PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

Deterministic and probabilistic analysis of great-depth braced excavations:A 32 m excavation case study in Paris

The Fort d’Issy-Vanves-Clamart(FIVC)braced excavation in France is analyzed to provide insights into the geotechnical serviceability assessment of excavations at great depth within deterministic and probabilistic frameworks.The FIVC excavation is excavated at 32 m below the ground surface in Parisian sedimentary basin and a plane-strain finite element analysis is implemented to examine the wall deflections and ground surface settlements.A stochastic finite element method based on the polynomial chaos Kriging metamodel(MSFEM)is then proposed for the probabilistic analyses.Comparisons with field measurements and former studies are carried out.Several academic cases are then conducted to investigate the great-depth excavation stability regarding the maximum horizontal wall deflection and maximum ground surface settlement.The results indicate that the proposed MSFEM is effective for probabilistic analyses and can provide useful insights for the excavation design and construction.A sensitivity analysis for seven considered random parameters is then implemented.The soil friction angle at the excavation bottom layer is the most significant one for design.The soil-wall interaction effects on the excavation stability are also given.

Theoretical Analysis on Deflection and Bearing Capacity of Prestressed Bamboo-Steel Composite Beams

A theoretical analysis of upward deflection and midspan deflection of prestressed bamboo-steel composite beams is presented in this study.The deflection analysis considers the influences of interface slippage and shear deformation.Furthermore,the calculation model for flexural capacity is proposed considering the two stages of loading.The theoretical results are verified with 8 specimens considering different prestressed load levels,load schemes,and prestress schemes.The results indicate that the proposed theoretical analysis provides a feasible prediction of the deflection and bearing capacity of bamboo-steel composite beams.For deflection analysis,the method considering the slippage and shear deformation provides better accuracy.The theoretical method for bearing capacity matches well with the test results,and the relative errors in the serviceability limit state and ultimate limit state are 4.95%and 5.85%,respectively,which meet the accuracy requirements of the engineered application.

A spatiotemporal deep learning method for excavation-induced wall deflections

Data-driven approaches such as neural networks are increasingly used for deep excavations due to the growing amount of available monitoring data in practical projects.However,most neural network models only use the data from a single monitoring point and neglect the spatial relationships between multiple monitoring points.Besides,most models lack flexibility in providing predictions for multiple days after monitoring activity.This study proposes a sequence-to-sequence(seq2seq)two-dimensional(2D)convolutional long short-term memory neural network(S2SCL2D)for predicting the spatiotemporal wall deflections induced by deep excavations.The model utilizes the data from all monitoring points on the entire wall and extracts spatiotemporal features from data by combining the 2D convolutional layers and long short-term memory(LSTM)layers.The S2SCL2D model achieves a long-term prediction of wall deflections through a recursive seq2seq structure.The excavation depth,which has a significant impact on wall deflections,is also considered using a feature fusion method.An excavation project in Hangzhou,China,is used to illustrate the proposed model.The results demonstrate that the S2SCL2D model has superior prediction accuracy and robustness than that of the LSTM and S2SCL1D(one-dimensional)models.The prediction model demonstrates a strong generalizability when applied to an adjacent excavation.Based on the long-term prediction results,practitioners can plan and allocate resources in advance to address the potential engineering issues.

Simulation of Steel Reinforcement on the Nonlinear Behaviour of Slender Glulam Beam Columns by Using the Newton-Raphson Method

The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.

Redesigned Surface Based Machining Strategy and Method in Peripheral Milling of Thin-walled Parts

Currently, simultaneously ensuring the machining accuracy and efficiency of thin-walled structures especially high performance parts still remains a challenge. Existing compensating methods are mainly focusing on 3-aixs machining, which sometimes only take one given point as the compensative point at each given cutter location. This paper presents a redesigned surface based machining strategy for peripheral milling of thin-walled parts. Based on an improved cutting force/heat model and finite element method（FEM） simulation environment, a deflection error prediction model, which takes sequence of cutter contact lines as compensation targets, is established. And an iterative algorithm is presented to determine feasible cutter axis positions. The final redesigned surface is subsequently generated by skinning all discrete cutter axis vectors after compensating by using the proposed algorithm. The proposed machining strategy incorporates the thermo-mechanical coupled effect in deflection prediction, and is also validated with flank milling experiment by using five-axis machine tool. At the same time, the deformation error is detected by using three-coordinate measuring machine. Error prediction values and experimental results indicate that they have a good consistency and the proposed approach is able to significantly reduce the dimension error under the same machining conditions compared with conventional methods. The proposed machining strategy has potential in high-efficiency precision machining of thin-walled parts.

Experiments on Deflecting & Oscillating Waterjet

A new type jet, the oscillating & deflecting jet, is put forward and its oscillating and deflecting characteristics are investigated. The nozzle of the self-oscillating & deflecting water jet consists of an upstream nozzle, a downstream nozzle, an oscillating chamber and two switches. It is experimentally shown that the deflective angle may reach 9.53 degree. The generated pressure fluctuation is very regular and the jet can efficiently increase the ability for breaking and cutting by eliminating the water cushion effect associated with a continuous jet.

Development of a seven-cell S-band standing-wave RF-deflecting cavity for Tsinghua Thomson scattering X-ray source

A 2856-MHz,π-mode,seven-cell standingwave deflecting cavity was designed and fabricated for bunch length measurement in Tsinghua Thomson scattering X-ray source(TTX)facility.This cavity was installed in the TTX and provided a deflecting voltage of 4.2 MV with an input power of 2.5 MW.Bunch length diagnoses of electron beams with energies up to 39 MeV have been performed.In this article,the RF design of the cavity using HFSS,fabrication,and RF test processes are reviewed.High-power operation with accelerated beams and calibration of the deflecting voltage are also presented.

Mechanical behavior of SiC foam-SiC particles/Al hybrid composites

The hybrid SiC foam-SiC particles/Al double interpenetrating composites to be used as the brake materials of high speed train were fabricated by squeeze casting technique. The influence of the type of matrix on the mechanical properties and the fracture mechanism of the hybrid composites was investigated. The interface bond in the hybrid composites is good for the composites have the unique double interpenetrating structure. The ductile matrix resists the propagation of the microcracks in the struts. During the microcrack propagation process, the energy absorption and the fracture surface area are increased, which increases the ductility of the hybrid composites. The compressive strength of the hybrid composite reinforced by the SiC with the total volume fraction of 53% is 660 MPa, which is higher than that of traditional composite reinforced by single SiC particles.

Critical Equatorial Trajectories of Massless Particles in a Kerr Spacetime

In the presented work a closed analytical expression is obtained that describes the critical photon orbits in the equatorial plane of a spinning Kerr black hole (BH). A significant difference in the behavior of photons with prograde and retrograde directions of rotation is shown. The photons with prograde rotation exhibit an exponential increase in the deflection angle together with the number of rotations around the BH as its spin parameter increases. The number of rotations exceeds 103 when spin parameter of the BH reaches 0.999. At the same time this value decreases insignificantly for reverse rotating photons and is less than that for the non-spinning Schwarzschild BH. The transition to a zero spin limit made it possible to determine the number of photon rotations along the critical trajectory for such BHs.

IMPROVING SOLIDS SUSPENSION USING DEFLECTING BAFFLES IN GASLIFT LOOP REACTORS

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Using Natural Formation Deflecting Tendency to Reach Targets

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6-36 Control System of High Voltage Power Supply for Deflecting Plate in HIMM

There are more than one hundred pulse power supplies in the project of HIMM (High Ion Medical Machine).The control protocol of them is unified. But the HVPS (high voltage power supply) for deflecting plate of the beam extracted system is different.The control of HVPS includes the current settings, the status display and the HV turn on/off.

Gravitational Deflection of Particles of Light by the Earth and by the Sun: A Reconstruction of the Calculations Done by Soldner in 1801

In 1801, the year of the discovery of Ceres, Johann Georg von Soldner calculated with classical means the gravitational deflection of a lightray grazing the surface of the Sun as 0.84”. According to General Relativity (GR) and using present-day data the deflection amounts to 1.75”. The formula for the deflection is derived with a classical method, with GR and as done by Soldner. The GR formula gives twice as large a deflection as the classical formula. It is shown that the formula of Soldner is equivalent to the classical one. Soldner’s numerical calculation of the classical deflection by the Earth comes out a factor 6.9 larger than using present-day data. This discrepancy is for a factor 6.25 due to a mistaken value for the velocity of the grazing lightray. This factor 6.25 can numerically be accounted for by assuming Soldner made a conceptual mistake related to the Axial Tilt of the Earth. The remaining discrepancy is due to the use of data less accurate than the present-day data. Soldner’s numerical calculation of the deflection by the Sun comes out correctly to the data of those days. In case of the Sun he did not give any further information regarding the data he used. A reconstruction reveals that for the surface gravity of the Sun he used a value close to the present-day value.

Fast prediction of the mechanical response for layered pavement under instantaneous large impact based on random forest regression

The layered pavements usually exhibit complicated mechanical properties with the effect of complex material properties under external environment.In some cases,such as launching missiles or rockets,layered pavements are required to bear large impulse load.However,traditional methods cannot non-destructively and quickly detect the internal structural of pavements.Thus,accurate and fast prediction of the mechanical properties of layered pavements is of great importance and necessity.In recent years,machine learning has shown great superiority in solving nonlinear problems.In this work,we present a method of predicting the maximum deflection and damage factor of layered pavements under instantaneous large impact based on random forest regression with the deflection basin parameters obtained from falling weight deflection testing.The regression coefficient R^(2)of testing datasets are above 0.94 in the process of predicting the elastic moduli of structural layers and mechanical responses,which indicates that the prediction results have great consistency with finite element simulation results.This paper provides a novel method for fast and accurate prediction of pavement mechanical responses under instantaneous large impact load using partial structural parameters of pavements,and has application potential in non-destructive evaluation of pavement structure.

Propagation and sealing efficiency of chemical grouting in a two-dimensional fracture network with flowing water

In this study, an orthogonal array experiment is conducted by using a transparent fracture network replica. Image processing and theoretical analysis are performed to investigate the model sealing efficiency(SE), factors influencing SE, and the effect of flowing water on propagation. The results show that grout propagation can be classified into three patterns in the fracture network: sealing off, partial sealing,and major erosion. The factors controlling the SE in a descending order of the amount of influence are the initial water flow speed, fracture aperture, grout take, and gel time. An optimal value for the combination of the gel time and grout take(artificial factors) can result in a good SE. The grouting and seepage pressures are measured, and the results reveal that their variations can indicate the SE to some extent. The SE is good when the seepage pressure at each point increases overall;the frequent fluctuations in the seepage pressure indicate a moderately poor SE, and an overall decline in the seepage pressure indicates a major erosion type. The deflection effect of grouting shows an approximately elliptical propagation with the long axis expanding along the wider fracture opening, demonstrating further application in grouting design.

Numerical study of hydraulic fracturing in the sectorial well-factory considering well interference and stress shadowing

In the Changqing Oilfield in northwest China, when traditional petroleum exploitation encounters forestry reserves or water source protection areas, sectorial well-factory design is proposed. The most distinct feature of a sectorial well-factory is the deviation of the well from the minimum horizontal principal stress, resulting in hydraulic fracture deflection after the initiation, along with possible well interference (i.e., fracture hit) and fracture coalescence in the oblique wells. Four indexes describing well deflection are then proposed according to fracture morphology. Several fracturing designs, including stage arrangement, fracturing sequences, and fracturing techniques are applied to study the feasibility of the sectorial well-factory design. The results show that the “gradual” or “sparse” stage arrangement, large injection rate, and simultaneous multifracture treatment can help to optimize the fracture morphology and stimulation design. However, the subsequent stress shadowing effect usually adversely affects the fracturing of adjacent wells. With a small initial horizontal stress difference, large injection rate and staggered stage arrangement can achieve ideal stimulation performance. Our results can provide a guidance for optimizing stimulation design in unconventional well-factory while taking into account environmental protection.

Research on the Bending Impact Resistance and Transverse Fracture Characteristics of Bamboo under the Action of Falling Weight

Drop weight impact tester was used to accurately measure the bending impact resistance of various parts of Phyllostachys edulis,commonly known as moso bamboo,with a growth cycle of 3–8 years.Cellulose crystallinity in the bottom(B),middle(M)and top(T)of bamboo at different ages was calculated using peak height analysis in X-ray diffraction.Heatmap of Spearman correlation analysis was used to represent the correlation between chemical composition and impact mechanics.The breaking load(BL),fracture energy(FE)and impact deflection(ID)of 3–8-year-old bamboo were found to be in the range of~670–2120 N,~5.17–15.55 J,and~3.60–~17.76 mm,respectively.As the growth period of bamboo rises,the cellulose crystallinity at the B and T decreases first and then increases,while that for the M increases first and then remains stable.Similarly,the bending impact performance of bamboo was found to become stable with its growth and age.The flexural impact and toughness of the 4-year-old bamboo base material were better than other specimens.The enhancement in the bending impact properties of bamboo at different growth periods was influenced by the lignin content,while the value of FE was mainly positively correlated with ash,cold and hot water extracts and benzyl alcohol content.However the content of holocellulose and pentosan,air-dry density and,base density negatively influenced the FE.With the change in the height of the bamboo,the correlation between its impact mechanical properties and chemical composition gradually decreased.This study provides data support and theoretical basis for the age-appropriate thinning and application of moso bamboo.

Height connection across sea by using satellite altimetry data sets,ellipsoidal heights,astrogeodetic deflections of the vertical,and an Earth Gravity Model

Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the mainland and the islands.In this study,we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas.First,the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model(EGM),and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets.Second,we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points.Third,we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle.Finally,we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach.Using observed data of normal heights,ellipsoidal heights,and astrogeodetic vertical deflections referring to height sites in Qingdao,Shandong Province,we conducted a numerical experiment involving the normal height connection across sea regions.We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10.The distance of the height connection across the sea was approximately 10.5 km.According to China's official leveling specifications,the experimental results met the criterion of third-class leveling precision.

Considerations of Area Parameter of the Deflection Basin on the Structural Evaluation of Flexible Pavements

By using the concept of modified structural number(SNC)and deflection measurements,a simplified calculation methodology,that permits the structural condition evaluation of an existing pavement,is being proposed.The values of SNC and the curvature parameters were first determined through simulations using the ELSYM-5 software.Deflection measurements were carried out in experimental segments of Brazilian highways.The resilient moduli of each layer were determined from backcalculation using the ELMOD program for a three-layer system.Theoretical correlation models between SNC and the basin deformation parameter were determined and later,calibrated with the results of experimental sections.Utilizing the studied models,a good correlation was found between SNC,area parameter and maximum deflection,enabling the determination of SNC through deflection measurements and assisting in the diagnostic of structural condition of asphalt pavements.