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damping plate structures #134
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e569eb4
unfinished work on damping plate
rebeccamccabe 945e61c
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github-actions[bot] a15f653
implement CF function in orthotropic damping plate
rebeccamccabe 5777600
Merge branch 'reaction-plate' of github.com:symbiotic-engineering/MDO…
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63 changes: 47 additions & 16 deletions
63
mdocean/simulation/modules/structures/distributed_plate_nondim.m
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,51 +1,82 @@ | ||
| function [w_nondim,Mr_nondim,Mt_nondim] = distributed_plate_nondim(a,b,F_heave,nu,rho) | ||
| A = pi*a^2; | ||
| q = F_heave/A; | ||
| P = F_heave; | ||
| function [w_nondim,Mr_nondim,Mt_nondim,Q_nondim] = distributed_plate_nondim(a,b,q,nu,rho) | ||
| % Roark's table 11.2, case 2L (page 467) | ||
| % a: outer radius | ||
| % b: inner radius | ||
| % r0: radius at which the distributed loading begins | ||
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| % A = pi*a^2; | ||
| % q = F_heave/A; | ||
| % P = F_heave; | ||
| v = nu; | ||
| r = rho*a; | ||
| r0 = b; | ||
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||
| C2 = 1/4*(1-(b/a)^2*(1+2*log(a/b))); | ||
| C2 = 1/4 * ( 1 - (b/a)^2 * (1 + 2*log(a/b)) ); | ||
| C3 = b/4/a*(((b/a)^2+1)*log(a/b)+(b/a)^2-1); | ||
| C8 = 1/2*(1+v+(1-v)*(b/a)^2); | ||
| C9 = b/a*((1+v)/2*log(a/b)+(1-v)/4*(1-(b/a)^2)); | ||
| C8 = 1/2 * (1+v+(1-v)*(b/a)^2); | ||
| C9 = b/a * ( (1+v)/2*log(a/b) + (1-v)/4*(1-(b/a)^2) ); | ||
| %L3 = r0/4/a*(((r0/a)^2+1)*log(a/r0)+(r0/a)^2-1); % for case 1L | ||
| %L9 = r0/a*((1+v)/2*log(a/r0)+(1-v)/4*(1-(r0/a)^2)); % for case 1L | ||
| L11 = 1/64*(1+4*(r0/a)^2-5*(r0/a)^4-4*(r0/a)^2*(2+(r0/a)^2)*log(a/r0)); % for end deflection only | ||
| L17 = 1/4*(1-(1-v)/4*(1-(r0/a)^4)-(r0/a)^2*(1+(1+v)*log(a/r0))); | ||
| L11 = 1/64 * (1+4*(r0/a)^2-5*(r0/a)^4-4*(r0/a)^2*(2+(r0/a)^2)*log(a/r0)); % for end deflection only | ||
| L17 = 1/4 * (1-(1-v)/4*(1-(r0/a)^4)-(r0/a)^2*(1+(1+v)*log(a/r0))); | ||
| F2 = 1/4 * (1 - (b./r).^2.*(1+2*log(r/b))); | ||
| F3 = b./(4*r) .* ( ( (b./r).^2 + 1 ).*log(r/b) + (b./r).^2 - 1); | ||
| F5 = 1/2 * (1 - (b./r).^2); | ||
| F6 = b./(4*r) .* ( (b./r).^2 - 1 + 2*log(r/b) ); | ||
| F8 = 1/2 * (1+v+(1-v)*(b./r).^2); | ||
| F9 = b./r .* (1/2*(1+v)*(log(r/b)) + 1/4*(1-v)*(1-(b./r).^2)); | ||
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| bracket = zeros(size(r)); | ||
| bracket(r > r0) = 1; | ||
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| ratio = r0./r; | ||
| G11 = 1/64 * (1 + 4*ratio.^2 - 5*ratio.^4 - 4*ratio.^2.*(2+ratio.^2).*log(1./ratio) ) .* bracket; | ||
| G14 = 1/16 * (1 - (r0./r).^4 - 4*(r0./r).^2 .* log(r/r0)) .* bracket; | ||
| G17 = 1/4 * (1 - ((1-v)/4)*(1-ratio.^4) - (ratio).^2.*(1+(1+v)*log(1./ratio))) .* bracket; | ||
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| % Mrb: reaction moment per unit length on inner edge | ||
| Mrb = -q*a^2/C8 * (C9*(a^2-r0^2)/(2*a*b) - L17); | ||
| % Qb: shear reaction force per unit length on inner edge | ||
| Qb = q/2/b * (a^2 - r0^2); | ||
| E = 0;% fixme - only needed for Mt | ||
| D = 0; % fixme E*h^3/12/(1-v^2); - only needed for Mt | ||
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| y_over_D = Mrb * r.^2 .* F2 ... | ||
| % case 2 general deflection equation p463, with first two terms | ||
| % ommitted since yb and theta_b are zero for case 2L | ||
| y_times_D = Mrb * r.^2 .* F2 ... | ||
| + Qb * r.^3 .* F3 ... | ||
| - q * r.^4 .* G11; | ||
| w_nondim = y_over_D * 2*pi/(P*a^2); | ||
| tilt_angle = 0; % fixme use equation for theta on p463 | ||
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| theta_times_D = Mrb * r .* F5 ... | ||
| + Qb * r.^2 .* F6 ... | ||
| - q * r.^3 .* G14; | ||
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| Mr = Mrb * F8 ... | ||
| + Qb * r .* F9 ... | ||
| - q * r.^2 .* G17; | ||
| Mt = theta_times_D * (1-nu^2) ./ r ... | ||
| + nu * Mr; | ||
| Q = Qb * b./r ... | ||
| - q./(2*r).*(r.^2 - r0.^2) .* bracket; | ||
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| Mr = Mrb*F8 + Qb*r.*F9 - q*r.^2.*G17; | ||
| Mt = tilt_angle*D*(1-nu^2)./r + nu*Mr; | ||
| % Roark's p463 nondimensionalization | ||
| K_y = y_times_D / (q * a^4); | ||
| K_Mt = Mt / (q * a^2); | ||
| K_Mr = Mr / (q * a^2); | ||
| K_theta = theta_times_D / (q * a^3); | ||
| K_Q = Q / (q * a); | ||
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| % nondimensionalize to be consistent with concentrated loading plate in Boedo and Prantil | ||
| % note: w_nondim = 2*Ky/(1-(b/a)^2) | ||
| P = q * pi * (a^2-b^2); % equivalent concentrated load | ||
| w_nondim = y_times_D * 2*pi/(P*a^2); | ||
| Mr_nondim = Mr * 2*pi/P; | ||
| Mt_nondim = Mt * 2*pi/P; | ||
| Q_nondim = Q * 2*pi/(P*a); | ||
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| % use sign convention that positive F_heave results in positive | ||
| % deflection at outer end and positive moment at inner end | ||
| w_nondim = -w_nondim; | ||
| Mr_nondim = -Mr_nondim; | ||
| Mt_nondim = -Mt_nondim; | ||
| Q_nondim = -Q_nondim; | ||
| end | ||
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units here are wrong: Q is force per length, P is force, the a would need to be in the numerator not denominator