Principal Values Research Articles

Effect of different implant locations and abutment types on stress and strain distribution under non-axial loading: A 3-dimensional finite element analysis

Background/purposeDental implants have been a popular treatment for replacing missing teeth. The purpose of this study was to investigate the impact of engaging (hexagonal) and non-engaging (non-hexagonal) abutments in various six-unit fixed prosthesis on the stress distribution and loading located in the implant neck, implant abutment, and surrounding bone. Materials and methodsThree implants were digitally designed and inserted parallel to each other in edentulous sites of the maxillary right canine, maxillary right central incisor, and maxillary left canine. Titanium base engaging abutments, non-engaging abutments and connecting screws were designed. Five distinct models of 6-unit fixed dental prosthesis were created, each featuring different combinations of various abutments. Forces (45-degree angle) were applied to the prosthesis, allowing for the analysis of the stress distribution on the implant neck and abutments, and the maximum and minimum principal stress values on the cortical and trabecular bone. ResultsVon Mises stress values and stress distributions located in the implant neck region due to the applied loading forces were analyzed. The overall stress values were highest while employing the hexagonal abutments. The maxillary left canine with a hexagonal abutment (model 5) reported the highest von mises value (64.71 MPa) while the maxillary right canine with a non-hexagonal abutment (model 4) presented lowest von mises value (56.69 MPa). ConclusionThe results suggest that both the various abutment combinations (engaging and non-engaging) on five different models have a similar influence on the distribution of stress within the implant system.

Assessment of biomechanical behavior of immature non-vital incisors with various treatment modalities by means of three-dimensional quasi–static finite element analysis

The objectives of this study were to evaluate the stress distribution and risk of fracture of a non-vital immature maxillary central incisor subjected to various clinical procedures using finite element analysis (FEA). A three-dimensional model of an immature central incisor was developed, from which six main models were designed: untreated immature tooth (C), standard apical plug (AP), resin composite (RC), glass-fibre post (GFP), regeneration procedure (RET), and regeneration with induced root maturation (RRM). Mineral trioxide aggregate (MTA) or Biodentine® were used as an apical or coronal plug. All models simulated masticatory forces in a quasi–static approach with an oblique force of 240 Newton at a 120° to the longitudinal tooth axis. The maximum principal stress, maximum shear stress, risk of fracture, and the strengthening percentage were evaluated. The mean maximum principal stress values were highest in model C [90.3 MPa (SD = 4.4)] and lowest in the GFP models treated with either MTA and Biodentine®; 64.1 (SD = 1.7) and 64.0 (SD = 1.6) MPa, respectively. Regarding the shear stress values, the dentine tooth structure in model C [14.4 MPa (SD = 0.8)] and GFP models [15.4 MPa (SD = 1.1)] reported significantly higher maximum shear stress values compared to other tested models (p < 0.001), while no significant differences were reported between the other models (p > 0.05). No significant differences between MTA and Biodentine® regarding maximum principal stress and maximum shear stress values for each tested model (p > 0.05). A maximum strain value of 4.07E−03 and maximum displacement magnitude of 0.128 mm was recorded in model C. In terms of strengthening percentage, the GFP models were associated with the highest increase (22%). The use of a GFP improved the biomechanical performance and resulted in a lower risk of fracture of a non-vital immature maxillary central incisor in a FEA model.

Confidence in Movement-Based Game Design Facilitation: Learning From a Novice Design Facilitator

Several movement-based and embodied design methods have been developed to supplement existing game design methods. Facilitating movement-based design methods is a practice that most game designers must master. Facilitation involves taking on several responsibilities and roles to ensure processes and activities follow the design project's principal values. For instance, the facilitator must possess design expertise and social awareness, be a direction setter and trust builder, facilitate stage engagement and mood, energise for commitment, and maintain a playful attitude. The many responsibilities and significant involvement will inevitably affect the facilitator, who enters an affective state facilitating the design activities. Through a phenomenological comparative analysis, this study explores how novice versus experienced facilitators perceive the emotion of confidence and its implications on the facilitation process. This analysis is based on a single case study of a two-day movement-based sports innovation camp for 80 K-12 high school students. Empirical data were generated using a combination of observations and interviews with seven of the involved facilitators: three experienced facilitators and four novice facilitators. Our research indicates that facilitation can be categorised into three stages focused on (1) Structure, (2) Process, and (3) Content. Reaching the Content stages requires a high bodily involvement closely linked to the facilitator’s confidence level, which we partially interpret as determined by the courage to use one’s body as a facilitation resource. Thus, the facilitation Process depends not only on the facilitator's level of expertise but also on confidence level and courage. Consequently, we recommend thorough preparation for each facilitation stage to support the facilitator's confidence. Structure: Outline a detailed playbook, organise the physical space and prepare necessary materials. Process: Prepare strategies for providing guidance and feedback. Content: Implement Movement-Modifiers and participate in warm-up activities.

Impact of permeability anisotropy misalignment on flow rates predicted by hydrogeological models

The notion of permeability is critical to compute underground fluid flow. In most cases rock permeability is anisotropic, due to physical processes including gravitational compaction, which often results in the principal permeability directions being approximately horizontal and vertical in undeformed rocks. However, rocks often are tilted and/or deformed over time, therefore permeability orientation varies. Anisotropic permeability with varying orientation is hard to quantify in three-dimensional (3D) models and is therefore sometimes approximated, for convenience, by setting the principal permeability directions to horizontal and vertical, and assuming that corresponding errors in fluid flow might be negligible when the change in orientation is minimal. This study shows how minor misalignment of the permeability tensor can lead to large errors in fluid flow magnitude and corresponding transport times for strongly anisotropic rocks. It also provides a method to set anisotropic permeability orientation appropriately in geometrically complex 3D models using implicit 3D geological modelling. The misalignment is particularly costly when fluid flow is localised in thin channels, where a misalignment of just 5° leads to errors of two orders of magnitude for anisotropy ratios (between the largest and smallest principal values of the permeability tensor) of 104. It is therefore recommended to set anisotropic permeability accurately, using longitudinal and transverse components along with their respective orientations, rather than horizontal and vertical components. This approach will become increasingly important as 3D models gain realism in their representation of complex geometries.

Influence of retainer design and number of inlay boxes on the biomechanical behavior of zirconia cantilever resin bonded fixed dental prosthesis.

The development of dental adhesives with enhanced bond strength has assisted minimally invasive dentistry. The aim of this study was to evaluate the fracture load and stress distribution pattern of two retainer designs for posterior cantilever resin bonded fixed dental protheses (RBFDPs). Forty human mandibular molars were divided into two groups according to the retainer design; lingual coverage (LC) and occlusal coverage (OC) retainers. Each main group was then divided according to the number of inlay boxes (n = 10); one inlay and two inlay boxes. High translucency (3Y) zirconia was used to manufacture all restorations, and a dual-polymerizing adhesive resin cement was used for bonding. All specimens underwent 10,000 cycles of thermocycling (5-55°C), 240,000 cycles of dynamic loading (50 N, descending speed v = 30 mm/second, frequency = 1.6 Hz), and failure load test. Both one-way and two-way ANOVA tests were used to analyze the data. The four models included in the in-vitro study are part of the finite element analysis (FEA). When the restorations failed, maximal principal stress values on restorations, enamel, dentin, and luting resin were investigated. A statistically significant (p = 0.018) higher failure load was recorded for OC1 (627.00 ± 153.4 N) than the other groups; (548.0 ± 75.6 N, 521.20 ± 11.3 N, and 509.20 ± 14.9 N for LC1, LC2, and OC2, respectively). With regard to failure mode, one inlay box designs showed more favorable failure pattern than those of two inlay boxes. FEA showed higher stress magnitude transmitted to the tooth structure in models LC2 and OC2. Lingual coverage and occlusal coverage retainers are promising designs capable to withstand the normal occlusal force for cantilever RBFDP in premolar area. The use of two inlay boxes decreased the fracture load of the two retainer designs and increased the stress transmitted to the tooth and resulted in high incidence of catastrophic failure. Monolithic high translucent zirconia RBFDP could be considered as a viable treatment option to substitute missing posterior tooth, with improved esthetics and biocompatibility.

Retail investors and overpricing of left-tail risk: evidence from the Korean stock market

The authors examined whether stocks with higher left-tail risk measures earn higher or lower futures returns. Specifically, the authors estimate the cross-sectional principal component of a battery of left-tail risk measures and analyze future returns on stocks with high principal component values. In contrast to finance theories on the risk–return trade-off relationship, the study results show that high left-tail risk stocks have lower future returns. This finding is robust to various left-tail risk measures and controls for other risk factors. Moreover, the negative relationship between the left-tail risk and returns is more pronounced for stocks that are actively traded by retail investors. This empirical result is consistent with behavioral theory that when investors make decisions based on experience, they tend to underweight the likelihood of rare events.

TL, OSL, EPR, and defect centers in Tb-doped strontium silicate phosphor synthesized by a solid-state reaction method

Strong thermoluminescence (TL) was observed in Tb-doped strontium silicate phosphor prepared by the solid-state reaction method. Two glow peaks are observed at 100 and 190 °C. TL emission spectra indicate three recombination centers. The number of peaks and the kinetic parameters associated with the TL glow peaks of Tb-doped Sr2SiO4 phosphor after gamma irradiation were analyzed by Tm-Tstop and deconvolution methods. A study of defect centers induced by γ-irradiation and identification of defect centers responsible for the observed TL glow peaks has been carried out using the electron paramagnetic resonance (EPR) technique. The observed spectrum at room temperature is a superposition of at least three defect centers. Center I is characterized by an axially symmetric g-tensor with principal values g|| = 2.019, and g⊥ = 2.0013 and is ascribed to a O2− ion. Center II has a rhombic g-tensor with principal values 2.0072, 2.0024, and 1.995 and is assigned to an F+ center (singly ionized oxygen vacancy) and correlates with the 190 °C TL peak. The third center (center III) has an isotropic g-value of 1.991 and is identified as an F+ center.

Improving consistency classification: An innovative benchmark‐based approach for the AHP

AbstractThe analytic hierarchy process (AHP) is a cornerstone of multi‐criteria decision analysis, enabling well‐informed choices across diverse contexts. This paper introduces an original benchmark‐based framework designed to enhance the precision of consistency classification for pairwise comparison matrices (PCMs) within the AHP methodology. This innovative approach quantifies the discrepancy between a given PCM and its benchmark matrix, comprising comparison ratios that faithfully reflect the relative preferences encapsulated within principal eigenvector values, thereby capturing the true degree of coherence. To ensure benchmark alignment with human perception, elements of the benchmark PCM are further rounded to the nearest values on the Fundamental Scale. The potency of our framework derives from two pivotal factors: the inherent Priority Preference Range within the principal eigenvector and the order of the PCM. Statistical thresholds for consistency are established using a technique based on simulated, logical PCMs, proposed by Bose [2022]. This rigorous method ensures an unbiased, objective and pragmatic evaluation of consistency, eliminating the subjectivity inherent in arbitrary thresholds based on random PCMs. Our approach rectifies the inconsistencies in the conventional CR method that yields false positives for PCMs of orders 3 and 4, and false negatives for higher orders. By harnessing customized benchmarks and eschewing random matrices, our framework systematically confronts the inherent consistency challenges within AHP, thus enhancing its decision‐making capability. The practical utility of our approach is aptly demonstrated through AHPtools, an R‐based library package designed to showcase our novel consistency evaluation method. The demonstration of the package in Appendix B will facilitate readers to easily apply our methodology to real‐world PCM classification scenarios within the AHP. In conclusion, our benchmark‐based framework heralds a transformative era in consistency classification within the AHP, empowering real‐world multi‐criteria decision‐making with unprecedented precision and reliability, and ushering in a new paradigm of informed and astute outcomes.

Towards an advanced fatigue assessment of welded steel joints with multiaxial stress states

AbstractAdvanced fatigue assessment methods, e.g. the Two‐Stage‐Model, are needed for the design of complex constructions or to accurately evaluate the remaining fatigue life of existing structures. The applicability of the Two‐Stage‐Model, including strain‐life approach and linear elastic fracture mechanics, was experimentally validated for uniaxial stress states only. However, typical construction details of steel and composite structures often exhibit a multiaxial non‐proportional stress state, which leads to variable principal stress values and directions. Comprehensive extensions of the Two‐Stage‐Model from uniaxial to multiaxial stress states are missing so far. This paper shows a study on advanced approaches that incorporate multiaxial stress states for both the crack initiation stage and the crack propagation stage, and their application in the Two‐Stage‐Model. For crack initiation, several approaches for the strain‐life approach, including multiaxial non‐proportional hardening and damage assessment based on critical planes are evaluated with respect to an application on the strain‐life approach. For the extension of the crack propagation stage, a computational procedure using XFEM and mixed‐mode approaches is presented.

A conceptual framework to incorporate fundamental values in the health and medical education system in Islamic Republic of Iran.

A 1985 law in the Islamic Republic of Iran integrated all health-related educational institutions into the Ministry of Health and established the Ministry of Health and Medical Education to set policies. We aimed to classify the value concept of the policies that prioritized and to develop a conceptual value-based framework, for the Islamic Republic of Iran's healthcare and medical education systems. We conducted this qualitative study using a critical, thematic content analysis of value-based statements and policy documents on health and the development of medical education published from 2009 to 2019 in the Islamic Republic of Iran. A total of 210 documents were reviewed and 7 were critically analysed. Value concepts were identified and coded. A total of 69 value concepts were classified into 28 subthemes and 5 main themes: mission values, principal values, procedural values, implementation values, and outcome values. We identified the pattern of the fundamental values to present our conceptual framework. This comprehensive value-based framework can help establish a supportive value-based culture among policymakers, identify under- and over-emphasized issues, and enhance the incorporation of fundamental values across the health and medical education system.

Intermediate pressure-normalized principal wall strain values are associated with increased abdominal aortic aneurysmal growth rates.

Current abdominal aortic aneurysm (AAA) assessment relies on analysis of AAA diameter and growth rate. However, evidence demonstrates that AAA pathology varies among patients and morphometric analysis alone is insufficient to precisely predict individual rupture risk. Biomechanical parameters, such as pressure-normalized AAA principal wall strain (/PP, %/mmHg), can provide useful information for AAA assessment. Therefore, this study utilized a previously validated ultrasound elastography (USE) technique to correlate /PP with the current AAA assessment methods of maximal diameter and growth rate. Our USE algorithm utilizes a finite element mesh, overlaid a 2D cross-sectional view of the user-defined AAA wall, at the location of maximum diameter, to track two-dimensional, frame-to-frame displacements over a full cardiac cycle, using a custom image registration algorithm to produce /PP. This metric was compared between patients with healthy aortas and AAAs (≥3 cm) and compared between small and large AAAs (≥5 cm). AAAs were then separated into terciles based on /PP values to further assess differences in our metric across maximal diameter and prospective growth rate. Non-parametric tests of hypotheses were used to assess statistical significance as appropriate. USE analysis was conducted on 129 patients, 16 healthy aortas and 113 AAAs, of which 86 were classified as small AAAs and 27 as large. Non-aneurysmal aortas showed higher /PP compared to AAAs (0.044 ± 0.015 vs. 0.034 ± 0.017%/mmHg, p = 0.01) indicating AAA walls to be stiffer. Small and large AAAs showed no difference in /PP. When divided into terciles based on /PP cutoffs of 0.0251 and 0.038%/mmHg, there was no difference in AAA diameter. There was a statistically significant difference in prospective growth rate between the intermediate tercile and the outer two terciles (1.46 ± 2.48 vs. 3.59 ± 3.83 vs. 1.78 ± 1.64 mm/yr, p = 0.014). There was no correlation between AAA diameter and /PP, indicating biomechanical markers of AAA pathology are likely independent of diameter. AAAs in the intermediate tercile of /PP values were found to have nearly double the growth rates than the highest or lowest tercile, indicating an intermediate range of /PP values for which patients are at risk for increased AAA expansion, likely necessitating more frequent imaging follow-up.

3D Finite-Element Numerical Failure Prediction of the E.T. Sea Stack Formation at Hopewell Rocks Provincial Park

Sea stacks, natural pillars of rock, are borne from shoreline rock cliffs and eventually collapse by wave action and other erosional processes. While historical instances of sea stack failure have occurred within Hopewell Rocks Provincial Park in New Brunswick, comprehensive assessments of sea stack stability and predictions of future failure are in their early stages. This study aims to forecast the future failure of the E.T. sea stack formation. Photographs taken from an unmanned aerial vehicle of the stack are used to construct a digital 3D geometry model of the formation using Structure-from-Motion photogrammetry. To determine the anticipated failure threshold, 3D finite-element (FEM) numerical models of the stack were developed in RocScience RS3 software. Erosion from wave action during high tides is simulated by progressively reducing the width of the stack within the erosion zone. The erosion rate is estimated, by comparing superimposed historical and current images of the stack, to be 19.19 mm/year perpendicular and 2.26 mm/year parallel to the shoreline. Two erosion types are modelled: symmetrical isotropic and asymmetrical anisotropic. Symmetrical isotropic models imply uniform erosion, while asymmetrical anisotropic models feature two orthogonal erosion rates with directional width reductions from the end of each erosion axis. Stability of the formation in the FEM model is evaluated using maximum shear strain, total displacement, yielded elements, and major principal stress values. The symmetrical isotropic models suggest a probable failure period between 101 and 127 years after 2021. The asymmetrical anisotropic models, however, indicate that failure could occur approximately 40 years earlier. Overall, failure of the stack experiencing asymmetrical anisotropic erosion seems to occur when the supporting pillar is about to erode under the stack’s centroid. With further validation, through additional modelling, the centroid of sea stacks has the potential to be used as a guideline for predicting sea stack failure.&#x0D; &#x0D;

Multi-objective design optimization of bioresorbable braided stents

Background and objectivesBioresorbable braided stents, typically made of bioresorbable polymers such as poly-l-lactide (PLLA), have great potential in the treatment of critical limb ischemia, particularly in cases of long-segment occlusions and lesions with high angulation. However, the successful adoption of these devices is limited by their low radial stiffness and reduced elastic modulus of bioresorbable polymers. This study proposes a computational optimization procedure to enhance the mechanical performance of bioresorbable braided stents and consequently improve the treatment of critical limb ischemia. MethodsFinite element analyses were performed to replicate the radial crimping test and investigate the implantation procedure of PLLA braided stents. The stent geometry was characterized by four design parameters: number of wires, wire diameter, initial stent diameter, and braiding angle. Manufacturing constraints were considered to establish the design space. The mechanical performance of the stent was evaluated by defining the radial force, foreshortening, and peak maximum principal stress of the stent as objectives and constraint functions in the optimization problem. An approximate relationship between the objectives, constraint, and the design parameters was defined using design of experiment coupled with surrogate modelling. Surrogate models were then interrogated within the design space, and a multi-objective design optimization was conducted. ResultsThe simulation of radial crimping was successfully validated against experimental data. The radial force was found to be primarily influenced by the number of wires, wire diameter, and braiding angle, with the wire diameter having the most significant impact. Foreshortening was predominantly affected by the braiding angle. The peak maximum principal stress exhibited contrasting behaviour compared to the radial force for all parameters, with the exception of the number of wires. Among the Pareto-optimal design candidates, feasible peak maximum principal stress values were observed, with the braiding angle identified as the differentiating factor among these candidates. ConclusionsThe exploration of the design space enabled both the understanding of the impact of design parameters on the mechanical performance of bioresorbable braided stents and the successful identification of optimal design candidates. The optimization framework contributes to the advancement of innovative bioresorbable braided stents for the effective treatment of critical limb ischemia.

Inter-subject correlations of EEG reflect subjective arousal and acoustic features of music.

Research on music-induced emotion and brain activity is constantly expanding. Although studies using inter-subject correlation (ISC), a collectively shared brain activity analysis method, have been conducted, whether ISC during music listening represents the music preferences of a large population remains uncertain; additionally, it remains unclear which factors influence ISC during music listening. Therefore, here, we aimed to investigate whether the ISCs of electroencephalography (EEG) during music listening represent a preference for music reflecting engagement or interest of a large population in music. First, we selected 21 pieces of music from the Billboard Japan Hot 100 chart of 2017, which served as an indicator of preference reflecting the engagement and interest of a large population. To ensure even representation, we chose one piece for every fifth song on the chart, spanning from highly popular music to less popular ones. Next, we recorded EEG signals while the subjects listened to the selected music, and they were asked to evaluate four aspects (preference, enjoyment, frequency of listening, and arousal) for each song. Subsequently, we conducted ISC analysis by utilizing the first three principal components of EEG, which were highly correlated across subjects and extracted through correlated component analysis (CorrCA). We then explored whether music with high preferences that reflected the engagement and interest of large population had high ISC values. Additionally, we employed cluster analysis on all 21 pieces of music, utilizing the first three principal components of EEG, to investigate the impact of emotions and musical characteristics on EEG ISC during music listening. A significant distinction was noted between the mean ISC values of the 10 higher-ranked pieces of music compared to the 10 lower-ranked pieces of music [t(542) = -1.97, p = 0.0025]. This finding suggests that ISC values may correspond preferences reflecting engagement or interest of a large population. Furthermore, we found that significant variations were observed in the first three principal component values among the three clusters identified through cluster analysis, along with significant differences in arousal levels. Moreover, the characteristics of the music (tonality and tempo) differed among the three clusters. This indicates that the principal components, which exhibit high correlation among subjects and were employed in calculating ISC values, represent both subjects' arousal levels and specific characteristics of the music. Subjects' arousal values during music listening and music characteristics (tonality and tempo) affect ISC values, which represent the interest of a large population in music.

Dirac points, new photonic band gaps, and effect of magnetically induced transparency in dichroic cholesteric liquid crystals with wavelength-dependent magneto-optical activity parameter.

We investigated the properties of cholesteric liquid crystals (CLCs) being in an external static magnetic field directed along the helix axis. We considered a dichroic CLC, that is, CLC with parameters ReΔ=Reɛ_{1}-Reɛ_{2}/2=0 and ImΔ=Imɛ_{1}-Imɛ_{2}/2≠0, where ɛ_{1,2} are the principal values of the local dielectric permittivity tensor. We have shown that in the case of the wavelength dependence of the magneto-optic activity parameter, new features appear in the optics of dichroic CLCs, in particular, in this case new Dirac points appear. Dirac points are points where there is an intersection of any two wave vector curves (they degenerate) and a linear law of the wave vector dependence on the frequency near these points. And moreover, at some Dirac points photonic band gaps (PBGs) appear; at others, lines of magnetically induced transparency (MIT), that is, a full transmission band appears, in an absorbing medium. In this case a polarization-sensitive transmission band appears too. At certain values of the helix pitch of the CLC and of the magnitude of the external magnetic field, three PBGs of different nature appear: a transmittance band, two narrow lines of MIT, and at others a broadband MIT, etc. This system is nonreciprocal, and the nonreciprocity changes over a wide range. It is observed both for reflection and transmittance and for absorption. The soft-matter nature of CLCs and their response to external influences lead to easily tunable multifunctional devices that can find a variety of applications. They can be applied as tunable narrow-band or broadband filters and mirrors, a highly tunable broad/narrow-band coherent perfect absorber, transmitter, ideal optical diode, and in other devices.

One-loop radiative corrections in bumblebee-Stueckelberg model

This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self-interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two-point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.

Gaussian type quadrature rules related to the oscillatory modification of the generalized Laguerre weight functions

In this paper we consider weighted integrals with respect to a modification of the generalized Laguerre weight functions wα(x)=xαe−x, α>−1, on (0,+∞) by the oscillatory factor exp(iζx), where ζ>0. For calculation of such integrals for analytic real-valued functions in D={z∈ℂ∣Rez≥0,Imz≥0} we construct polynomials orthogonal with respect to the linear functional L:P→ℂ, given by L[p]=∫0+∞p(x)wα(x)exp(iζx)dx, where P is a linear space of all algebraic polynomials, as well as the corresponding quadrature rules of Gaussian type. The existence of such orthogonal polynomials and the corresponding three-term recurrence relations are proved. A few numerical examples are presented, including computation of the Cauchy principal value integrals.

Estimation Method for an In Situ Stress Field along a Super-Long and Deep-Buried Tunnel and Its Application

Aiming at some stress-induced failure phenomena in surrounding rock that occur during the construction of super-long and deep-buried tunnels, a method for estimating the in situ stress in the tunnels based on multivariate information integration is proposed, which uses a small amount of in situ stress measurement, stereographic projection technology, and a numerical simulation method. Firstly, by conducting a macroscopic analysis of the regional geological structure, topography, and pre-excavated small tunnels (such as exploration of adits and pilot tunnels), the strength of the tectonic stress field and the orientation of the principal stresses in the tunnel sections are preliminarily determined. Secondly, the reliability of the in situ stress measurement data were analyzed using full-space stereographic projection and the plane stress projection method. Then, some representative measurement points that reflected the distribution characteristics of in situ stress in the project area, on the whole, were determined. Thirdly, the finite difference (FDM) and multiple regression analysis (MRA) methods were used to inverse the in situ stress field in the project area. The proposed method was applied to a super-long and deep-buried tunnel project in Qinling, and the in situ stress distribution characteristics of the tunnel sections at different mileages were obtained. The results show that both the calculated principal stress values and the azimuth angle of the maximum horizontal principal stress are in good agreement with the measured ones, indicating that the method used in this study is reasonable. Finally, the typical surrounding rock failure phenomena encountered during the excavation of the project were investigated, and targeted treatment measures were proposed. The research results can provide references for support design and disaster management of surrounding rock in deep-buried long tunnels.

Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

To improve the accuracy of Displacement Discontinuity Method and enhance its adaptivity, a general-purpose two-dimensional displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering discontinuity problems where cracks or cavities are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity, respectively. Both of them belong to the discontinuous element type, in which the geometry shape functions are different from the interpolation shape functions. A new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains singular and strongly singular integrals which can be evaluated in the sense of Cauchy principal value and Hadamard principal value, respectively. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Five numerical examples, most of which have analytic solutions, are given to illustrate the improved accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the numerical results by using the present isoparametric displacement discontinuity elements show better accuracy.

Effect of process parameters on crack characteristics in laser welding of Al2O3 ceramic

The crack of ceramic weld is a worldwide problem for brittle material, high energy laser beam is expected to solve this problem. In this paper, the crack of fiber laser welding of Al2O3 ceramics was studied. The weld crack rate was used to characterize the crack condition of weld, and the influences of laser power, welding speed and defocusing distance on crack characteristics were carried out. The results showed that Al2O3 ceramics weld has obvious crack tendency, and the cracks mainly appeared on the weld center line. When the crack appeared on the weld center line, there was crack-free on the base metal. When the defocusing distance increased from +3 mm to +20 mm, the number of cracks gradually decreased. When the defocusing distance was greater than +17 mm, cracks-free appeared on the weld and base metal. Abaqus software was used to simulate the relationship between crack and stress based on thermal elastoplastic theory. The high crack areas, few crack areas and free crack areas were divided according to the maximum principal stress value. No matter what welding conditions, as long as the maximum principal stress was less than 1576 MPa, there was crack-free on the weld and base metal.