ESD.77 FINAL PROJECT SPRING 2010

Barge Design Optimization Anonymous MIT Students Abstract— In this project, three members of the Armed Forces tested the multi-disciplinary system design optimization approach to concept evaluation on a simplified platform, a barge. A barge is a non-self propelled vessel that incorporates the basic disciplines of ship building: hydrodynamics, hydrostatics, and structural mechanics. Using four bounded design variables, we attempt to optimize the payload, in tons, that a barge could carry within the physical constraints. We conduct a design of experiments to select an initial design to further optimize. Sequential quadratic programming (SQP) was used to solve the nonlinear program (NLP) in computer software MATLAB. The NLP was also solved using the genertic algorithm (GA) heurisitic. SQP converged quickly and found the optimal solution. The problem was expanded to include another objective, structural weight. The multi-objective problem was solved to create a Pareto front to show the trade-offs for each objective. The results of the study show this approach is feasible for these types of platforms and allow the opportubnity for expansion of included disciplines as well as increased fidelity of the model used. Thus, eventually, a warship or some other such complex system could be designed with this approach. Index Terms—Barge, MDO, SQP, Genetic Algorithm

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1 INTRODUCTION barge is a typically non-self propelled , flatbottom ed vessel u sed initially for river or canal transportation of heavy good s. Althou gh other m eans of transportation have been d eveloped since their introd u ction, barges are still u sed all over the w orld as a low -cost solu tion for carrying either low -valu e or heavy and bu lky item s. Althou gh a barge is very sim plistic com p ared to m ost of its w aterborne brethren, it still presents am ple op po rtu nity to experim ent w ith balanced d esigns. A cu stom er m ay d esire to carry as m u ch payload as p ossible to gain effeciencies in their transportation costs, bu t m axim izing these payload s m u st be balanced by engineers to operate w ithin the law s of physics (inclu d ing stability, bu oyancy, pow ering, resistance, stru ctu res, etc.) and balanced b y financiers to operate w ithin a cu stom er ’s allow able lim its of cost. These tw o very obviou s consid erations alone can create qu ite a com plex balancing act, since these forces requ irem ents, feasibility, cost - tend to oppose each other.

Technology, they have taken a range of cou rses inclu d ing Marine H yd rod ynam ics, Design Principles for Ocean Vehicles, Principles of N aval Architectu re, Pow er and Propu lsion, Stru ctu ral Mechanics, Plates and Shells, Ship Stru ctu ral Analysis and Design, and Ship Design and Constru ction. Each of these cou rses had one of tw o ap proaches. Either the cou rse exam ined a particu lar d iscip line of ship d esign and m entioned that a d esigner shou ld not forget other d isciplines, or the cou rse exam ined the d esign as a process and recognized the m any d isciplines bu t encou raged an iterative, ―throw -it-over-the-w all‖ ap proach to converge to a point d esign. To fu rther em phasize, even the cou rses that recognized the m u ltid isciplinary aspects of ship d esign only d esigned for co nvergence to any feasible d esign w ithin the space, not necessarily an optim al d esign. Thu s, the team w ished to explore the p ossibility of an optim al d esign am ongst each of the d isciplines. We w anted to create an optim al d esign from a m u ltid isciplinary stand point and u nd erstand the associated trad e-offs w ithin the d esign vector. Meanw hile, we 2 MOTIVATION w anted to acqu ire know led ge and skills by u sing the m eThe team ’s interest and backgrou nd in m any asso- thod s and tools of this new trad e. ciated d isciplines has prim arily m otivated this project. The team knew, how ever, that u sing these tools to d eDu ring the team ’s tenu re at Massachu setts Institu te of sign any stand ard sea-going vessel w ou ld provid e d im inishing retu rns d u e to the incred ibly com plex and ———————————————— cou pled natu re of the en tire set of d esign variables. Thu s, the team u sed a sim plified , low -fid elity m od el on a sim Student A is pursuing a Naval Engineer’s Degree and an M S in Engineering M anagement through the Systems Design and Management pro- ple vessel – a barge – to d em onstrate the benefit of these gram, both at the M assachussetts Institute of Technology in Cambridge, tools w ithin the m arine d esign environm ent. The u nd erM A 02139. stand ing w as that the d esign vector cou ld grow and th e Student B i s pursuing a N aval Engineer’s Degree and an M S in fid elity of the m od el cou ld increase m od u larly to accom Engineering M anagement through the Systems Design and Management program, both at the M assachussetts Institute of Technology in Cambridge, m od ate increasingly com plex d esigns for m ore typical ocean platform s. Ind eed , tw o team m em bers have the M A 02139. task of perform ing a clean slate d esign of a w arship for Student C is pursuing an M S in Operational Research at M assachusetts Institute of Technology in Cambridge, M A 02139. the next year, so, shou ld they incorporate these tools in the d esign process, the d esign vector w ill grow and the

A

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ESD.77 FINAL PROJECT SPRING 2010

fid elity and com pu tational expense of the m od el w ill increase very qu ickly. This project proved a good proof of concept for the team m em bers to grow and ad d variables, param eters, constraints, and fid elity to at a later d ate.

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PROBLEM FORMULATION

As w ith any vessel operating in the m arine enviro nm ent, the d esigner has to d eal w ith stability, seakee ping and stru ctu ral strength issu es – to nam e a few - all of w hich com e from d ifferent d isciplines: hyd rostatics, hyd rod ynam ics, and stru ctu ral m echanics. The team u sed the m ethod s and tools of m u lti-d isciplinary system d esign optim ization to optim ize the d esign of a barge w ith respect these d isciplines. The prim ary d esign objective w as to m axim ize the p ayload (i.e. the cargo cap acity) that the barge can effectively carry. Eventu ally, this project also balanced that optim ization against the cost of the vessel, represented by the barge’s w eight. To start, the team u tilized a MATLAB® cod e im plem ented to m od el a barge’s seakeeping behavior (the hyd rod ynam ics of the vessel) d u ring a Design Princip les of Ocean Vehicles term project. The cod e w as lim ited to non self-propelled vehicles, and only ev alu ated heave and pitch m otions. The origin al cod e also only stu d ied one particu lar hu ll shape w ith a particu lar beam to d raft ratio. Ou t of a d esire to elim inate d iscrete variables, the hyd r od ynam ic properties represented in the cod e for each beam to d raft ratio w ere first fitted to cu rves in ord e r to allow for a continu ou s d esign space exploration instead of lim iting the beam to be either 2-, 4-, or 8- tim es the d raft of the barge. Ad d itionally, the team m od eled the hyd rostatics and stru ctu ral strength of the barge. The hyd rostatics requ irem ents and im plem entation w ere d erived from Principles of N aval Architectu re, and provid ed the basic r equ irem ents that the barge float (bu oyancy equ als w eight) and that it floats u pright (positive m etacentric height). The stru ctu ral m echanics m od u le w as d erived from the Am erican Bu ereau of Shipping (ABS) ru les for steel vessels assu m ing m ild steel as the type of m aterial. Originally, the team d esignated 8 d esign variables to be changed d u ring the exporation of the d esign sp ace. These variables w ere length, beam , d raft, d epth, vertical center of gravity (VCG), speed , cross-sectional area coefficient, and d isplacem ent. H ow ever, cross-sectional area coefficient w as a resu lt of beam and d raft, so it w as elim inated and only u sed as an interm ed iate variable. Also, d isplacem ent and VCG w ere a resu lt of length, beam , d raft, and the p ayload – ou r objective – so they w ere elim inated as d esign variables, also, and only u sed as an interm ed iate variables. Becau se d raft w as also a resu lt of payload , it w as elim inated as a d esign variable. Finally, speed w as rem oved as a d esign variable becau se it only affected the hyd rod ynam ics, not the hyd rostatics or stru ctu ral m echanics, so the team thou ght it u ninteresting to explore at this tim e, besid es the fact that typically a speed is d e signated as a requ irem ent by a cu stom er. Thu s, the rem aining d esign variables for this project

w ere:

The length (L) The beam (B) The d ep th (D) The thickness of the steel p lates (t) The bou nd s for ou r d esign variables are typical of barges.

3-1: D esign Variables and Bounds

Ad d itionally, im plem entation of the cod e requ ired several other inpu ts that the team consid ered fixed for the pu rposes of this exploration. These p aram eters w ere r equ ired by one or m ore m od u les to ad equ ately m od el the ap prop riate responses of the m od u les to the d esign vector. These d esign p aram eters w ere: v kg lcg

Design Parameters Speed Payload vertical center of gravity Payload longitudinal center of gravity

Value 10 1.2D 0.5L

Unit knots

ω

Peak spectral f requency

0.7

rad/sec

H

Signif icant wave height

2.5

m

ρ

Sea water density

1025

kg/m3

ρstr

Material thickness

7850

kg/m3

3-2: D esign Parameters and Values

The significant w ave height of the assu m ed ocean cond itions (H ) Peak sp ectral frequ ency of the assu m ed ocean cond itions (ω) Mild steel m aterial d ensity (ρ) You ng’s Mod u lu s of m ild steel (E) The longitu d inal p osition of the center of gravity (LCG) Sea-w ater d ensity (ρsw ) Fresh w ater d ensity (ρfw ) Like any typical engineering problem , the team recognized there w ou ld be constraints that lim ited ou r potential solu tion set. Steel beam s and plates cannot extend to infinite w ithou t bu ckling u nd er their ow n w eight at som e point, let alone su stain ad d ed pressu re from a payload w ithou t bu ckling. Other p hysical constrainsts w ere a ccou nted for. There w ere also assu m ed cu stom er constraints, for instance the frequ ency that the cu stom er w ou ld allow the cargo to get w et given the assu m ed sea state. The team d id their best to accou nt for several physical and cu stom er constraints on this problem , finally end ing w ith: Inequ ality constraints:

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