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<p> Mixed transitional finite elements, which enable the simultaneous use of the three-node triangular mixed and eight-node isoparametric displacement finite elements, are developed to reduce the amount of computer storage required in the mixed finite element method. Numerical testing of the simultaneous use of the above mixed, mixed transitional and displacement finite elements are also carried out to investigate numerical instability, orientation problems and convergence in the energy sense. The examples of a plane stress cantilever subjected to parabolically varying end shear and a plane strain, square plate with a circular hole in the middle are analyzed and the results obtained are found to be in very good agreement with those reported in the literature.</p> <p> The three-element scheme above is then applied to problems in linear elastic fracture mechanics. The energy release rate approach using the direct derivative method is incorporated to compute the Mode I stress intensity factor KI. Two plane stress isotropic rectangular plates with symmetric edge cracks and a central crack, respectively, and a plane stress orthotropic square plate with a central crack are analyzed. The stress intensity factors obtained are in excellent agreement with the available numerical results, and with significant reduction in computer storage requirements compared to that of the mixed finite element method alone.</p> <p> Mixed mode linear elastic fracture problems are also considered. In this case, Ishikawa's scheme of decomposing the near crack tip stress and displacement fields is used along with the direct derivative method to compute the mixed mode stress intensity factors KI and KII. The stress intensity factors KI and KII obtained for a deep cantilever with an edge crack subjected to end shear are within 0.62 and 3.74 percent of the numerical results reported in the literature. The prediction of the branching angles for crack extensions are examined and the criterion of maximum energy release rate is used along with Ishikawa's scheme to calculate the angles of crack branching for a plane stress square plate with an oblique crack, subject to uniaxial tension. Good agreement with the results using the maximum stress criterion is observed.</p> / Thesis / Master of Engineering (MEngr)

The project is a research on liquid methane. It is stored in a standing and static pressure vessel specially calculated for cryogenic purposes. All the simulations have been done using the finite element method.  The  finite  element  method  (FEM)  or  finite  element  analysis  (FEA)  is  a  numerical technique to find approximate solutions for partial differential equations and it is used to simulate the strength of materials. FEM allows the user to visualize the distribution of stresses and displacements. There is a wide range of software to do FEM simulations, the software chosen for the project is Pro/Engineer Wildfire 4.0.  Pro-Engineer  is  a  CAD/CAM/CAE  software  developed  by  Parametric  Technology Corporation (PTC).  It provides solid modeling, assembly modeling and finite element analysis.  The  results  obtained  in  the  mechanical  analysis  executed  with  the  application  Pro-mechanica show that the designed container holds the loads applied and stands stable.  The thermal analysis of the insulation verifies that the amount of heat exchanged with the environment is on acceptable levels. Finally, to protect the integrity of the structure the proper paints have been selected.

<p> In this work the direct, kinematic, small-displacement theory has been developed for the analysis of thin, elastic members which are curved and twisted in their natural configurations. Principles of continuum mechanics have been used to derive the equations of equilibrium. Throughout this investigation the three-dimensional aspect of the problem is preserved. Local kinematic compatibility of the displacement field has been investigated by the formal Saint-Venant's method. This development serves to substantiate the validity of the kinematic tridimensional approach. By the judicious neglection of small terms of higher order throughout this analysis, the basic system of equations arrived at by the author admit favourable comparison with the existing equations by other authors.</p> / Thesis / Master of Engineering (MEngr)

To support the trust in the design development of adhesively bonded joints, it is important to precisely predict their mechanical failure load. A numerical simulation model with a two-dimensional linear elastic cohesive zone model using a combination of a soft and a stiff adhesive is developed to optimize the strength of a lap-joint. Separation under mixed-mode conditions (normal and shear direction) is considered. By varying the length of the adhesives, the fracture load is optimized. The results obtained from the numerical experiments show an improvement in strength.

Although many fracture models are based on two-dimensional plane strain approximations, accurately predicting fracture propagation geometry requires accounting for the three-dimensional aspects of fractures. In this study, we implemented 3-D displacement discontinuity (DD) boundary element modeling to investigate the following intrinsically 3-D natural or hydraulic fracture propagation problems: the effect of fracture height on lateral propagation of vertical natural fractures, joint development in the vicinity of normal faults, and hydraulic fracture height growth and non-planar propagation paths. Fracture propagation is controlled by stress intensity factor (SIF) and its determination plays a central role in LEFM. The DD modeling is used to evaluate SIF in Mode I, II and III at the tip of an arbitrarily-shaped embedded crack by using crack-tip element displacement discontinuity. We examine the accuracy of SIF calculation is for rectangular, penny-shaped, and elliptical planar cracks. Using the aforementioned model for lateral propagation of overlapping fractures shows that the curving path of overlapping fractures is strongly influenced by the spacing-to-height ratio of fractures, as well as the differential stress magnitude. We show that the angle of intersection between two non-coincident but parallel en-echelon fractures depends strongly on the fracture height-to-spacing ratio, with intersection angles being asymptotic for "tall" fractures (large height-to-spacing ratios) and nearly orthogonal for "short" fractures. Stress perturbation around normal faults is three-dimensionally heterogeneous. That perturbation can result in joint development at the vicinity of normal faults. We examine the geometrical relationship between genetically related normal faults and joints in various geologic environments by considering a published case study of fault-related joints in the Arches National Park region, Utah. The results show that joint orientation is dependent on vertical position with respect to the normal fault, the spacing-to-height ratio of sub-parallel normal faults, and Poisson's ratio of the media. Our calculations represent a more physically reasonable match to measured field data than previously published, and we also identify a new mechanism to explain the driving stress for opening mode fracture propagation upon burial of quasi-elastic rocks. Hydraulic fractures may not necessarily start perpendicular to the minimum horizontal remote stress. We use the developed fracture propagation model to explain abnormality in the geometry of fracturing from misaligned horizontal wellbores. Results show that the misalignment causes non-planar lateral propagation and restriction in fracture height and fracture width in wellbore part. / text

In the present work, an investigation of the fatigue life benefits emerging from fillet weld geometries optimization has been carried out. At first, an introduction to ageing mechanisms, corrosion and especially fatigue, acting on operating marine structures has been made. Residual stresses at weld toes, stress modes, and types, geometrical factors (weld angle, toe radius, leg length), welding techniques selected, post-welding treatment and plate‟s material are some of the principal factors affecting the fatigue life of a fillet weld joint. Especially, the accuracy of various approaches in fatigue life estimation of specific geometries under pre-set types and levels of stress is studied. It is evident so far that even the notch stress concept is the most accurate method based on S-N curves, the Fracture Mechanics approach can offer more accurate solutions of a crack development through the material. Towards this, a literature review on crack evolution aspects in welded and non-welded plates under bending and tension was performed; substantial parameters were determined and finally implemented in the LEFM model which was used for the simulation purposes of Chapter 6. As far as the crack aspect ratio evolution is concerned, an extensive reference is available in literature since many researchers have investigated its contribution to the determination of geometrical paths, commonly known as “Preferred Propagation Paths”. Their significance is related with our ability to determine accurate SIF solutions leading to precise fatigue life estimations. A typical fillet weld joint 2-D model has been developed in CAE Abaqus software and a Finite Element Analysis of subject T-profile has been carried out. Through this analysis, the fillet weld angle, the weld leg length, the weld toe curvature radio ρ and the carrying load plate thickness are examined for their impacts on the maximum surface stress. Finally, a number of stress mitigating measures are proposed and their effects are analyzed. Undoubtedly, the notch stress concept today is gradually gaining more and more acceptance among other fatigue analysis practices, hence the need for an estimation of the actual surface stresses along fillet weld toes, has become imperative. Towards this, different 2-D geometries are tested against stress concentration factors developed at weld toes, which are calculated on the basis of maximum in-plane principal stresses over nominal stresses in mode I pure bending and pure tension respectively. Moreover, validation with corresponding results from literature is provided. Finally, three different concepts for reducing the maximum surface stresses are presented. The first one proposes grinding of the weld toe area and formulation of an artificial U-notch or a part- circular profile. The second one applies to non-penetrating welds and assumes the existence of a root gap of a specific geometry which is related to the fatigue life and stress concentration factor of the fillet weld joint. Last but not least, the relatively recent concept of the variable radius notch is discussed, even though it is applicable mostly to notched bodies, not weld joints. Afterwards, a Linear Elastic Fracture Mechanics analysis of reference 2D fillet weld model is demonstrated. A number of geometrical parameters considered at previous stage for their impact on surface Stress Concentration levels at the weld toe region, have been correlated to fatigue life benefits in terms of increased number of stress cycles till failure. An extensive analysis of 9 different T-butt weld joint geometries has been provided in order to investigate how positively a possible SCF reduction can affect the fatigue life of a weld joint. Essential geometric variations (weld angle, length, toe radius, root slot) were considered in the 2D model. All calculated benefits both in pure bending and pure tension cases have been reported accordingly. Based on a linear interpolation of the points scatter (SCF, N-cycles) both in banding and tension, it was observed that a surface stress mitigation of 1% could lead to 1,33 up to 2,5% fatigue life benefit in the range of SCF=2 – 2,5. It is evident so far that the geometrical optimization of a weld joint in respect of notch stress mitigation can be a powerful tool both in shipbuilding and maintenance practice in the future. However, technically wise their application may incur high initial costs of improved tools of welding and post welding treatment and robots even though it would consist a cost effective solution in a medium/long term basis. Finally, the above process is followed by a reliability analysis of the most critical geometrical parameters affecting the fatigue life of a fillet weld joint. Reliability assessment results concerning medium, high and low cycle fatigue are provided and a comparative analysis of each factor‟s impact on fatigue life has been carried out.

This study aims to comprehend the bistable and multi-stable behaviour of flexible straws with the intention of utilising it for future engineering applications. This behaviour is achieved by the multiple inversions of conical frustum shells within the corrugation of a flexible straw. This study examined the effects of various material models, geometry variables and loading methods on the inversion of close-top and open-top conical frustum shells via experiments and FEM simulations. This thesis consists of three main parts, and the second and the third parts are complementary to each other: First, we investigated the effects of applying a uniform vertical load to the upper rim of open-top frustum shells via FEM simulations. A reference model was simulated based on the measurements of an ordinary polypropylene flexible straw specimen, using two material models - linear elastic and elastically perfectly plastic. The effects of the interactions between frusta of the corrugated segment of a flexible straw were also studied by evaluating the difference in responses between an individual frustum and conjugated models of two or three frusta. It was found that by constraining the rotation of its bottom rim, an individual frustum can fairly reproduce the complex bistable behaviour of the shorter frustum within the corrugated part of a flexible straw. Furthermore, detailed parametric studies that focused on the effects of various geometric parameters were conducted and generalised formulas that predicted the critical force were derived. A comparison between the simulated results and the analytical model in predicting progressive inversion was made to distinguish the geometric boundaries that separate the one-off snap-through to the progressive inversion of frustum shells. Next, the behaviour of close-top frustum shells in response to vertical point loading at various locations on the top surface was evaluated. A hyperelastic material was used to fabricate the physical specimens. During the experiments, the corresponding deformed shapes were recorded by 3D scanning in addition to measurements of the displacement and reaction force. We observed a close resemblance between the experimental and FEM simulated results, which validated the FEM models. Two local peaks were observed before the structure was fully inverted into its secondary stable state and the overall critical force of the structure was defined by the higher one of the two. The relationship between their magnitudes and the loading locations was analysed and an optimal loading location which gave the minimum critical force was proposed and verified by additional simulations. Furthermore, generalised formulas in predicting critical force were also acquired based on parametric studies. The optimal loading location was found to be constant in spite of variations in height and thickness. The third part of this thesis discussed the effects of lateral point loading on both close-top and open-top frustum shells at various locations on the side surface and supplemented the second part. It is found that the removal of the top surface could cause the critical force to decrease if a point load was applied laterally. Moreover, we were able to fully invert the structure with a lower critical force through lateral loading in comparison to vertical loading.

Tanks are storage vessels for liquids. They can have different appearances; some are short and wide, others are tall and slim, some are small, others are large. In this thesis a tank of 6 m in both diameter and height has been used to obtain numerical results of the stresses in the tank. Tanks are most often thin-walled with stepwise variable shell thickness with thicker wall sections at the bottom of the tank and thinner at the top. Since they are thin-walled they are susceptible to buckling and there are conditions the shell construction must meet. The conditions that has to be met are determined by the laws and regulations that govern tank design. The National Board of Housing, Building and Planning (Boverket) is the new Swedish authority for rules of tank design and the Eurocodes are the new family of standards that should be followed. Sweco Industry AB is the outsourcer of this thesis and wants to clarify what rules that apply now when the Eurocodes are to be followed. The thesis project has produced a calculation document in Mathcad for tank shell design according to the Eurocodes with stress calculations according to membrane theory and linear elastic shell analysis. This thesis has also produced a comparison of stresses calculated using membrane theory, linear elastic shell analysis and finite element method (FEM). The comparison has been made for numerical results given for an arbitrarily designed tank wall. The loads acting on the tank included in the description were self-weight, internal and hydrostatic pressure as well as wind and snow loads. The loads were described in accordance with the Eurocodes. Some assumptions had to be made where the standard was vague or deficient in order to make calculations by hand possible. For example, the wind load had to be described as an axisymmetrically distributed load rather than an angularly varying. The stresses in the tank wall were calculated through creating free-body diagrams and declaring equations for force and moment equilibrium. The loads and boundary conditions were set in a corresponding manner in the FEM software Ansys as in the calculation document in order to obtain comparable results. When compared, the stress results calculated with membrane theory and FEM were quite similar while the stresses calculated with linear analysis were a lot larger. The bending moments were assumed to be too large which make the results of the linear analysis dominated by the moments. The arbitrarily dimensions set for the tank did thus not fullfill the conditions when linear analysis was used but did so for membrane theory and FE-analysis. Since the results calculated with membrane theory were very close to FEM in most cases, even without expressions for local buckling, it was assumed to be an adequate method in this application. Expressions for local buckling are although needed for the meridional normal stress. The conclusions of the results obtained are that membrane theory is a simple and adequate method in most cases. Linear analysis thus becomes redundant since it is more complicated and more easily leads to faulty results. Furthermore it cannot be used for higher consequence classes than membrane theory. FEM, with a computer software such as Ansys, is although the most usable calculation method since it can conduct more complicated calculations and is allowed to be used for all consequence classes.