Mbot at 13:34, 8 November 2011

2011-11-08T13:34:57Z

← Older revision		Revision as of 09:34, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: con		Problem type appears to be: con
	Time for symbolic processing: 0.~~16817~~ seconds		Time for symbolic processing: 0.16741 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 16 GradEv 14 ConstrEv 14 ConJacEv 14 Iter 13 MinorIter 20		FuncEv 16 GradEv 14 ConstrEv 14 ConJacEv 14 Iter 13 MinorIter 20
	CPU time: 0.031200 sec. Elapsed time: 0.~~020000~~ sec.		CPU time: 0.031200 sec. Elapsed time: 0.024000 sec.

	</pre>		</pre>

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2011-11-02T21:03:02Z

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{{Part Of Manual|title=the TomSym Manual|link=[[TomSym|TomSym Manual]]}}

TomSym implementation of GAMS Example (SHIP,SEQ=22)

This model designs a vertically corrugated transverse bulkhead of an oil tanker. The objective is to design for minimum weight and meet stress, moment of inertia and plate thickness constraints.

Bracken, J, and McCormick, G P, Chapter 6. In Selected Applications of Nonlinear Programming. John Wiley and Sons, New York, 1968.

<source lang="matlab">
% s: bulkhead sections (top, middle, bottom)

toms 3x1 s

gam = 0.001; % specific gravity of water
sig = 1200; % maximum bending stress
dnv = 3.9; % det norske veritas factor
ha = 250; % height above panel
gamsteel = .0078; % specific weight of steel

% Length of panel
l = [495; 385; 315];

% Height at the base of panel
hb = ha+sum(full(spdiags(repmat(l',3,1),[0 1 2],3,3)))';

% Height at the middle of panel
h = hb - l/2;

% Constant number one
k1 = gam*h.*l.*l/12/sig;

% Constant number two
k2 = dnv*1.05e-4*sqrt(hb);

e = 0.8;
width = 500;
ca = 0.2;
tlow = 1.05;

toms 3x1 z th % module, plate thickness
% width of flange, length of web, depth of corrugation, width of
% corrugation, weight of structure
toms wl lw d wc w

% Module definition
eq1 = {z == d*th*(lw/3+wl*e)/2};

% Width of corrugation - definition
eq2 = {(wc-wl)^2 == lw^2 - d^2};

% Bending stress
eq3 = {z >= k1*wc};

% Moment of inertia
eq4 = {z*d/2 >= 2.2*(k1*wc).^(4/3)};

% Plate thickness - width of flange
eq5 = {th >= k2*wl + ca};

% Plate thickness - length of web
eq6 = {th >= k2*lw + ca};

% Geometric constraint
eq7 = {lw >= d};

% Total weight of structure

obj = gamsteel*width*(wl+lw)*sum(th.*l)/wc/1000;

% Bound on th
cbnd = {th >= tlow};

% Starting point
x0 = {th == [1.2;1.2;1.3]; wl == 45.8; lw == 43.2
d == 30.5; wc == wl+sqrt(lw^2-d^2)
z == d*th*(lw/3+wl*e)/2};

cons = {cbnd; eq1; eq2; eq3; eq4; eq5; eq6; eq7};
solution = ezsolve(obj,cons,x0);
</source>

<pre>
Problem type appears to be: con
Time for symbolic processing: 0.16817 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Problem 1 f_k 5.540914709534572300
sum(|constr|) 0.000000000717364057
f(x_k) + sum(|constr|) 5.540914710251936300
f(x_0) 6.658577357100706500

Solver: snopt. EXIT=0. INFORM=1.
SNOPT 7.2-5 NLP code
Optimality conditions satisfied

FuncEv 16 GradEv 14 ConstrEv 14 ConJacEv 14 Iter 13 MinorIter 20
CPU time: 0.031200 sec. Elapsed time: 0.020000 sec.

</pre>

TomSym Structural Optimization - Revision history

Mbot at 13:34, 8 November 2011

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} TomSym implementation of GAMS Example (SHIP,SEQ=22) This model designs a vertically corrugated transver..."