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 STATIC MIXERS FOR MISCIBLE FLUIDS IN LAMINAR FLOW WITH THE USE OF COMPUTATIONAL FLUID DYNAMICS (CFD)

Static mixers with improved performance were developed from CFD simulations in a stepwise approach. The relevant geometric features of simple mixer designs and the corresponding mixing mechanisms-laminar shear, elongational flow, and distributive mixing-were identified first. This information was used to formulate guidelines for the development of new geometries. The solid elements of the static mixer should: (a) provide restrictions to the flow; (b) deflect the flow; (c) be sequentially rotated around the flow direction to provide symmetry; (d) extend from the center of the pipe to the vicinity of the walls to avoid short-circuiting; and (e) distribute and remix the flow. Based on these guidelines, two improved mixer designs were developed: the DS A-I mixer has a good mixing efficiency and an acceptable pressure drop; the Fins 35 degrees mixer is more efficient and compact, but requires a larger pressure drop. Their performance indicates that their use is possible on industrial applications.

Modelling and aerodynamic simulation of a vehicle and failure analysis of a laminated front fender

Master Thesis in Mechanical Engineering field of Maintenance and Production

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM). A finite element model considering solid elements of the ABAQUS® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.

The influence of the boundary conditions on low-velocity impact composite damage

The objective of this work was to study the influence of the boundary conditions on low-velocity impact behaviour of carbon-epoxy composite plates. Experimental work and numerical analysis were performed on [04,904]s laminates. The influence of different boundary conditions on the impacted plates was analysed considering rectangular and square plates. The X-radiography was used as a non-destructive technique to evaluate the internal damage caused by impact loading. A three-dimensional numerical analysis was also performed considering progressive damage modelling. The model includes three-dimensional solid elements and interface finite elements including a cohesive mixed-mode damage model, which allows simulating delamination between different oriented layers. It was verified that plate’s boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of the delamination was obtained.

Digitaalisen valmistuksen vaikutus hitsatun rakenteen väsymiskestävyyteen

Tässä työssä tutkittiin kuinka eri tavoin rakenteen mallintaminen vaikuttaa laskettuun väsy-misikään. Työssä tutkittavana rakenteena toimi Sandvik Mining and Construction OY:n las-tauskoneen nostovarsi. Nostovarrelle väsytyskokeet suoritettiin Lappeenrannan teknillisen yliopiston teräsrakenteiden laboratoriossa. Työn tavoitteena oli tutkia miten eri digitaalinen valmistuksen tasot vaikuttavat hitsatulle rakenteelle saatuun kestoikään. Työssä tutkittiin myös miten todellista geometriaa voidaan hyödyntää rakenteen kestoiän arvioinnissa. Väsytyskoejärjestely mallinnettiin FE-menetelmällä, ja järjestelystä tehtiin useita malleja käyttäen solidi- ja laattaelementtejä. Malleista laskettiin väsymisiät hot spot- ja tehollisen lovijännityksen menetelmällä, ja saatuja tuloksia vertailtiin toisiinsa ja väsytyskokeen tulok-siin. Väsytyskokeessa vaurioituneista kohdista tarkemman tutkimuksen kohteena oli nosto-varren palstalevyn kärki. Hot spot-menetelmällä saadut kestoiät vaihtelivat paikoin melko paljon eri mallien välillä. Tehollisen lovijännityksen menetelmällä saaduissa tuloksissa erot olivat pienempiä mallien välillä. FE-mallin ja venymäliuskojen jännitykset poikkesivat toisistaan paikoin melko pal-jon. Todellisen hitsatun rakenteen kestoikään vaikuttaa moni asia, ja täten FE-menetelmällä las-kettu kestoikä voi poiketa huomattavasti todellisesta kestoiästä. Varsinkin hot spot-menetel-mällä tulokset voivat poiketa hyvinkin paljon todellisuudesta, mikäli jännitystila tutkitta-vassa kohdassa on moniaksiaalinen. Todellisen geometrian mallintaminen vaatii tarkkuutta, ja alkuperäisdatan tulee olla mahdollisimman tarkkaa ja riittävän suurelta alueelta, jotta malli vastaa tarpeeksi todellista.

Sekaelementit absoluuttisten solmukoordinaattien menetelmässä

Tässä lisensiaatintyössä käsitellään sekaelementtien sovellusmahdollisuuksia absoluuttisten solmukoordinaattien menetelmässä. Absoluuttisten solmukoordinaattien menetelmä on uudentyyppinen lähestymistapa elementtimenetelmän elementtien koordinaattien määrittämiseksi ja sen yhtenä tavoitteena on tehostaa suuria siirtymiä tai kiertymiä sisältävien elementtien laskentatehokkuutta. Tässä työssä absoluuttisten solmukoordinaattien menetelmä esitellään pääpiirteittäin sekä annetaan esimerkkejä muutamista tyypillisimmistä elementeistä lausuttuna edellä mainittujen koordinaattien perusteella. Sekaelementeiksi kutsutaan elementtityyppejä, missä tuntemattomien muuttujien joukkoja on aina enemmän kuin yksi. Sekaelementit erottavat redusoitumattomista elementeistä siirtymäkentän sisältyminen muuttujaryhmään ja hybridielementeistä muuttujien identtiset ulottuvuudet. Sekaelementtejä käytetään esimerkiksi kokoonpuristumattomien materiaalien rakenneanalyyseissä, alentamaan elementiltä vaadittavia jatkuvuusehtoja tai mallintamaan ilmiöitä, missä fysikaaliset ominaisuudet ovat jostain syystä voimakkaasti toisistaan riippuvaisia. Tämän lisensiaatintyön kirjoittamiseksi on tehty tutkimusta sekaelementtien mahdollisuuksista toimia absoluuttisten solmukoordinaattien menetelmässä. Tutkimuksen tuloksena on saatu aikaan kaksi tässä työssä esiteltävää, varsin rajatun toimintakyvyn omaavaa sekaelementtityyppiä, joiden siirtymäkentät on määritelty globaalien koordinaattien suhteen sisältäen myös orientaatiotermit. Tutkimusaihe vaatii kuitenkin vielä paljon lisätyötä, ennen kuin sekaelementtityyppejä voidaan kauttaaltaan soveltaa absoluuttisten solmukoordinaattien menetelmällä toteutetuissa rakenneanalyyseissä.

Convenience of scallops in plate structures

In this thesis was performed comprehensive study about the convenience of scallops in plate structures. A literature review was performed and lack of knowledge was fulfilled with fatigue tests performed in the laboratory of Steel Structures at the Lappeenranta University of Technology and with finite element method. The aim of this thesis was to produce design guidance for the use of scallops for different structural details and different loading conditions. An additional aim was to include more precise instructions for scallop design to produce good fatigue resistance and appropriate manufacturing quality. The literature review was performed searching bridge engineering and maritime standards and design guides and studies from scientific databases and reference lists from the literature of this field. Fatigue tests were used to research the effect of using scallops or not using scallops to fatigue strength of bracket specimen. Tests were performed on three specimens with different scallop radii and to five specimens without scallops with different weld penetration depths. Finite element method using solid elements, symmetry and submodels was used to determine stress concentration factors for I-beams with scallops. Stresses were defined with hot spot stress method. Choosing to use a scallop or not in the structure is affected by many factors, such as structural and loading conditions and manufacturability. As a rule of thumb, scallops should be avoided because those cause stress concentration points to the structure and take a lot of time to manufacture. When scallops are not used, good quality welding should be provided and full weld penetration is recommended to be used in load carrying corner weld areas. In some cases, it is advisable to use scallops. In that case, circular scallops are recommended to be used and radius should be chosen from fatigue strength or manufacturing point of view.

Analysis of the Stresses in Corrugated Sheets under Bending

This paper presents three different numerical models for the evaluation of the stresses in corrugated sheets under bending. Regarding the numerical simulations different approaches can be considered, i.e., a elastic linear analysis or a physical nonlinear analysis, that considers criteria to fail for the sheet material. Moreover, the construction of the finite element mesh can be used shell elements or solid elements. The choice of each finite element must be made from the consideration of their representativity before behavior to be simulated. Thus, the numerical modelling in this manuscript was performed from the three-dimensional models using the SAP2000Nonlinear software, version 7.42, which has as base the finite elements method (FEM). It was considered shell elements in the build the mesh of finite elements and an analysis of type elastic linear in this case. Five mm thick sheets were evaluated considering three different longitudinal dimensions (spans), i.e., 1100 mm, 1530 mm and 1830 mm. The applied load to the models was 2500 N/m and it was verified that the spans of support of sheets have a significant influence on the results of stresses. The sheets with larger spans present larger stresses for the same applied load. The most intense values of tension occur in the troughs (low waves) of the sheets, on the lower surface, while the most intense values of compression occur in the crests (high waves), on the upper surface of the sheet. The flanks, which are the parts among the troughs and crests of the sheets, are submitted to low levels of stresses. The numeric results of the stresses showed a good agreement with the results obtained from other researchers(3) and these results can be used to predict the behavior of corrugated sheets under bending.

Estudo de tensões residuais em juntas soldadas utilizando o método dos elementos finitos

Pós-graduação em Engenharia Mecânica - FEG

A Comparative Wet Collapse Buckling Study for the Carcass Layer of Flexible Pipes

When there is a failure on the external sheath of a flexible pipe, a high value of hydrostatic pressure is transferred to its internal plastic layer and consequently to its interlocked carcass, leading to the possibility of collapse. The design of a flexible pipe must predict the maximum value of external pressure the carcass layer can be subjected to without collapse. This value depends on the initial ovalization due to manufacturing tolerances. To study that problem, two numerical finite element models were developed to simulate the behavior of the carcass subjected to external pressure, including the plastic behavior of the materials. The first one is a full 3D model and the second one is a 3D ring model, both composed by solid elements. An interesting conclusion is that both the models provide the same results. An analytical model using an equivalent thickness approach for the carcass layer was also constructed. A good correlation between analytical and numerical models was achieved for pre-collapse behavior but the collapse pressure value and post-collapse behavior were not well predicted by the analytical model. [DOI: 10.1115/1.4005185]

Analysis of Combined Bending and Punching Tests of Reinforced Concrete Slabs within IMPACT III Project

The paper reports on a collaborative effort between the Swiss Federal Nuclear Safety Inspectorate (ENSI) and their consultants Principia and Stangenberg. As part of the IMPACT III project, reduced scale impact tests of reinforced concrete structures were carried out. The simulation of test X3 is presented here and the numerical results are compared with those obtained in the test, carried out in August 2013. The general object is to improve the safety of nuclear facilities and, more specifically, to demonstrate the capabilities of current simulation techniques to reproduce the behaviour of a reinforced concrete structure impacted by a soft missile. The missile is a steel tube with a mass of 50 kg and travelling at 140 m/s. The target is a 250 mm thick, 2,1 m by 2,1 m reinforced concrete wall, held in a stiff supporting frame. The reinforcement includes both longitudinal and transverse rebars. Calculations were carried out before and after the test with Abaqus (Principia) and SOFiSTiK (Stangenberg). In the Abaqus simulation the concrete is modelled using solid elements and a damaged plasticity formulation, the rebars with embedded beam elements, and the missile with shell elements. In SOFiSTiK the target is modelled with non-linear, layered shell elements for the reinforcement on both sides; non-linear shear deformations of shell/plate elements are approximately included. The results generally indicate a good agreement between calculations and measurements.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Development and implementation of strategies for the incorporation of reinforcing elements in aluminium alloys by solid state processing

Dissertação para obtenção do Grau de Mestre em Engenharia Mecânica