',2) -plot([sparCaps(3).posX sparCaps(4).posX],[sparCaps(3).posZ sparCaps(4).posZ],'-k','linewidth',2) -plot([sparCaps.posX],[sparCaps.posZ],'.b','markersize',sparCapSize) -plot([topStringers.posX],[topStringers.posZ],'.r','markersize',stringerSize) -plot([bottomStringers.posX],[bottomStringers.posZ],'.r','markersize',stringerSize) -plot([noseTopStringers.posX],[noseTopStringers.posZ],'.r','markersize',stringerSize) -plot([noseBottomStringers.posX],[noseBottomStringers.posZ],'.r','markersize',stringerSize) -plot(centroid.posX,centroid.posZ,'.k','markerSize',18) -plot(sc.posX,sc.posZ,'.g','markersize',18) diff --git a/wing_scripts/stringersBeamExample.m b/wing_scripts/stringersBeamExample.m deleted file mode 100644 index cd3bcb6..0000000 --- a/wing_scripts/stringersBeamExample.m +++ /dev/null @@ -1,47 +0,0 @@ -close all; -force = 8000; % lbs -stringer_A = 0.5; % in^2 -thickness = 0.04; % in - -top_stringers_y = 6; % in -middle_stringers_y = 2; % in - -I = 2*stringer_A*top_stringers_y^2 + 2*stringer_A*middle_stringers_y^2; - -% solve for shear stress distribution. this calc ignores the thickness of -% the web between teh stringers (assumes bending taken by stringers) -% V / (I * t) * int(y*da) - -shear_top_web = force / (I*thickness) * top_stringers_y * stringer_A; -shear_middle_web = shear_top_web + (force / (I*thickness) * middle_stringers_y * stringer_A); - -figure; grid on; hold on;set(gcf,'color',[1 1 1]); - - -plot([shear_top_web shear_top_web],[middle_stringers_y top_stringers_y],'linewidth',2); -plot([shear_middle_web shear_middle_web],[-middle_stringers_y middle_stringers_y],'linewidth',2); -plot([shear_top_web shear_top_web],[-middle_stringers_y -top_stringers_y],'linewidth',2); - -plot([0 shear_top_web],[top_stringers_y top_stringers_y],'linewidth',2); -plot([0 shear_top_web],[-top_stringers_y -top_stringers_y],'linewidth',2); -plot([shear_middle_web shear_top_web],[middle_stringers_y middle_stringers_y],'linewidth',2); -plot([shear_middle_web shear_top_web],[-middle_stringers_y -middle_stringers_y],'linewidth',2); -xlabel('shear stress (lb/in^2)','fontsize',16,'fontweight','bold');ylabel('Distance from Center (in)','fontsize',16,'fontweight','bold') -set(gca,'FontSize',16,'fontweight','bold'); - -%Alternate approach.. compute change in bending stress at each stringer to -%find the change in shear load - -%at top stringer -d_sigma = force * top_stringers_y / I; %(lbs/in^2) -d_force_top = d_sigma * stringer_A; - -%at middle stringer.. -d_sigma = force * middle_stringers_y / I; %(lbs/in^2) -d_force_middle = d_force_top + d_sigma*stringer_A; - -%check if load balances -check_load = 2*d_force_top*4 + d_force_middle*4; - - - diff --git a/wing_scripts/wingAnalysis_190422.m b/wing_scripts/wingAnalysis_190422.m deleted file mode 100644 index a7d65e2..0000000 --- a/wing_scripts/wingAnalysis_190422.m +++ /dev/null @@ -1,579 +0,0 @@ -%wing shear flow -clear all; -close all; - - - - -Vx = 1; Vz = 1; My = 1; %test loads will be applied individually - -%define a few -numTopStringers = 6; -numBottomStringers = 8; -numNoseTopStringers = 4; -numNoseBottomStringers = 4; - -t_upper = 0.02/12; -t_lower = 0.02/12; -t_upper_front = 0.02/12; -t_lower_front = 0.02/12; -t_frontSpar = 0.04/12; -t_rearSpar = 0.04/12; - -frontSpar = 0.2; -backSpar = 0.7; -chord = 5; - -sparCaps(1).posX = frontSpar*chord; -sparCaps(2).posX = frontSpar*chord; -sparCaps(3).posX = backSpar*chord; -sparCaps(4).posX = backSpar*chord; - -sparCaps(1).posZ = get_z(frontSpar,1)*chord; -sparCaps(2).posZ = get_z(frontSpar,0)*chord; -sparCaps(3).posZ = get_z(backSpar,1)*chord; -sparCaps(4).posZ = get_z(backSpar,0)*chord; - -sparCaps(1).area = .1; -sparCaps(2).area = .1; -sparCaps(3).area = .1; -sparCaps(4).area = .1; - -upperStringerGap = (sparCaps(3).posX - sparCaps(1).posX)/(numTopStringers + 1); -lowerStringerGap = (sparCaps(3).posX - sparCaps(1).posX)/(numBottomStringers + 1); -upperNoseStringerGap = (sparCaps(1).posX - 0)/(numNoseTopStringers + 1); -lowerNoseStringerGap = (sparCaps(1).posX - 0)/(numNoseBottomStringers + 1); - - -%set stringers spaced evenly along X axis betwen Spars -%top Stringers -for i=1:numTopStringers - topStringers(i).posX = sparCaps(1).posX + upperStringerGap*i; - topStringers(i).posZ = get_z(topStringers(i).posX/chord,1)*chord; - topStringers(i).area = .1; -end - -%bottom Stringers -for i=1:numBottomStringers - bottomStringers(i).posX = sparCaps(4).posX - lowerStringerGap*i; - bottomStringers(i).posZ = get_z(bottomStringers(i).posX/chord,0)*chord; - bottomStringers(i).area = .1; - -end - -%nose bottom Stringers -for i=1:numNoseBottomStringers - noseBottomStringers(i).posX = sparCaps(2).posX - lowerNoseStringerGap*i; - noseBottomStringers(i).posZ = get_z(noseBottomStringers(i).posX/chord,0)*chord; - noseBottomStringers(i).area = .1; -end - -%nose top Stringers -for i=1:numNoseTopStringers - noseTopStringers(i).posX = upperNoseStringerGap*i; - noseTopStringers(i).posZ = get_z(noseTopStringers(i).posX/chord,1)*chord; - noseTopStringers(i).area = .1; -end - - -centroid.posX = sum([sparCaps.posX].*[sparCaps.area]) + ... - sum([topStringers.posX].*[topStringers.area]) + ... - sum([bottomStringers.posX].*[bottomStringers.area]) + ... - sum([noseTopStringers.posX].*[noseTopStringers.area]) + ... - sum([noseBottomStringers.posX].*[noseBottomStringers.area]); - -centroid.posX = centroid.posX / ( sum([sparCaps.area]) + sum([topStringers.area]) + ... - sum([bottomStringers.area]) + sum([noseTopStringers.area]) + sum([noseBottomStringers.area])); - -centroid.posZ = sum([sparCaps.posZ].*[sparCaps.area]) + ... - sum([topStringers.posZ].*[topStringers.area]) + ... - sum([bottomStringers.posZ].*[bottomStringers.area]) + ... - sum([noseTopStringers.posZ].*[noseTopStringers.area]) + ... - sum([noseBottomStringers.posZ].*[noseBottomStringers.area]); - -centroid.posZ = centroid.posZ / ( sum([sparCaps.area]) + sum([topStringers.area]) + ... - sum([bottomStringers.area]) + sum([noseTopStringers.area]) + sum([noseBottomStringers.area])); - -%summing contributions for inertia terms -Ix = 0; Iz = 0; Ixz = 0; - -for i=1:4 %spar caps - Ix = Ix + sparCaps(i).area*(sparCaps(i).posZ-centroid.posZ)^2; - Iz = Iz + sparCaps(i).area*(sparCaps(i).posX-centroid.posX)^2; - Ixz = Ixz + sparCaps(i).area*(sparCaps(i).posX-centroid.posX)*(sparCaps(i).posZ-centroid.posZ); -end - - -for i=1:numTopStringers %top stringers - Ix = Ix + topStringers(i).area*(topStringers(i).posZ-centroid.posZ)^2; - Iz = Iz + topStringers(i).area*(topStringers(i).posX-centroid.posX)^2; - Ixz = Ixz + topStringers(i).area*(topStringers(i).posX-centroid.posX)*(topStringers(i).posZ-centroid.posZ); -end -for i=1:numBottomStringers %bottom stringers - Ix = Ix + bottomStringers(i).area*(bottomStringers(i).posZ-centroid.posZ)^2; - Iz = Iz + bottomStringers(i).area*(bottomStringers(i).posX-centroid.posX)^2; - Ixz = Ixz + bottomStringers(i).area*(bottomStringers(i).posX-centroid.posX)*(bottomStringers(i).posZ-centroid.posZ); -end -for i=1:numNoseTopStringers %nose top stringers - Ix = Ix + noseTopStringers(i).area*(noseTopStringers(i).posZ-centroid.posZ)^2; - Iz = Iz + noseTopStringers(i).area*(noseTopStringers(i).posX-centroid.posX)^2; - Ixz = Ixz + noseTopStringers(i).area*(noseTopStringers(i).posX-centroid.posX)*(noseTopStringers(i).posZ-centroid.posZ); -end -for i=1:numNoseBottomStringers %nose bottom stringers - Ix = Ix + noseBottomStringers(i).area*(noseBottomStringers(i).posZ-centroid.posZ)^2; - Iz = Iz + noseBottomStringers(i).area*(noseBottomStringers(i).posX-centroid.posX)^2; - Ixz = Ixz + noseBottomStringers(i).area*(noseBottomStringers(i).posX-centroid.posX)*(noseBottomStringers(i).posZ-centroid.posZ); -end - -%Ixz = -Ixz; - -%define webs - -%% web cell 1 - -%upper webs -numStringers = numTopStringers; -stringerGap = upperStringerGap; -webThickness = t_upper; -tempStringers = topStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(1).posX + stringerGap*(i-1); - web(i).xEnd = sparCaps(1).posX + stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,1)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord; - if i==1 - web(i).dp_area = sparCaps(1).area; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = 0; - web(i).qPrime_Z = 0; - else - web(i).dp_area = tempStringers(i-1).area; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); %just Vx - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); %just Vz - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2; %integral of airfoil function - triangle1 = abs( (web(i).xStart - sparCaps(1).posX)*web(i).zStart/2); - triangle2 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); -end -webTop = web; -web = []; - -%rear spar -i=1; -web(i).xStart = sparCaps(3).posX; -web(i).xEnd = sparCaps(4).posX; -web(i).thickness = t_rearSpar; -web(i).zStart = sparCaps(3).posZ; -web(i).zEnd = sparCaps(4).posZ; -web(i).dp_area = sparCaps(3).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webTop(numTopStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webTop(numTopStringers+1).qPrime_Z - web(i).dP_Z; - -web(i).Area = (sparCaps(3).posX-sparCaps(1).posX)*sparCaps(3).posZ/2 + ... - abs((sparCaps(3).posX-sparCaps(1).posX)*sparCaps(4).posZ/2); -web(i).ds = abs(sparCaps(3).posZ - sparCaps(4).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; - -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webRearSpar = web; -web = []; - - -%lower webs -numStringers = numBottomStringers; -stringerGap = lowerStringerGap; -webThickness = t_lower; -tempStringers = bottomStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(4).posX - stringerGap*(i-1); - web(i).xEnd = sparCaps(4).posX - stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,0)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - if i==1 - web(i).dp_area = sparCaps(4).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = webRearSpar.qPrime_X - web(i).dP_X; - web(i).qPrime_Z = webRearSpar.qPrime_Z - web(i).dP_Z; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz, Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz, 0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - - tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2; %integral of airfoil function - triangle2 = abs((web(i).xStart - sparCaps(1).posX)*web(i).zStart/2); - triangle1 = abs((web(i).xEnd - sparCaps(1).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X*(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z*(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X*(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z*(web(i).zEnd-web(i).zStart); - - %web(i).radCurv = ... Example: get_curve(web(i).xStart,web(i).xEnd,1) -end -webBottom = web; -web = []; - -%front Spar -i=1; -web(i).xStart = sparCaps(2).posX; -web(i).xEnd = sparCaps(1).posX; -web(i).thickness = t_frontSpar; -web(i).zStart = sparCaps(2).posZ; -web(i).zEnd = sparCaps(1).posZ; -web(i).dp_area = sparCaps(2).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webBottom(numBottomStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webBottom(numBottomStringers+1).qPrime_Z - web(i).dP_Z; -web(i).Area = 0; -web(i).ds = abs(sparCaps(2).posZ - sparCaps(1).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; - -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webFrontSpar = web; -web = []; - - - - -%% web cell 2 - -%lower nose webs -numStringers = numNoseBottomStringers; -stringerGap = lowerNoseStringerGap; -webThickness = t_lower_front; -tempStringers = noseBottomStringers; - -for i=1:(numStringers+1) - web(i).xStart = sparCaps(2).posX - stringerGap*(i-1); - web(i).xEnd = sparCaps(2).posX - stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,0)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,0)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - - if i==1 - web(i).dp_area = sparCaps(2).area; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = 0; - web(i).qPrime_Z = 0; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xEnd/chord,web(i).xStart/chord,0)*chord^2; %integral of airfoil function - triangle1 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2); - triangle2 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,0)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - - %web(i).radCurv = ... Example: get_curve(web(i).xStart,web(i).xEnd,1) -end -webLowerNose = web; -web = []; - -%upper nose webs -numStringers = numNoseTopStringers; -stringerGap = upperNoseStringerGap; -webThickness = t_upper_front; -tempStringers = noseTopStringers; - -for i=1:(numStringers+1) - web(i).xStart = stringerGap*(i-1); - web(i).xEnd = stringerGap*(i); - web(i).thickness = webThickness; - web(i).zStart = get_z(web(i).xStart/chord,1)*chord; - web(i).zEnd = get_z(web(i).xEnd/chord,1)*chord; - dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - if i==1 - web(i).dp_area = 0; - web(i).dP_X = 0; - web(i).dP_Z = 0; - web(i).qPrime_X = webLowerNose(numNoseBottomStringers+1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = webLowerNose(numNoseBottomStringers+1).qPrime_Z - web(i).dP_Z; - else - web(i).dp_area = tempStringers(i-1).area; - web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); - web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); - web(i).qPrime_X = web(i-1).qPrime_X - web(i).dP_X; - web(i).qPrime_Z = web(i-1).qPrime_Z - web(i).dP_Z; - end - tempInt = get_int(web(i).xStart/chord,web(i).xEnd/chord,1)*chord^2; %integral of airfoil function - triangle2 = abs((web(i).xStart - sparCaps(2).posX)*web(i).zStart/2); - triangle1 = abs((web(i).xEnd - sparCaps(2).posX)*web(i).zEnd/2); - web(i).Area = tempInt + triangle1 - triangle2; - web(i).ds = get_ds(web(i).xStart/chord,web(i).xEnd/chord,1)*chord; - web(i).dS_over_t = web(i).ds / web(i).thickness; - - web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; - web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; - web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; - web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; - web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); - web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); - web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); - web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -end -webUpperNose = web; -web = []; - - -%front Spar -i=1; -web(i).xStart = sparCaps(1).posX; -web(i).xEnd = sparCaps(2).posX; -web(i).thickness = t_frontSpar; -web(i).zStart = sparCaps(1).posZ; -web(i).zEnd = sparCaps(2).posZ; -web(i).dp_area = sparCaps(1).area; -dx = web(i).xStart-centroid.posX; dz = web(i).zStart-centroid.posZ; - -web(i).dP_X = get_dp(dx,dz,Vx,0,Ix,Iz,Ixz,web(i).dp_area); -web(i).dP_Z = get_dp(dx,dz,0,Vz,Ix,Iz,Ixz,web(i).dp_area); -web(i).qPrime_X = webUpperNose(numNoseTopStringers+1).qPrime_X - web(i).dP_X; -web(i).qPrime_Z = webUpperNose(numNoseTopStringers+1).qPrime_Z - web(i).dP_Z; -web(i).Area = 0; -web(i).ds = abs(sparCaps(1).posZ - sparCaps(2).posZ); -web(i).dS_over_t = web(i).ds / web(i).thickness; -web(i).q_dS_over_t_X = web(i).qPrime_X * web(i).dS_over_t; -web(i).q_dS_over_t_Z = web(i).qPrime_Z * web(i).dS_over_t; -web(i).two_A_qprime_X = 2*web(i).Area*web(i).qPrime_X; -web(i).two_A_qprime_Z = 2*web(i).Area*web(i).qPrime_Z; -web(i).qp_dx_X = web(i).qPrime_X *(web(i).xEnd-web(i).xStart); -web(i).qp_dx_Z = web(i).qPrime_Z *(web(i).xEnd-web(i).xStart); -web(i).qp_dz_X = web(i).qPrime_X *(web(i).zEnd-web(i).zStart); -web(i).qp_dz_Z = web(i).qPrime_Z *(web(i).zEnd-web(i).zStart); - -webFrontSparCell2 = web; -web = []; - - -%check that q'*dx sums up to Vx - -Fx = sum([webTop.qp_dx_X])+webRearSpar.qp_dx_X+ sum([webBottom.qp_dx_X])+webFrontSpar.qp_dx_X; %cell 1 -Fx = Fx + sum([webLowerNose.qp_dx_X])+ sum([webUpperNose.qp_dx_X]); %cell 2 -Fx -Fz = sum([webTop.qp_dz_X])+webRearSpar.qp_dz_X+ sum([webBottom.qp_dz_X])+webFrontSpar.qp_dz_X; %cell 1 -Fz = Fz + sum([webLowerNose.qp_dz_X])+ sum([webUpperNose.qp_dz_X]); %cell 2 -Fz - -%check that q'*dz sums up to Vz - - -Fx = sum([webTop.qp_dx_Z])+webRearSpar.qp_dx_Z+ sum([webBottom.qp_dx_Z])+webFrontSpar.qp_dx_Z; %cell 1 -Fx = Fx + sum([webLowerNose.qp_dx_Z])+ sum([webUpperNose.qp_dx_Z]); %cell 2 -Fx -Fz = sum([webTop.qp_dz_Z])+webRearSpar.qp_dz_Z+ sum([webBottom.qp_dz_Z])+webFrontSpar.qp_dz_Z; %cell 1 -Fz = Fz + sum([webLowerNose.qp_dz_Z])+ sum([webUpperNose.qp_dz_Z]); %cell 2 -Fz - -%% - -% sum up the ds/t and q*ds/t to solve 2 equations, 2 unknowns - -% [A]*[q1s q2s] = B - -A11 = sum([webTop.dS_over_t])+webRearSpar.dS_over_t+ sum([webBottom.dS_over_t])+webFrontSpar.dS_over_t; -A22 = sum([webLowerNose.dS_over_t])+ sum([webUpperNose.dS_over_t])+webFrontSparCell2.dS_over_t; -A12 = -webFrontSpar.dS_over_t; -A21 = -webFrontSparCell2.dS_over_t; - -B1_X = sum([webTop.q_dS_over_t_X])+webRearSpar.q_dS_over_t_X+ sum([webBottom.q_dS_over_t_X])+webFrontSpar.q_dS_over_t_X; -B2_X = sum([webLowerNose.q_dS_over_t_X])+ sum([webUpperNose.q_dS_over_t_X])+webFrontSparCell2.q_dS_over_t_X; -B1_Z = sum([webTop.q_dS_over_t_Z])+webRearSpar.q_dS_over_t_Z+ sum([webBottom.q_dS_over_t_Z])+webFrontSpar.q_dS_over_t_Z; -B2_Z = sum([webLowerNose.q_dS_over_t_Z])+ sum([webUpperNose.q_dS_over_t_Z])+webFrontSparCell2.q_dS_over_t_Z; - -Amat = [A11 A12; A21 A22]; -Bmat_X = -[B1_X;B2_X]; -Bmat_Z = -[B1_Z;B2_Z]; - -qs_X = inv(Amat)*Bmat_X; -qs_Z = inv(Amat)*Bmat_Z; - - - -sum_2_a_q_X = sum([webTop.two_A_qprime_X])+webRearSpar.two_A_qprime_X+ sum([webBottom.two_A_qprime_X]); %cell 1 qprimes -sum_2_a_q_X = sum_2_a_q_X + sum([webLowerNose.two_A_qprime_X])+ sum([webUpperNose.two_A_qprime_X]); %cell 2 qprimes -sum_2_a_q_X = sum_2_a_q_X + 2*qs_X(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area])); -sum_2_a_q_X = sum_2_a_q_X + 2*qs_X(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area])); - -sum_2_a_q_Z = sum([webTop.two_A_qprime_Z])+webRearSpar.two_A_qprime_Z+ sum([webBottom.two_A_qprime_Z]); %cell 1 qprimes -sum_2_a_q_Z = sum_2_a_q_Z + sum([webLowerNose.two_A_qprime_Z])+ sum([webUpperNose.two_A_qprime_Z]); %cell 2 qprimes -sum_2_a_q_Z = sum_2_a_q_Z + 2*qs_Z(1)*(sum([webTop.Area])+webRearSpar.Area+ sum([webBottom.Area])); -sum_2_a_q_Z = sum_2_a_q_Z + 2*qs_Z(2)*(sum([webLowerNose.Area])+ sum([webUpperNose.Area])); - -%shear center -sc.posX = sum_2_a_q_Z / Vz + frontSpar*chord; -sc.posZ = - sum_2_a_q_X / Vx; - - -% now consider the torque representing shifting the load from the quarter -% chord to the SC (need to check signs on these moments) - -torque_Z = Vz*(sc.posX - 0.25*chord); -torque_X = -Vx*sc.posZ; - - -Area1 = sum([webTop.Area]) + webRearSpar.Area + sum([webBottom.Area]); -%check area -Area1_check = get_int(frontSpar,backSpar,1)*chord^2 + get_int(frontSpar,backSpar,0)*chord^2; - -Area2 = sum([webLowerNose.Area]) + sum([webUpperNose.Area]); -Area2_check = get_int(0,frontSpar,1)*chord^2 + get_int(0,frontSpar,0)*chord^2; - - -%for twist equation (see excel spreadsheet example) - -q1t_over_q2t = (A22/Area2 + webFrontSpar.dS_over_t/Area1)/(A11/Area1 + webFrontSpar.dS_over_t/Area2); - -q2t = torque_X/(2*Area1*q1t_over_q2t + 2*Area2); -q1t = q2t*q1t_over_q2t; -qt_X = [q1t;q2t]; - -q2t = torque_Z/(2*Area1*q1t_over_q2t + 2*Area2); -q1t = q2t*q1t_over_q2t; -qt_Z = [q1t;q2t]; - - - -% --- - add up all shear flows: qtot = (qPrime + qs) + qt - - - - -%--- insert force balance to check total shear flows --- - -% --- -- - - -%end - -sc - - -%plotting airfoil cross-section - -xChord = 0:.01:1; -xChord = xChord*chord; -upperSurface = zeros(1,length(xChord)); -lowerSurface = zeros(1,length(xChord)); - -for i=1:length(xChord) - upperSurface(i) = get_z(xChord(i)/chord,1)*chord; - lowerSurface(i) = get_z(xChord(i)/chord,0)*chord; -end - -figure; hold on; axis equal; grid on; -%plot(xChord,z_camber,'-') -plot(xChord,upperSurface,'-k','linewidth',2) -plot(xChord,lowerSurface,'-k','linewidth',2) -plot([0 1],[0 0],'--k','linewidth',1) - - -for i = 1:length(webTop) - vecX = [frontSpar*chord webTop(i).xStart webTop(i).xEnd]; - vecZ = [0 webTop(i).zStart webTop(i).zEnd]; - fill(vecX,vecZ,[0.9 0.9 0.9]) -end - -for i = 1:length(webBottom) - vecX = [frontSpar*chord webBottom(i).xStart webBottom(i).xEnd]; - vecZ = [0 webBottom(i).zStart webBottom(i).zEnd]; - fill(vecX,vecZ,[0.9 0.9 0.9]) -end - -for i = 1:length(webUpperNose) - vecX = [frontSpar*chord webUpperNose(i).xStart webUpperNose(i).xEnd]; - vecZ = [0 webUpperNose(i).zStart webUpperNose(i).zEnd]; - fill(vecX,vecZ,[0.7 0.9 1.0]) -end - -for i = 1:length(webLowerNose) - vecX = [frontSpar*chord webLowerNose(i).xStart webLowerNose(i).xEnd]; - vecZ = [0 webLowerNose(i).zStart webLowerNose(i).zEnd]; - fill(vecX,vecZ,[0.7 0.9 1.0]) -end - - vecX = [frontSpar*chord sparCaps(3).posX sparCaps(4).posX]; - vecZ = [0 sparCaps(3).posZ sparCaps(4).posZ]; - fill(vecX,vecZ,[0.9 0.9 0.9]) - - -sparCapSize = 18; -stringerSize = 18; -plot([sparCaps(1).posX sparCaps(2).posX],[sparCaps(1).posZ sparCaps(2).posZ],'-k','linewidth',2) -plot([sparCaps(3).posX sparCaps(4).posX],[sparCaps(3).posZ sparCaps(4).posZ],'-k','linewidth',2) -plot([sparCaps.posX],[sparCaps.posZ],'.b','markersize',sparCapSize) -plot([topStringers.posX],[topStringers.posZ],'.r','markersize',stringerSize) -plot([bottomStringers.posX],[bottomStringers.posZ],'.r','markersize',stringerSize) -plot([noseTopStringers.posX],[noseTopStringers.posZ],'.r','markersize',stringerSize) -plot([noseBottomStringers.posX],[noseBottomStringers.posZ],'.r','markersize',stringerSize) -plot(centroid.posX,centroid.posZ,'.k','markerSize',18) -plot(sc.posX,sc.posZ,'.g','markersize',18) |