A semi-infinite beam theoretical model on predicting rock slope subsidence induced by underground mining

When the mining goaf is close to the cliff,rock slope subsidence induced by underground mining is significantly affected by its boundary conditions.In this study,an analytical method is proposed by considering the key strata as a semi-infinite Euler-Bernoulli beam rested on a Winkler foundation with a local subsidence area.The analytical solutions of deflection are derived by analyzing the boundary and continuity conditions of the cliff.Then,the analytical solutions are verified by the results from experimental tests,FEM and InSAR,respectively.After that,the influence of changing parameters on deflections is studied with sensitivity analysis.The results show that the distance between goaf and cliff significantly affects the deflection of semi-infinite beam.The response of semi-infinite beam is obviously determined by the length of goaf and the bending stiffness of beam.The comparisons between semi-infinite beam and infinite beam illustrate the ascendancy of the improved model in such problems.

Failure of Semi-infinite Beams of Variable Thickness and Curvature on Elastic Foundation under Contact Loading

In early winter it is usual, in cold regions, that ice features approach offshore structures, like offshore platforms, impacting them, in a slow process of constant deformation build up. Interaction follows, in many cases, up to the point where ice-failure caused by bending fracture takes place. This supposes very large contact forces that the structure has to resist. Therefore, quantification of these efforts is of vital importance to the structural design of platforms. In several designs, these platforms are constructed with inclined walls so as to cause ice to fail in a flex-compression mode. In such a case the ice feature is analyzed as a beam constituted of a linear elastic material in brittle state with constant ice thickness. The simplification renders the problem solvable in a close form. However, this hypothesis goes against field observations. Marine currents action, wind and the sequence of contacts among features lead to thickness variations. Here this factor is addressed in the construction of a model, for harmonic forms of variation of thickness profile, and the accompanying curvature variations, whose solution determines field variables used to address the failure question. Due to the deformation dependency of the loading, a numerical scheme for the two-point boundary value problem in the semi-infinite space is developed. Failure pressures are computed based on a Rankine locus of failure. Variations of the order of 20% in the failure loads, as compared to the uniform beam model, are observed.

Data-driven prediction of dimensionless quantities for semi-infinite target penetration by integrating machine-learning and feature selection methods

This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.

A novel solution treatment and aging for powder bed fusion-laser beam Ti-6Al-2Sn-4Zr-6Mo alloy:Microstructural and mechanical characterization

Ti-6Al-4Zr-2Sn-6Mo alloy is one of the most recent titanium alloys processed using powder bed fusion-laser beam(PBF-LB)technology.This alloy has the potential to replace Ti-6Al-4V in automotive and aerospace applications,given its superior mechanical properties,which are approximately 10%higher in terms of ultimate tensile strength(UTS)and yield strength after appropriate heat treatment.In as-built conditions,the alloy is characterized by the presence of soft orthorhombicα″martensite,necessitating a postprocessing heat treatment to decompose this phase and enhance the mechanical properties of the alloy.Usually,PBFed Ti6246 components undergo an annealing process that transforms theα″martensite into anα-βlamellar microstructure.The primary objective of this research was to develop a solution treatment and aging(STA)heat treatment tailored to the unique microstructure produced by the additive manufacturing process to achieve an ultrafine bilamellar microstructure reinforced by precipitation hardening.This study investigated the effects of various solution temperatures in theα-βfield(ranging from 800 to 875℃),cooling media(air and water),and aging time to determine the optimal heat treatment parameters for achieving the desired bilamellar microstructure.For each heat treatment condition,differentα-βmicrostructures were found,varying in terms of theα/βratio and the size of the primaryα-phase lamellae.Particular attention was given to how these factors were influenced by increases in solution temperature and how microhardness correlated with the percentage of the metastableβphase present after quenching.Tensile tests were performed on samples subjected to the most promising heat treatment parameters.A comparison with literature data revealed that the optimized STA treatment enhanced hardness and UTS by13%and 23%,respectively,compared with those of the annealed alloy.Fracture surface analyses were conducted to investigate fracture mechanisms.

Vibration response of Euler-Bernoulli-damped beam with appendages subjected to a moving mass

This paper addresses the problem of a viscoelastic Euler-Bernoulli beam under the influence of a constant velocity moving mass and different types of appendages.Four types of boundary conditions are considered:pinned-pinned,fixed-pinned,fixed-free(or cantilever),and fixed-fixed.Appendages considered include lumped masses,dampers,and springs.The modal decomposition method is employed to derive the equation of motion of the beam,for which an analytical closed-form expression of the dynamic vibration response is generated.The proposed method enables the study of the effect of a single appendage or a combination of the three types of appendages on the non-dimensional dynamic response of the beam.Numerical examples are presented to illustrate the effects of these appendages and compare them to the reference cases of a beam with no appendages.The results demonstrate the importance of considering these parameters in the design of structures.The proposed method is compared to other techniques in the literature and found to be advantageous due to its direct approach.The method also offers a versatile tool for investigating various configurations,aiding in engineering design and structural analysis for which establishing a precise prediction of beam vibrations is crucial.

Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid

Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.

Investigation on the penetration of jacketed rods with striking velocities of 0.9-3.3 km/s into semi-infinite targets

In this study, a combined experimental, numerical and theoretical investigation is conducted on the penetration of semi-infinite 4340 steel targets by a homogeneous 93 W rod and two types of jacketed rods with striking velocities of 0.9-3.3 km/s. The results show that the jacketed rods produced typical“co-erosion” damage at all test velocities, except for the 93 W/1060 Al jacketed rod, which switched from an early “bi-erosion” damage to later “co-erosion” damage at a striking velocity of 936 m/s. However, the homogeneous 93 W rod always forms a large mushroom head during the penetration process. The damage mechanisms of these two types of jacketed rods differ for striking velocities of 0.9-2.0 km/s, but this difference gradually decreases with increased striking velocity. For velocities of 2.0-3.3 km/s, all three types of projectiles exhibit typical hydrodynamic penetration characteristics, and the damage mechanisms of the two types of jacketed rods are almost identical. For the same initial kinetic energy, the penetration performance of the jacketed rods is distinctly superior to that of the homogeneous 93 W rods.Compared with jacket density, jacket strength shows a more significant influence on the damage mechanism and penetration performance of the jacketed rod. Finally, an existing theoretical prediction model of the penetration depth of jacketed rods on semi-infinite targets in the co-erosion mode is modified. It transpires that-in terms of penetration depth-the modified theoretical model is in good agreement with the experimental and numerical observations for 93 W/TC4 and 93 W/1060 Al jacketed rods penetrating semi-infinite 4340 steel targets.

ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.

Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal

By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Analytical models for the penetration of semi-infinite targets by rigid,deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model

The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.

Miniature tunable Airy beam optical meta-device

Tunable Airy beams with controllable propagation trajectories have sparked interest in various fields,such as optical manipulation and laser fabrication.Existing research approaches encounter challenges related to insufficient compactness and integration feasibility,or they require enhanced tunability to enable real-time dynamic manipulation of the propagation trajectory.In this work,we present a novel method that utilizes a dual metasurface system to surpass these limitations,significantly enhancing the practical potential of the Airy beam.Our approach involves encoding a cubic phase profile and two off-axis Fresnel lens phase profiles across the two metasurfaces.The validity of the proposed strategy has been confirmed through simulation and experimental results.The proposed meta-device addresses the existing limitations and lays the foundation for broadening the applicability of Airy beams across diverse domains,encompassing light-sheet microscopy,laser fabrication,optical tweezers,etc.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.

Deriving Vibration Modes of Semi-infinite Chain Model by “Invariant Eigen-operator”Method

For the first time, we introduce a fully quantum mechanical Hamiltonian for a semi-infinite chain model of atoms. We then derive the vibration modes of this model by virtue of the ＂invariant eigen-operator＂ method in two different cases, which is concise and revealing.

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅱ)——SPECIAL CASES AND NUMERICAL EXAMPLES

In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅰ)——GENERAL THEORY

In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.

Fully automatic AI segmentation of oral surgery-related tissues based on cone beam computed tomography images

Accurate segmentation of oral surgery-related tissues from cone beam computed tomography(CBCT)images can significantly accelerate treatment planning and improve surgical accuracy.In this paper,we propose a fully automated tissue segmentation system for dental implant surgery.Specifically,we propose an image preprocessing method based on data distribution histograms,which can adaptively process CBCT images with different parameters.Based on this,we use the bone segmentation network to obtain the segmentation results of alveolar bone,teeth,and maxillary sinus.We use the tooth and mandibular regions as the ROI regions of tooth segmentation and mandibular nerve tube segmentation to achieve the corresponding tasks.The tooth segmentation results can obtain the order information of the dentition.The corresponding experimental results show that our method can achieve higher segmentation accuracy and efficiency compared to existing methods.Its average Dice scores on the tooth,alveolar bone,maxillary sinus,and mandibular canal segmentation tasks were 96.5%,95.4%,93.6%,and 94.8%,respectively.These results demonstrate that it can accelerate the development of digital dentistry.