A New Higher Order Displacement Discontinuity Method Based on the Joint Element for Analysis of Close-Spacing Planar Fractures

Summary The 2D displacement discontinuity method (DDM) has been widely used to characterize the hydraulic fracture geometry and the induced in-situ stresses in the oil and gas industry owing to its simplicity and accuracy. As smaller fracture spacing is used by multistage fracturing, the constant DDM (CDDM) loses its accuracy in predicting the fracture behaviors, especially for the inner fractures in a stage where they are subjected to the strong stress shadowing effect. In this paper, the 2D higher order DDM (HDDM) based on the joint elements was developed to overcome this limitation. The higher order displacement discontinuity intensively increases the accuracy of CDDM but maintains the same amount of computation time by using patched-element pattern. The joint elements are introduced to simultaneously determine the opening, shearing, and closing of each fracture element based on the stress boundary condition, which can avoid the “negative width” of the inner fractures given by CDDM which are mechanically closed under the strong stress shadowing effect. The developed 2D joint element HDDM (JE-HDDM) gives the same results with the CDDM when the fracture spacing is relatively large, but shows its outperformance in both efficiency and accuracy over the CDDM in predicting the displacement discontinuities and induced in-situ stresses in close fracture-spacing case.

Enhanced learning through joint instrumental education

The perspectives of music teachers and students on the main benefits of collaborative musical learning are explored in this chapter. Qualitative data from two recently conducted studies are discussed through the main conceptual resources of the “embodied approach” to mind. In these studies, an open-ended questionnaire was administered to expert music teachers and students from the European Union and North America who took part in individual and collective instrumental music classes. The overall results indicate that the joint element of the tuition allowed students to become more responsible for their own learning, helping teachers foster more inclusive settings where interactions among peers are prioritized. Having considered the relevance of the results in light of classic views on peer-learning by Piaget and Vygotsky, it is argued that an embodied approach can help researchers and educators better capture the relational dynamics of collective pedagogies.

Comparison of Bone Tissue Trace Element Content in the Different Radiological Stages of Hip Osteoarthritis

Bone metabolism and the trace element content associated with it change at each stage of degenerative disease. The aim of this study was to find out about the role of the analyzed elements in different stages of hip osteoarthritis. Elements associated with oxidative and enzymatic processes were analyzed depending on the changes in the radiological images of the hip joint. Element content analysis was performed by the inductively coupled plasma mass spectrometry analytical technique. The femoral head in severely osteoarthritic hips (KL3–4) compared to mild grade osteoarthritis (KL2) had a greater content of Cu (median 1.04 vs. 0.04), Sr (median 38.71 vs. 29.59), and Zn (median 75.12 vs. 63.21). There were no significant differences in the content of Mo, Cr, and Fe in the femoral head and neck between the groups. The Cu/Fe correlation was negative in the KL2 group (−0.47) and positive in the KL3–4 groups (0.45). Changes in the content and correlation of trace elements in the hip joint explain the changes in metabolism dependent on the severity of degenerative changes.

Nonlinear dynamic properties of the rotor-bearing system involving bolted disk-disk joint

Bolted joints are major components to connect the multiple stages of disks in the aero-engine, which directly influences the motion state of the rotor system. This paper studies the effect of some typical structure parameters on the time-varying bending stiffness of the bolted disk-disk joint through finite-element simulations. Based on the Lagrange’s equations, a two-node element used to represent the bolted joint is derived, which is called the joint element. Then, a mathematical model of the rotor system with a bolted disk-disk joint supported by ball bearings is established through the Timoshenko beam and the joint element. The dynamic model is numerically solved using the Newmark-β method. The largest Lyapunov exponent, three-dimension spectral plots, and frequency-response curves are employed to reveal the effect of the bending behavior on the rotor dynamics. Comparisons indicate that the structural parameter of the bolted joint has a slight influence on motion stability, critical speed, and amplitude corresponding to the critical speed. Finally, an experimental study is conducted through a bolted-disk joint rotor test rig with an electrical tightening wrench, showing that the increase of pre-tightening torque will lead to a decrease of the amplitude corresponding to critical speed due to the hardening effect. The modeling method proposed in the present work paves a way for modeling and analyzing of the rotor system with a bolted disk-disk joint.

Computational Modal Analysis on Finite Element Model of Body-in-white Structure and Its Correlation with Experimental Data

Nowadays, computational modelling and simulation are highly popular to increase the efficiency, productivity and shorten the product development period. The quality of a structure also can be determined by using computational analysis such as finite element analysis. Body-in-white structure, as one of the most important structures in the automotive field, has gained a lot of interest as the topic of research. This increase the demand of having a good finite element model of the structure. However, since body-in-white is a highly complicated structure, sometimes modelling simplification cannot be avoided. This study intended to investigate the level of accuracy of the simplified body-in-white model that was modelled by using several modelling strategies. The first body-in-white finite element model was modelled by neglecting the existing joint element in its actual structure. The other body-in-white model includes the joint element by including two different one-dimensional elements to replicate the joining in BIW actual structure. Validation on these body-in-white models are performed by correlating the finite element modal properties with the experimental modal properties. The discrepancies that had surfaced after the correlation was reduced by using a model updating method. The discussed results showed that as the model is under major simplification, several parameters were inaccurately assumed in the initial body-in-white model. Thus, the model updating method has successfully determined the less accurate parameter and the level of discrepancies between the model and experimental data were successfully reduced.

Simulation of fracture propagation in fibre-reinforced concrete using FDEM: an application to tunnel linings

The application of the combined finite-discrete element method (FDEM) to simulate fracture propagation in fibre-reinforced-concrete (FRC)-lined tunnels has been investigated. This constitutes the first attempt of using FDEM for the simulation of fracture in FRC structures. The mathematical implementations of the new FDEM joint-element constitutive model are first introduced, and the numerical model is then validated comparing the results for plain and FRC beams with three-point bending experimental data. The code has also been applied to two practical tunnel design case studies, showing different behaviours depending on the type of concrete and shape of tunnel section. The FDEM simulations of the linings are also compared with results from a finite element code that is commonly used in the engineering design practise. These results show the capabilities of FDEM for better understanding of the fracture mechanics and crack propagation in FRC tunnels. A methodology for directly inferring the numerical parameters from three-point bending tests is also illustrated. The results of this research can be applied to any FRC structure.

Dynamics of a Rod-Fastened Rotor Considering the Bolt Loosening Effect

Rod-fastened rotors are widely applied in heavy duty gas turbines and aircraft engines due to a good stiffness-to-weight behavior compared to conventional forged rotors. In order to achieve a continuous and stable power output, it is critical to guarantee the mechanical integrity. Therefore, the clamping force is of great importance which influences the distribution of the contact pressure. In an extreme condition, the bolt loosening resulting in an additional bending moment entails a different dynamic response. In this paper, the dynamics of a rod-fastened rotor subjected to the unbalance force, combined loads from the residual bow as well as the bolt loosening will be analyzed. First of all, an accurate rod-fastened rotor model is generated incorporating 1D beam element and zero-length joint element. Next, the mode superposition method is applied to derive the equations of motion and the analytical solution of the rod-fastened rotor will be achieved. Furthermore, experimental results are used to verify the simulations. It has demonstrated that the rod loosening yields a remarkably different behavior compared to the normal rotor after balancing. The dynamic response is also closely dependent on the unbalance as well as the relative phase angle between the location of unbalance and rod loosening. This paper provides a fundamental insight into the steady response of the rod-fastened rotor and may be used for fault identification as well as balancing of combined rotors.

Hollow bridge columns with triangular confining reinforcement

The purpose of this study is to assess the structural performance of hollow bridge columns with triangular confining reinforcement. The proposed triangular reinforcement details were equal to the conventional reinforcement details in terms of required structural performance. The triangular confining reinforcement is also economically feasible and rational, and facilitate shorter construction periods. Three hollow cast-in-situ concrete and three precast concrete bridge columns were tested. The behavior of the hollow columns is discussed in terms of their lateral load-drift relationship, cumulative dissipated energy, and lateral load-strain curves. The nonlinear finite element analysis program RCAHEST (reinforced concrete analysis in higher evaluation system technology) was used to analyze hollow bridge columns, and adopted a modified joint element for the precast concrete bridge columns. The results showed that the proposed innovative reinforcement details were superior to the conventional reinforcement details, in terms of the required structural performance.

Numerical and Experimental Investigations of the Interactions between Hydraulic and Natural Fractures in Shale Formations

Natural fractures (NFs) have been recognized as the dominant factors that increase hydraulic fracture complexity and reservoir productivity. However, the interactions between hydraulic and natural fractures are far from being fully understood. In this study, a two-dimensional numerical model based on the displacement discontinuity method (DDM) has been developed and used to investigate the interaction between hydraulic and pre-existing natural fractures. The inelastic deformation, e.g., stick, slip and separation, of the geologic discontinuities is captured by a special friction joint element called Mohr-Coulomb joint element. The dynamic stress transfer mechanisms between the two fracture systems and the possible location of secondary tensile fracture that reinitiates along the opposite sides of the NF are discussed. Furthermore, the model results are validated by a series of large tri-axial hydraulic fracture (HF) tests. Both experimental and numerical results showed that the displacements and stresses along the NFs are all in highly dynamic changes. When the HF is approaching the NF, the HF tip can exert remote compressional and shear stresses on the NF interface, which results in the debonding of the NF. The location and value of the evoked stress is a function of the far-field horizontal differential stress, inclination angle of the NF, and the net pressure used in fracturing. For a small approaching angle, the stress peak is located farther away from the intersection point, so an offset fracture is more likely to be generated. The cemented strength of the NF also has an important influence on the interaction mechanism. Weakly bonded NF surfaces increase the occurrence of a shear slippage, but for a moderate strength NF, the hybrid failure model with both tensile and shear failures, and conversion may appear.