This thesis deals with glued laminated beams with holes. Different hole geometries, circular and quadratic,  and reinforcement methods were investigated. A total of 24 tests were performed using two types of reinforcements (glass fiber and plywood) and testing unreinforced beam. During testing of the beams without reinforcement a contact free deformation measurement system was used to capture the deformation pattern. A commercial finite element software package was used to perform numerical calculations of the response of the beams. The FE-analyses were also compared with the experimental results. The test results showed that the reinforcement with plywood was more efficient than the reinforcement with glass fiber. In addition, the two hole geometries showed different failure behaviors. The beams with quadratic holes showed a less brittle behavior, although at a lower load level than the beams with circular holes. / Denna rapport behandlar limträbalkar med hål. Olika hålgeometrier, cirkulära och kvadratiska hål, och olika metoder att förstärka balkarna vid hålet undersöktes. Totalt 24 enskilda provningar genomfördes med två olika förstärkningsmetoder (glasfiber och plywood) samt med balkar utan förstärkning. Vid provning av de oförstärkta balkarna användes ett system för beröringsfri deformationsmätning för att få en bild av deformationsmönstret. Ett kommersiellt finita elementprogram användes också för att analysera balkarnas respons och för att jämföra med provningsresultaten. Provningarna visade att förstärkningen med plywood var effektivare än förstärkningen med glasfiber. Vidare uppvisade de olika hålgeometrierna olika brottbeteenden, där de kvadratiska hålen gav mindre spröda brott, dock vid en i genomsnitt lägre brottlast än de cirkulära hålen.

<p>This thesis deals with glued laminated beams with holes. Different hole geometries, circular and quadratic,  and reinforcement methods were investigated. A total of 24 tests were performed using two types of reinforcements (glass fiber and plywood) and testing unreinforced beam. During testing of the beams without reinforcement a contact free deformation measurement system was used to capture the deformation pattern. A commercial finite element software package was used to perform numerical calculations of the response of the beams. The FE-analyses were also compared with the experimental results. The test results showed that the reinforcement with plywood was more efficient than the reinforcement with glass fiber. In addition, the two hole geometries showed different failure behaviors. The beams with quadratic holes showed a less brittle behavior, although at a lower load level than the beams with circular holes.</p> / <p> </p><p>Denna rapport behandlar limträbalkar med hål. Olika hålgeometrier, cirkulära och kvadratiska hål, och olika metoder att förstärka balkarna vid hålet undersöktes. Totalt 24 enskilda provningar genomfördes med två olika förstärkningsmetoder (glasfiber och plywood) samt med balkar utan förstärkning. Vid provning av de oförstärkta balkarna användes ett system för beröringsfri deformationsmätning för att få en bild av deformationsmönstret. Ett kommersiellt finita elementprogram användes också för att analysera balkarnas respons och för att jämföra med provningsresultaten. Provningarna visade att förstärkningen med plywood var effektivare än förstärkningen med glasfiber. Vidare uppvisade de olika hålgeometrierna olika brottbeteenden, där de kvadratiska hålen gav mindre spröda brott, dock vid en i genomsnitt lägre brottlast än de cirkulära hålen.</p>

In recent years, hydraulic fracturing has led to a dramatic increase in the worldwide production of natural gas. In a typical hydraulic fracturing treatment, millions of gallons of water, sand and chemicals are injected into a reservoir to generate fractures in the reservoir that serve as pathways for fluid flow. Recent research has shown that both the effectiveness of fracturing treatments and the productivity of fractured reservoirs can be heavily influenced by the presence of pre-existing natural fracture networks. This work presents a fully implicit hydro-mechanical algorithm for modeling hydraulic fracturing in complex fracture networks using the two-dimensional discontinuous deformation analysis (DDA). Building upon previous studies coupling the DDA to fracture network flow, this work emphasizes various improvements made to stabilize the existing algorithms and facilitate their convergence. Additional emphasis is placed on validation of the model and on extending the model to the stochastic characterization of hydraulic fracturing in naturally fractured systems. To validate the coupled algorithm, the model was tested against two analytical solutions for hydraulic fracturing, one for the growth of a fixed-length fracture subject to constant fluid pressure, and the other for the growth of a viscosity-storage dominated fracture subject to a constant rate of fluid injection. Additionally, the model was used to reproduce the results of a hydraulic fracturing experiment performed using high-viscosity fracturing fluid in a homogeneous medium. Very good agreement was displayed in all cases, suggesting that the algorithm is suitable for simulating hydraulic fracturing in homogeneous media. Next, this work explores the relationship between the maximum tensile stress and Mohr-Coulomb fracture criteria used in the DDA and the critical stress intensity factor criteria from linear elastic fracture mechanics (LEFM). The relationship between the criteria is derived, and the ability of the model to capture the relationship is examined for both Mode I and Mode II fracturing. The model was then used to simulate the LEFM solution for a toughness-storage dominated bi-wing hydraulic fracture. Good agreement was found between the numerical and theoretical results, suggesting that the simpler maximum tensile stress criteria can serve as an acceptable substitute for the more rigorous LEFM criteria in studies of hydraulic fracturing. Finally, this work presents a method for modeling hydraulic fracturing in reservoirs characterized by pre-existing fracture networks. The ability of the algorithm to correctly model the interaction mechanism of intersecting fractures is demonstrated through comparison with experimental results, and the method is extended to the stochastic analysis of hydraulic fracturing in probabilistically characterized reservoirs. Ultimately, the method is applied to a case study of hydraulic fracturing in the Marcellus Shale, and the sensitivity of fracture propagation to variations in rock and fluid parameters is analyzed.

This Thesis describes a method for determining and analysing the deformations in peat caused by a driven rigid wheel. Markers were placed in the peat sample and radiographs were taken as the wheel travelled over the surface of the peat. An analysis of the data revealed that a unique relationship existed between the positions of the markers and the positions of the wheel. The paths of the principal stress trajectories were determined by a graphical method; from the principal stress trajectories, it was possible to find the surfaces of maximum shear. The purpose of determining these surfaces is to allow the equilibrium of the soil mass to be investigated by the present theories in soil mechanics; it is to draw an analogy to the analysis of slope stability problems. / Thesis / Master of Engineering (ME)

Discontinuous deformation analysis (DDA) is a newly developed simulation method for discontinuous systems. It was designed to simulate systems with arbitrary shaped blocks with high efficiency while providing accurate solutions for energy dissipation. But DDA usually exhibits damping effects that are inconsistent with theoretical solutions. The deep reason for these artificial damping effects has been an open question, and it is hypothesized that these damping effects could result from the time integration scheme. In this thesis two time integration methods are investigated: the forward Euler method and the Newmark method. The work begins by combining the Newmark method and the DDA. An integrated Newmark method is also developed, where velocity and acceleration do not need to be updated. In simulations, two of the most widely used models are adopted to test the forward Euler method and the Newmark method. The first one is a sliding model, in which both the forward Euler method and the Newmark method give accurate solutions compared with analytical results. The second model is an impacting model, in which the Newmark method has much better accuracy than the forward Euler method, and there are minimal damping effects. / Master of Science

<p dir="ltr">This thesis investigates the large deflection behavior of cantilever beams under various configurations and loading conditions. The primary objective is to uset an analytical model using elliptic integrals to solve the second-order non-linear differential equations that govern the deflection of these beams. The analytical model is implemented in Python and compared against Finite Element Analysis (FEA) results obtained from ANSYS, ensuring the accuracy and reliability of the model. The study examines multiple beam configurations, including straight and inclined beams, with both free and fixed tip slopes. Sensitivity analysis is conducted to assess the impact of key parameters, such as Young’s modulus, beam height, width, and length, on the deflection behavior. This analysis reveals critical insights into how variations in material properties and geometric dimensions affect beam performance. A detailed error analysis using Root Mean Square Error (RMSE) is performed to compare the analytical model's predictions with the FEA results. The error analysis highlights any discrepancies, demonstrating the robustness of the analytical approach. The results show that the analytical model, based on elliptic integrals, closely matches the FEA results across a range of configurations and loading scenarios. The insights gained from this study can be applied to optimize the design of cantilever beams in various engineering applications, including prosthetics, robotics, and structural components. Overall, this research provides a comprehensive understanding of the large deflection behavior of cantilever beams and offers a reliable analytical tool for engineers to predict beam performance under different conditions. The integration of Python-based numerical methods with classical elliptic integral solutions presents a useful approach that enhances the precision and applicability of beam deflection analysis.</p>

Auf der von der Hochschule für Technik und Wirtschaft Dresden betriebene EDM-Basislinie im Großen Garten in Dresden werden regelmäßig die Sollstrecken überprüft. Die Ergebnisse deuten auf Punktbewegungen hin. Durch Vergleiche zweier Epochen wird versucht, solche Punktbewegungen statistisch nachzuweisen, sowohl mittels statistischer Hypothesentests, als auch mit einem Informationskriterium. Punktbewegungen von bis zu 0,25 mm/a wurden geschätzt. Über die Ursachen wird noch spekuliert.

The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this approach lie in keeping the DDA and the FEM algorithms separate and solving FEM equations individually for each block. Based on a number of numerical examples presented in this dissertation, it is concluded that from a computational efficiency standpoint, the implicit solution scheme may not be appropriate for discrete element modelling. Although for quasi-static problems where inertia effects are insignificant, implicit schemes have been successfully used for linear analyses, they do not prove to be advantageous for contact-type problems even in quasi-static mode due to the highly nonlinear behavior of contacts.

Hard ceramic films of micrometric thickness deposited on a soft metallic substrate have ushered in a new era in the fabrication of structural, tribological, microelectronic and optical components. The mechanical performance of these components is however critically dependent on the strength and toughness of these films as well as on those of the film-substrate interface. Recent studies have shown that cylindrical and radial cracks can propagate through the film during nanoindentation tests with spherically tipped and pointed indenters, resulting in steps in the load versus displacement curve. In this thesis, the mechanics of fracture of thin hard films bonded to soft substrates, during nanoindentation is studied by carrying out finite element analyses. The role of plastic yielding in the substrate on the above issue is examined. Another important objective of this work is to propose a method by which finite element simulations can be employed to interpret nanoindentation test results and yield information related to the fracture behaviour of hard films. To this end, axisymmetric finite element analyses of spherical nanoindentation of a TiN film of thickness t = 1 //m, on a steel substrate are carried out. Numerical algorithms for large deformation, contact simulation and computation of energy release rate are employed in the analyses. The film is assumed to be linear elastic, whereas, an elastic-plastic constitutive model is used for the substrate. A nanoindentation analysis of the uncracked film is first carried out. The development of plastic yielding in the substrate and its influence on the load P versus penetration h characteristics is examined. The stress fields around the indenter for different depths of indentation are studied. The results show that the radial stress attains a tensile peak at the film surface, just outside the indented zone. However, it becomes compressive with increasing distance below the surface. Interestingly, a tensile radial stress prevails at the film-substrate interface at large indentation depth. The shear stress increases to a peak value at a distance of 0.052 to OAt below the film surface depending upon the radial location and then reduces. Next, circumferential cracks extending downwards from the film surface are introduced at different radial distances R from the axis of symmetry. Finite element analyses are carried out till the indented zone extends almost up to the crack surface. The energy release rate J is computed as a function of indentation depth for different crack lengths c (in the range from O.lt to 0.9t). The results show that shallow cracks are essentially under Mode II loading with closure of crack faces caused by compressive radial stresses. However, a mixed-mode state prevails if the crack length is large (c > 0.62), with crack faces opening out due to tensile radial stress near the film-substrate interface. The variation of J with c/t for cracks located at different radial distances R is examined. It is found that for small R, there is a decreasing branch in the J versus c variation between c = 0.2i to 0.75£ which indicates that crack extension in this range will be stable. On the other hand, for large R, J increases monotonically with c/t which implies that unstable fracture of the full film thickness will occur following crack initiation. A composite nomogram is generated in the P — h plane where constant J lines are plotted along with load-displacement curves for different crack lengths. If now a nanoindentation (experimental) load-displacement behaviour is superimposed on this nomogram, the initial crack length (of a pre-existing flaw), the final crack length and fracture energy of the film can be inferred. In the last part of the thesis, the effect of the substrate yield strength on the indentation mechanics is studied. It is found that upon decreasing the yield strength, the load at a given indentation depth decreases while the residual depth at unloading increases. Also, the energy release rate for a given radial location and crack length reduces considerably at large depths of indentation.

The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this approach lie in keeping the DDA and the FEM algorithms separate and solving FEM equations individually for each block. Based on a number of numerical examples presented in this dissertation, it is concluded that from a computational efficiency standpoint, the implicit solution scheme may not be appropriate for discrete element modelling. Although for quasi-static problems where inertia effects are insignificant, implicit schemes have been successfully used for linear analyses, they do not prove to be advantageous for contact-type problems even in quasi-static mode due to the highly nonlinear behavior of contacts.