3D Modelling of a Net and Design of a Flexible Mounting Rod

3D modellering af et net og design af en fleksibel monteringsstang

Knutzen, Daniel Jacobi ; Marciniak, Jonas Støttrup

4. term

Design of Mechanical Systems, Master

2016

2016-06-01

99

Specialet undersøger et system, hvor et net er opspændt af fleksible stænger, og præsenterer både en beregningsmodel og et redesign af stængerne. Modellen forudsiger nettets og stængernes form ved store deformationer og håndterer geometrisk ulinearitet (adfærd, der ændrer sig markant, når systemet deformeres meget) ved at minimere systemets samlede elastiske energi (det totale elastiske potentiale). Denne energibaserede tilgang er robust. Brugeren kan konfigurere netstørrelse og stangplacering, påføre kræfter og randbetingelser, samt opdele stængerne i sektioner for at tilpasse deres opførsel. Både net og stænger kan have ulineær stivhed (stivhed, der ændrer sig med deformation). Modellen er implementeret i MATLAB og bruger den indbyggede, gradientbaserede optimeringsrutine fmincon til at løse for forskydninger. Resultaterne kan visualiseres med både start- og deformeret form. For at kunne simulere det udleverede net og de medfølgende stænger er deres stivheder bestemt eksperimentelt. Modellen er derefter valideret mod et fysisk system. Sammenligningen viser en afvigelse, især fordi netknuderne ikke er medtaget i modellen; deres opførsel er kompleks og vanskelig at beskrive enkelt. Redesignet af stængerne begynder med en morfologisk analyse (en systematisk kortlægning af funktioner og løsningsmuligheder) og fokuserer på at forbedre stængernes udbøjningsegenskaber for at reducere systemets energi ved store deformationer. Dette opnås ved at give stængerne ulineær stivhed gennem et skift fra massivt til hult tværsnit, så de ved bøjning ovaliserer og på et tidspunkt kan kollapse. Designprincippet bygger på Brazier-effekten (tyndvæggede rør bliver ovale under bøjning og mister stivhed). Det nye design forstørrer og fastholder yderdiameteren i stangens midtersektion, mens vægtykkelsen fastlægges via et parameterstudie i ANSYS for at opnå den ønskede stivhedskarakteristik. Geometrisk ulineære analyser peger på 5 mm som passende tykkelse. En prototype blev fremstillet med 6 mm på grund af en databehandlingsfejl opdaget efter produktion. Test af prototypen viste tydelig ovalisering som forventet, og simuleringer for 6 mm stemte godt overens med prototypens opførsel, taget antagelser og fremstillingskvalitet i betragtning. Konklusionen er, at modellen repræsenterer det udleverede net-stang system tilfredsstillende, men kan forbedres ved at inkludere netknuder. Redesignet kan reducere energien i systemet ved store deformationer, og prototypetesten bekræfter designmetoden.

This thesis studies a system where a net is tensioned by flexible rods and presents both a computational model and a redesign of the rods. The model predicts the net and rod shapes under large deformations and handles geometric nonlinearity (behavior that changes significantly when the system deforms) by minimizing the system’s total elastic potential energy. This energy-based approach is robust. Users can configure net size and rod placement, apply forces and boundary conditions, and discretize rods into sections to tailor their behavior. Both the net and rods can have nonlinear stiffness (stiffness that changes with deformation). The model is implemented in MATLAB and uses the built-in, gradient-based optimization routine fmincon to solve for displacements. Results can be visualized with both the initial and deformed shapes. To simulate the provided net and rods, their stiffnesses were measured experimentally. The model was then validated against a physical setup. The comparison shows a discrepancy, mainly because net nodes are not included in the model; their behavior is complex and difficult to capture simply. The rod redesign begins with a morphological analysis (a systematic mapping of functions and solution options) and focuses on improving bending properties to reduce the system’s energy at large deformations. This is achieved by introducing nonlinear stiffness through changing the cross-section from solid to hollow, so the rods ovalize during bending and may eventually collapse. The design principle is based on the Brazier effect (thin-walled tubes become oval under bending and lose stiffness). The new design enlarges and fixes the outer diameter in the rod’s midsection, while the wall thickness is determined via a parameter study in ANSYS to achieve the desired stiffness characteristics. Geometrically nonlinear analyses indicate 5 mm as a suitable thickness. A prototype was produced with 6 mm due to a data processing error discovered after manufacturing. Tests showed clear ovalization as expected, and simulations for 6 mm matched the prototype’s behavior well, considering assumptions and manufacturing quality. In conclusion, the model represents the provided net–rod system satisfactorily but could be improved by including net nodes. The redesign can reduce energy in the system under large deformations, and prototype testing validates the design method.

[This abstract was generated with the help of AI]

Net ; Non-linear ; Buckling ; Prototype ; FEM

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