Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

A computationally efficient shear deformable beam element for large deformation multibody applications

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Relationship of breast fillet deboning time to shear force, pH, cooking loss and color in broilers stunned by high electrical current

Selostus: Korkealla virranvoimakkuudella tainnutettujen broilereiden rintafileen irroitushetken vaikutus lihaksen leikkausvoiman vastukseen, pH:hon, keittohävikkiin ja väriin

Experimental insights into deformation dynamics and intermittency in rapid granular shear flows

This work concerns the experimental study of rapid granular shear flows in annular Couette geometry. The flow is induced by continuous driving of the horizontal plate at the top of the granular bed in an annulus. The compressive pressure, driving torque, instantaneous bed height and rotational speed of the shearing plate are measured. Moreover, local stress fluctuations are measured in a medium made of steel spheres 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity in intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of spherical steel balls. The shearing granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus using a piezoelectric sensor. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations are then investigated by different means through monodisperse and bidisperse packings. Another important feature of rapid granular shear flows is the formation of ordered structures upon shearing. It requires a certain range for the amount of granular material (uniform size distribution) loaded in the system in order to obtain stable flows. This is studied more deeply in this thesis. The results of the current work bring some new insights into deformation dynamics and intermittency in rapid granular shear flows. The experimental apparatus is modified in comparison to earlier investigations. The measurements produce data for various quantities continuously sampled from the start of shearing to the end. Static failure and dynamic shearing ofa granular medium is investigated. The results of this work revealed some important features of failure dynamics and structure formation in the system. Furthermore, some computer simulations are performed in a 2D annulus to examine the nature of kinetic energy dissipation. It is found that turbulent flow models can statistically represent rapid granular flows with high accuracy. In addition to academic outcomes and scientific publications our results have a number of technological applications associated with grinding, mining and massive grain storages.

The Dynamics of Force Fluctuations in Shear Granular Flows

Tämän työn tavoitteena oli tutkia rakeisen materiaalin kinematiikkaa ja rakentaa koelaitteisto rakeisen materiaalin leikkausjännitysvirtauksien tutkimiseen. Kokeellisessa osassa on keskitytty sisäisiin voimaheilahteluihin ja niiden ymmärtämiseen. Teoriaosassa on käyty läpi rakeisen materiaalin yleisiä ominaisuuksia ja lisäksi on esitetty kaksi eri tapaa mallintaa fysikaalisien ominaisuuksien heilahteluja rakeisessa materiaalissa. Nämä kaksi esitettyä mallinnusmenetelmää ovat skalaarinen q-malli ja simulointi. Skalaarinen q-malli määrittelee jokaiseen yksittäiseen rakeeseen kohdistuvan jännityksen, rakeen ollessa osa 2- tai 3-dimensionaalista asetelmaa. Tämän mallin perusidea on kuvata jännityksien epähomogeenisuutta, joka johtuu rakeiden satunnaisasettelusta. Simulointimallinnus perustuu event-driven algoritmiin, missä systeemin dynamiikkaa kuvataan yksittäisillä partikkelien törmäyksillä. Törmäyksien vaiheet ratkaistiin käyttämällä liikemääräyhtälöitä ja restituution määritelmää. Teoriaosuudessa käytiin vielä pieniltä osin läpi syitä jännitysheilahteluihin ja rakeisen materiaalin lukkiintumiseen. Tutkimuslaitteistolla tutkittiin rakeisen materiaalin käyttäytymistä rengasmaisessa leikkausjännitysvirtauksessa. Tutkimusosuuden päätavoitteena oli mitata partikkelien kosketuksista ja törmäyksistä johtuvia hetkellisiä voimaheilahteluja rengastilavuuden pohjalta. Rakeisena materiaalina tutkimuksessa käytettiin teräskuulia. Jännityssignaali ajan funktiona osoittaa suurta heilahtelua, joka voi olla jopa kertalukua keskiarvosta suurempaa. Tällainen suuren amplitudin omaava heilahtelu on merkittävä haittapuoli yleisesti rakeisissa materiaaleissa käytettyjen jatkuvuusmallien kanssa. Tällainen heilahtelu tekee käytetyt jatkuvuusmallit epäpäteviksi. Yleisellä tasolla jännityksien todennäköisyysjakauma on yhtäpitävä skalaarisen q-mallin tuloksien kanssa. Molemmissa tapauksissa todennäköisyysjakaumalla on eksponentiaalinen muoto.

Diodilaserin käytön edellytykset ohutlevyjen hitsauksessa

Diplomityössä tutkitaan diodilaserhitsausta mahdollisena teollisuuden menetelmänä ja menetelmän vaatimuksia hitsattaessa ohutlevyjä. Työssä tutkittavat materiaalit ovat kylmävalssattu teräs ja ruostumaton teräs sekä liitosmuotoina päittäis-, laippa- ja päällekkäisliitos. Materiaalivahvuudet ovat 0,50 mm:stä 1,50 mm:iin. Työn tavoitteena on määrittää näille kyseisille materiaaleille ja liitosmuodoille hitsausnopeus levynvahvuuden funktiona. Lisäksi käsitellään diodilaserin rakennetta, säteen muodostusta, säteen muokkaamista, säteen analysointia ja säteen turvallisuuteen liittyviä asioita. Suoritetaan vertailua käytössä oleviin muihin lasertyöstömenetelmiin konepajoissa ja tehdään arvio mahdollisen diodilaserinvestoinnin kannattavuudesta. Diodilaserhitsauskokeissa käytettiin Hämeen ammattikorkeakoulun Riihimäen yksikön 1 kW:n tehoista diodilaseria. Koekappaleet leikattiin suuntaisleikkurilla. Osalle hitsatuista kappaleista tehtiin poikittaiset vetokokeet ja mitattiin mikrokovuudet. Virheitä tutkittiin silmämääräisesti sekä radiografisella kuvauksella. Kaikille tutkituille liitoksille, materiaaleille ja vahvuuksille saatiin määriteltyä hitsausnopeudet. Tehtyjen testien perusteella suuntaisleikkurin käyttö on mahdollista. Lisäksi havaittiin suojakaasun käytön myötä, että kirkkaan sulan aiheuttama heijastavuuden kasvu edellyttää hitsausnopeuden pienentämistä.

The Sottunga-Jurmo shear zone : structure and deformation history of a crustal-scale ductile shear zone in SW Finland

The aim of this study is to gain a better understanding of the structure and the deformation history of a NW-SE trending regional, crustal-scale shear structure in the Åland archipelago, SW Finland, called the Sottunga-Jurmo shear zone (SJSZ). Approaches involving e.g. structural geology, geochronology, geochemistry and metamorphic petrology were utilised in order to reconstruct the overall deformation history of the study area. The study therefore describes several features of the shear zone including structures, kinematics and lithologies within the study area, the ages of the different deformation phases (ductile to brittle) within the shear zone, as well as some geothermobarometric results. The results indicate that the SJSZ outlines a major crustal discontinuity between the extensively migmatized rocks NE of the shear zone and the unmigmatised, amphibolite facies rocks SW of the zone. The main SJSZ shows overall dextral lateral kinematics with a SW-side up vertical component and deformation partitioning into pure shear and simple shear dominated deformation styles that was intensified toward later stages of the deformation history. The deformation partitioning resulted in complex folding and refolding against the SW margin of the SJSZ, including conical and sheath folds, and in a formation of several minor strike-slip shear zones both parallel and conjugate to the main SJSZ in order to accommodate the regional transpressive stresses. Different deformation phases within the study area were dated by SIMS (zircon U-Pb), ID-TIMS (titanite U-Pb) and 40Ar/39Ar (pseudotachylyte wholerock) methods. The first deformation phase within the ca. 1.88 Ga rocks of the study area is dated at ca. 1.85 Ga, and the shear zone was reactivated twice within the ductile regime (at ca. 1.83 Ga and 1.79 Ga), during which the strain was successively increasingly partitioned into the main SJSZ and the minor shear zones. The age determinations suggest that the orogenic processes within the study area did not occur in a temporal continuum; instead, the metamorphic zircon rims and titanites show distinct, 10-20 Ma long breaks in deformation between phases of active deformation. The results of this study further imply slow cooling of the rocks through 600-700ºC so that at 1.79 Ga, 2 the temperature was still at least 600ºC. The highest recorded metamorphic pressures are 6.4-7.1 kbar. At the late stages or soon after the last ductile phase (ca. 1.79 Ga), relatively high-T mylonites and ultramylonites were formed, witnessing extreme deformation partitioning and high strain rates. After the rocks reached lower amphibolite facies to amphibolite-greenschist facies transitional conditions (ca. 500-550ºC), they cooled rapidly, probably due to crustal uplift and exhumation. The shear zone was reactivated at least once within the semi-brittle to brittle regime between ca. 1.79 Ga and 1.58 Ga, as evidenced by cataclasites and pseudotachylytes. In summary, the results of this study suggest that the Sottunga-Jurmo shear zone (and the South Finland shear zone) defines a major crustal discontinuity, and played a central role in accommodating the regional stresses during and after the Svecofennian orogeny.

The Sottunga-Jurmo shear zone : structure and deformation history of a crustal-scale ductile shear zone in SW Finland

The aim of this study is to gain a better understanding of the structure and the deformation history of a NW-SE trending regional, crustal-scale shear structure in the Åland archipelago, SW Finland, called the Sottunga-Jurmo shear zone (SJSZ). Approaches involving e.g. structural geology, geochronology, geochemistry and metamorphic petrology were utilised in order to reconstruct the overall deformation history of the study area. The study therefore describes several features of the shear zone including structures, kinematics and lithologies within the study area, the ages of the different deformation phases (ductile to brittle) within the shear zone, as well as some geothermobarometric results. The results indicate that the SJSZ outlines a major crustal discontinuity between the extensively migmatized rocks NE of the shear zone and the unmigmatised, amphibolite facies rocks SW of the zone. The main SJSZ shows overall dextral lateral kinematics with a SW-side up vertical component and deformation partitioning into pure shear and simple shear dominated deformation styles that was intensified toward later stages of the deformation history. The deformation partitioning resulted in complex folding and refolding against the SW margin of the SJSZ, including conical and sheath folds, and in a formation of several minor strike-slip shear zones both parallel and conjugate to the main SJSZ in order to accommodate the regional transpressive stresses. Different deformation phases within the study area were dated by SIMS (zircon U-Pb), ID-TIMS (titanite U-Pb) and 40Ar/39Ar (pseudotachylyte wholerock) methods. The first deformation phase within the ca. 1.88 Ga rocks of the study area is dated at ca. 1.85 Ga, and the shear zone was reactivated twice within the ductile regime (at ca. 1.83 Ga and 1.79 Ga), during which the strain was successively increasingly partitioned into the main SJSZ and the minor shear zones. The age determinations suggest that the orogenic processes within the study area did not occur in a temporal continuum; instead, the metamorphic zircon rims and titanites show distinct, 10-20 Ma long breaks in deformation between phases of active deformation. The results of this study further imply slow cooling of the rocks through 600-700ºC so that at 1.79 Ga, 2 the temperature was still at least 600ºC. The highest recorded metamorphic pressures are 6.4-7.1 kbar. At the late stages or soon after the last ductile phase (ca. 1.79 Ga), relatively high-T mylonites and ultramylonites were formed, witnessing extreme deformation partitioning and high strain rates. After the rocks reached lower amphibolite facies to amphibolite-greenschist facies transitional conditions (ca. 500-550ºC), they cooled rapidly, probably due to crustal uplift and exhumation. The shear zone was reactivated at least once within the semi-brittle to brittle regime between ca. 1.79 Ga and 1.58 Ga, as evidenced by cataclasites and pseudotachylytes. In summary, the results of this study suggest that the Sottunga-Jurmo shear zone (and the South Finland shear zone) defines a major crustal discontinuity, and played a central role in accommodating the regional stresses during and after the Svecofennian orogeny.

Eri MAG-hitsausprosessien ja -parametrien vaikutus suurlujuusteräksestä valmistetun otsapienahitsin äärikestävyyteen, muodonmuutoskykyyn ja vauriomuotoon

Työssä tutkittiin Ruukki Oyj:n suorasammutetusta S960QC-teräksestä valmistetun kuormaakantavan levyjen ristiliitoksen pienahitsien lujuutta, muodonmuutoskykyä ja vaurioitumismekanismia laajaan kokeelliseen aineistoon perustuen. Tärkeimpänä muuttujana koematriisissa olivat eri MAG-hitsausprosessit. Perinteisen kuumakaarihitsauksen vertailukohteena oli Kemppi Oy:n uusi adaptiivinen valokaaren pituutta säätävä WiseFusion-hitsaustoiminto kuuma- ja pulssikaarihitsauksessa. Näiden kolmen hitsausprosessin rinnalla varioitiin erisuuruisia a-mittoja, eri hitsauslisäaineita ja hitsin erikylkisyyttä. Lisäksi juuritunkeuman estämisen vaikutusta hitsien käyttäytymiseen tutkittiin täydentävällä koesarjalla, jossa tunkeuman muodostuminen estettiin levyjen väliin asetetulla volframilevyllä. Työn perimmäisenä tavoitteena oli selvittää syy aiemmassa tutkimuksessa havaitulle pienahitsien vaurioitumiselle leikkautumalla sularajaa pitkin. Sularajan suhteellista pituutta saadaan kasvatettua estämällä hitsin juuritunkeuma ja absoluuttista pituutta saadaan lisää kateettipoikkeaman avulla. Lisäksi tutkimuksessa oli tarkoitus tuoda esille suurlujuusteräksisen liitoksen eri mitoituslähtökohdat (mm. lämmöntuonnin kontrollointi). Tämän vuoksi hitsausparametrit mitattiin jännitteen ja virran hetkellisiin arvoihin perustuen, jolloin kuuma- ja pulssikaarihitsauksen laskennalliset hitsaustehot ovat vertailukelpoisia. Koehitseistä valmistettiin hieet hitsien tarkan geometrian määrittämiseksi ja liitoksen mekaaniset ominaisuudet tutkittiin vetokokeella. Tulosten perusteella sularajavaurio aktivoituu pulssikaarella hitsatuissa koekappaleissa. Tämä aiheutunee pulssi- ja kuumakaarihitsauksen sularajan mikrorakenteiden eroavaisuudesta. Sularajavaurio näyttää huonontavan hitsien muodonmuutoskykyä, mutta jatkokokeita tuloksen verifioimiseksi on tehtävä. S960QC-teräkselle ominaisen pehmenneen vyöhykkeen vaurio ei aktivoitunut, vaikka Ruukin antamat jäähtymisaikasuositukset ylitettiin reilusti.