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Investigating Strains on the Oseberg Ship Using Photogrammetry and Finite Element Modeling

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MAT-VET-F 20002 Examensarbete 15 hp June 2020 Investigating strains on the Oseberg ship using photogrammetry and finite element modeling Andreas Eriksson Erik Thermaenius Abstract Investigating strains on the Oseberg ship using photogrammetry and finite element modeling Andreas Eriksson, Erik Thermaenius Teknisk- naturvetenskaplig fakultet UTH-enheten The Oseberg ship is known as one of the finest surviving artifacts from the Viking age, with origins dated back to the 800s. The ship has been displayed in the Viking ship Besöksadress: museum in Oslo since 1926. The nearly 100 years on museum display along with the Ångströmlaboratoriet Lägerhyddsvägen 1 over 1000 years it was buried has weakened the structure of the ship. To slow down Hus 4, Plan 0 the deterioration, several research projects has been initiated, among them the project ''Saving Oseberg''. A part of ''Saving Oseberg'' is contributing to the planning Postadress: of a new museum for the ship. As a basis for the planning, the ship has been Box 536 751 21 Uppsala monitored with photogrammetry. This is intended as a way to visualise the deformation and displacements of the ship due to seasonal changes in indoor Telefon: temperature and humidity. 018 – 471 30 03 Telefax: In this thesis the photogrammetry data from the hull of the ship was used to make a 018 – 471 30 00 finite element model, and through this model calculate the average strain on each element. The method was based on a previous research project conducted on the Hemsida: Swedish warship Vasa by a research group at the Division of Applied Mechanics at http://www.teknat.uu.se/student Uppsala University. The measurements of the ship was formed into a hull by Delaunay triangulation. The strain was approximated as a Green strain and evaluated using isoparametric mapping of the elements. Through the nodal displacements, the strain was evaluated by approximating the elements as tetrahedrons and calculating the average strain from these elements between the measurements. The result showed an oscillating behavior of the displacements, proving the proposal of seasonal depending displacements. The measured principal strains also matched to the corresponding relative humidity fluctuation during the year. The strain magnitude was relatively even throughout the ship, mostly varying between ±0.4% but certain areas were more subjected than others. A few elements on the starboard side showed very large strains through most of the measurements, this seemed very unusual and was probably the result of inaccuracies or errors in the data. Though the ship is subjected to relative small strains and permanent displacements after annual cycles, the mechano-sorptive strains may lead to accumulated deformation and eventually failure in the weak parts of the wood or at the high stress concentraion parts. In addition, the cyclic strain even in elastic range may cause fatigue failure in any material which could pose a large threat for the future conservation of the ship. Handledare: Kristofer Gamstedt, Reza Afshar Ämnesgranskare: Johan Gising Examinator: Martin Sjödin ISSN: 1401-5757, MAT-VET-F 20002 Tryckt av: Uppsala Populärvetenskaplig sammanfattning Osebergsskeppet är känd som en av de bäst bevarade och mest åtråvärda artefakterna som överlevt från Vikingatiden. Det stora långskeppet med en omkrets på över 40 meter hittades i en gravplats utanför staden Tønsberg i Norge år 1904 och grävdes upp följande år av arkeologerna Haakon Shetelig och Gabriel Gustafson. Till en början förvarades skeppet i en av Oslo Universitets lokaler till dess att Vikingaskeppsmuséet slog upp sina dörrar år 1926, där det befunnit sig sedan dess. Trots att skeppet inte brytits ned under de 1000 år det varit begravet har denna process nu ökat takten. Ett flertal forskningsprojekt har initierats för att sakta ned nedbrytningen och möjliggöra skeppets förefintlighet, bland annat det pågående ”Saving Oseberg”. Då museet som huserar Osbergsskeppet är en gammal byggnad som saknar en modern klimatanläg- gning vilken kan reglerar inomhustemperatur och luftfuktighet till ideala förhållanden så ingår det i ”Saving Oseberg” att bidra med projekteringen till det nya muséet. En forskare har som underlag till projekteringen för den nya muséebyggnaden gjort punktmätningar över skrovet på skeppet med jämna mellanrum. Målet med dessa mätningar är att se hur de uppmätta punkterna förflyttas mellan mättillfällena vilket ger möjlighet att analysera deformationen av skeppet. Detta var syftet med det presenterade kandidatarbetet, som innebar att skapa en modell av skeppet från all mätdata och utifrån förflyttningarna i mätdatan översätta det till töjningar i skrovet på skeppet i %. Mätdatan på skeppet analyserades med programvaran Matlab, där det sammanfogades och tri- angulerades till ett tvådimensionellt skal av skrovet. Utifrån förflyttningarna av mätpunkterna, beräknades den genomsnittliga töjningen på varje triangel (även kallat element) som bygger upp skrovet för varje mätning. Töjning visualiserades med hjälp av en färgskala, där negativ och positiv töjning färgade elementen blå respektive röda. Detta gjorde det enkelt att överblicka skeppet och identifiera s.k. ”hotspots” som utsätts för större töjningar än övriga delar på skeppet. Dessutom visualiserades medelvärdet av mätpunkternas förflyttningar vid varje mättillfälle för de två sidorna på skeppet i en graf. Resultatet visade att det fanns delar på skeppet som var mer utsatta än andra, särskilt utsatt var relingen runt båten och delar av kölen. Detta förklarades enklast av att relingen saknar samma stöd som resten av skrovet och eftersom ungefär halva tyngden av skeppet vilar på kölen medför detta en högre belastning och därmed större töjningar. Halva tyngden eftersom den andra halvan är fördelat på stöttor runt sidorna av skeppet. När medelvärdet av förflyttningarna studerades uppmärksammades ett cykliskt beteende av förflyttningarna på babordsidan vilket troligen beror på årstidsvariationer i temperatur och luftfuktighet, då förflyttningar återfanns på ungefär samma positioner ett år senare. Styrbordsidan var dock mycket mer utsatt och hade ett delvis cyklisk beteende men att utslagen var betydligt högre. För alla skeppets delar syntes även flera element vars töjning var flera storleksordningar högre än elementen runt om. Detta var väldigt orimligt, och vad det berodde på blev inte klarlagt. Troligen något fel i den ursprungliga mätdatan. Slutsatsen blev att skeppet utsätts för töjningar, att dessa skiljde sig på olika delar av skeppet och att förflyttningarna varierade cykliskt under året. Med viss osäkerhet inkluderat så var resultatet relativt väntat och rimligt. i Acknowledgements We, the authors of this thesis, would first of all like to express our gratitude towards our supervi- sors, professor Kristofer Gamstedt and researcher Reza Afshar from the Division of Applied Mechanics at Uppsala University. Both for introducing the project to us and for their guidance and valuable input throughout the project. Along with their previous work on a similar project which has been a helpful inspiration for the general structure of this thesis. Secondly, we want to thank doctoral research fellow David Hauer from the Department of Col- lection Management at Oslo University who is the researcher from ”Saving Oseberg” behind this project. His help with supplying us with the data and answering all our question regarding the data and ”Saving Osberg”-project in general was much appreciated. We would also like to thank our project mentor, researcher Johan Gising from the Division of Drug Design and Discovery and the Division of Nanotechnology and Functional Materials at Uppsala University. His effort in managing the stage-gates, and his positive feedback and support when the project was falling behind the planned time schedule was a great help in keeping us on track. Finally, we would like to acknowledge our dear classmates who kept us company during the whole time span of the project. From the lunches in the sun, to the activities on the nights and weekends was truly delightful highlights which kept our moral high considering the unexpected pandemic which fully broke out just days prior to the start of the project. Without their contributions, this thesis would not had been made possible. Andreas Eriksson Erik Thermaenius Uppsala, May 2020 ii Contents 1Introduction 1 1.1 Background ......................................... 1 1.2 Objective .......................................... 2 1.3 Aims . 2 2Theory 3 2.1 Strainanddeformation................................... 3 2.2 Finiteelements ....................................... 7 2.3 Isoparametricmapping................................... 10 2.4 Delaunaytriangulation................................... 13 2.5 Mapping between vector spaces . 14 3Method 17 3.1 Calculatingthestrain ................................... 17 3.2 Verifyingthestraincalculation . 18 3.3 Measurementsoftheship ................................. 20 3.4 Utilisingthemeasurementdata . 22 4Results 25 5Discussion 38 6 Conclusions 39 Appendix A Strain analysis A.1 A.1 strain.m ..........................................A.1 A.2 elementInOnePlane.m ...................................A.2 A.3 colourFromStrain.m ....................................A.2 A.4 assemble.m .........................................A.4 A.5 centerDataInSphere.m ..................................A.7 iii Glossary aft The direction towards the stern, or rear of a ship. 26, 28, 38 bow The direction towards the stem, or front of a ship. 26, 28, 38 engineering strain
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