Numerical Program Research Articles

Three-dimensional smoothed particle hydrodynamics modeling of near-shore current flows over rough topographic surface

In this study, a three-dimensional (3D) numerical model based on the smoothed particle hydrodynamics (SPH) approach was developed to simulate the near-shore current flows over a rough topographic surface in the coastal area, where the flows are shallow and demonstrate strong turbulent characteristics. The numerical program is based on the open-source code SPHysics (http://www.sphysics.org), and two major improvements are made to treat the turbulence and rough boundary effects: A modified sub-particle-scale (SPS) eddy viscosity model is developed to address the turbulence transfer of flows, and a drag force equation is included in the momentum equations to account for the influence of roughness element on the bed and lateral boundaries. The computed results of flow velocity, shear stress, and free surface characteristics are compared with the laboratory measurements for a variety of test conditions. It has shown that the present SPH model can accurately simulate 3D-free surface near-shore current flows over a realistic topography with roughness.

NUMERICAL MODELING OF AIR POLLUTION NEAR THE HIGHWAY WITH PROTECTIVE BARRIERS

Problem statement. The problem of predicting chemical pollution zones near the highway, where protective barriers are located, is considered. The protective barriers influence the aerodynamics of air flow and reduce the level of working areas chemical pollution near the highway. It is necessary to have mathematical models that allow such evaluation at the design stage in order to evaluate the effectiveness of protective barriers promptly. The purpose of the article. Development of a numerical multi-parameter model and computer program for evaluating the effectiveness of the protective barriers using near the highway to reduce the chemical contamination level of work areas. Methodology. A two-dimensional mass transfer equation is used for mathematical modeling of chemical hazardous substances spreading that are emitted from a car and spread near the highway. This simulation equation takes into account the wind direction, atmospheric diffusion, the intensity of chemically hazardous substance emission from the car, the emission source location, the car body and the location of protective barriers near the highway. The Navier − Stokes equation and the potential motion model both are used to solve the aerodynamics problem of determining the uneven air velocity field near the highway. An implicit splitting difference scheme is used to numerically integrate the vortex transfer equation. Two numerical schemes are used to numerically integrate the equation for the current function. An explicit difference scheme is used to numerically integrate the Laplace equation for the velocity potential. Based on the constructed numerical model the package of programs is developed. To solve numerically equation of pollutant transfer the finite difference schemes of splitting are used. Scientific novelty. To calculate the formation of chemical pollution areas for atmospheric air near the highway during emissions from vehicles numerical model is proposed. This model allow to estimate the protective barriers effectiveness for reducing air pollution in the working areas. Practical significance. Based on the developed model the code for quickly calculation of air pollution process both near the highway and in work areas protecting with barriers is created. Conclusions. The developed numerical model and the computer code implementing it allow to investigate the process of chemical hazardous substance spreading in the atmospheric air near the highway. The model allows to quickly determine the effectiveness of protective barriers using near the highway. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

Testing, numerical modelling and design of S690 high strength steel channel-to-plate connections

This paper describes experimental and numerical studies of S690 high strength steel channel-to-plate connections failing by net section fracture. Experiments were conducted on 27 S690 high strength steel channel-to-plate connection specimens, with each consisting of a channel section member bolted to two gusset plates by web or flange. The test ultimate loads, load–elongation curves, failure modes and strain distribution at critical cross-sections were fully reported and analysed. The influences of the number of bolt holes, longitudinal pitch, connection length and out-of-plane eccentricity on net section efficiency were discussed. The experimental programme was followed by a numerical modelling programme, where finite element models were firstly developed and validated against the test results and then used to conduct parametric studies to generate further numerical data. Based on the test and numerical data, the accuracy of the relevant design rules, as set out in the European code, American specification and Australian standard, was assessed. The assessment results revealed that the European code leads to overly conservative and scattered ultimate load predictions, while the American specification and Australian standard result in unsafe and scattered ultimate load predictions. Finally, a new design approach was proposed and shown to provide substantially improved ultimate load predictions for S690 high strength steel channel-to-plate connections over the design codes. The reliability of the new design approach was also demonstrated by means of statistical analyses.

TEMPERATURE DEFORMATIONS OF PVC WINDOW PROFILES WITH REINFORCEMENT

Modern window structures made of PVC profiles can experience significant temperature deformation during both winter and summer operation. This effect is not considered in the current engineering methods of PVC windows calculation, which causes a number of problems in their operation (freezing and blowing through the windows, the failure of fittings, etc.). The use of laboratory methods of testing windows for temperature loads is limited due to their labor intensity and the high cost of testing equipment. We propose to develop an engineering method for calculating the mechanical operation of PVC windows under the action of temperature loads, which can be used at an early stage of design. One of the stages of its creation is a theoretical description of the temperature deformation of a PVC window profile when it works together mechanically with a reinforcing core. The article describes the nature of the forces transmitted by the PVC profile on the core during thermal bending (the case of temperature deformation at negative outside temperatures is considered). It was proposed to decompose these forces into two components: longitudinal, caused by different values of temperature shrinkage of PVC profile and reinforcing core, and transverse, caused by thermal bending of PVC profile. Mathematical models have been developed to calculate both force components and temperature deformation of the profile at different numbers and spacing of attachment points. A physical model has been proposed for implementation in the numerical calculation program, which allows a more accurate description of the temperature deformation of a long profile. Calculation of the test problem according to the proposed methodology and by means of full-fledged three-dimensional finite-element modeling in the COMSOL Multiphysics program was performed. A comparison of the results showed a discrepancy of less than 10%. It was found that the key influence on the deformations of PVC window profiles with a reinforcing core will have characteristics of the outermost joints "PVC profile – reinforcing core", because the greatest forces arise in them under the action of temperature loads.

Experimental and numerical investigations of recycled aggregate concrete-filled stainless steel tube stub columns under combined compression and bending

This paper reports experimental and numerical investigations into the behaviour and resistance of recycled aggregate concrete-filled stainless steel tube stub columns under combined compression and bending. Eccentric compression tests were conducted on twelve stub column specimens fabricated from austenitic stainless steel tubes with two cross-section sizes and concretes with three recycled coarse aggregate replacement ratios (0%, 35% and 70%). The test results, including the failure loads, load–mid-height lateral deflection curves, evolution of neutral axis and confinement effect, were discussed in detail. The testing programme was followed by a numerical modelling programme, where finite element models were developed and validated against the test results and then used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. Given that there are no existing design codes for recycled aggregate concrete–stainless steel composite structures, the relevant codified design rules for natural aggregate concrete filled-carbon steel tube stub columns under combined compression and bending, as set out in the European code, American specification and Australian/New Zealand standard, were evaluated for their applicability to recycled aggregate concrete filled-stainless steel tube stub columns, based on the test and numerical data. The evaluation results revealed that the European code and Australian/New Zealand standard generally provide an acceptable level of design accuracy, while the American specification yields unduly conservative failure load predictions.

Are astrophysical “black” holes leaky?

We continue a study by Adler and Ramazanoǧlu (AR) of “black” holes as modified by a scale invariant dark energy action. For the spherically symmetric Schwarzschild-like case, AR found that there is no event horizon; hence spacetime is not divided by the “black” hole into causally disconnected regions. We review the formalism for locating trapped surfaces and apparent horizons, and show that the modified “black” hole has no trapped surfaces. Thus, one suspects that it is “leaky,” and that there will be a “black hole wind” of particles streaming out from the location of the nominal horizon. This will have astrophysical consequences, for example, the wind may feed and stabilize star formation in the vicinity of the “black” hole. We initiate a study of the stationary axially-symmetric rotating “black” hole as modified by a scale invariant dark energy action, i.e. one that is Kerr-like. To set-up the axial case, we note that the conserving completion of the dark energy stress-energy tensor can be calculated algebraically by solving a [Formula: see text] matrix equation. Using Mathematica we calculate and simplify the modified system of Einstein equations for the axial case in quasi-isotropic coordinates, and give appropriate boundary conditions. Solution of these equations, which may require developing a special purpose numerical program, is rendered tricky by a residual general coordinate invariance of quasi-isotropic coordinates. This leads to the interesting mathematical question of representing a positive planar function as the gradient squared of a harmonic function.

Strain energy form coefficients for bending of short beams having full and thin-walled arbitrary cross section with application for FEM and Airfoils

The aim of this work is to develop a new generalized formula and a numerical computation program for evaluating the energy form coefficient of a complex and arbitrary cross section for full and thin-walled cross section with respect to any central axis, for the bending of beams of small lengths in comparison with the transverse dimension of the section. This coefficient plays a very important role in the calculation of the deformation energy of beams subjected to bending under the effect of a shearing force for short beams. It also enters in the formulation of FEM bending model, in order to calculate the stresses and the strains due to the external forces. The application is made for complex sections used in various fields of construction and in particular for airfoils designed for aerospace construction. A method is developed to calculate this coefficient as a function of the rotation of the central axes. The calculation of the area, the moments, and the product of inertias with respect to the central axes is necessary. The formula for calculating this coefficient is presented as a definite integral of a non-analytical function determined point by point along the direction of the application of the shear force. This function is based on the calculation of the partial static moments. The calculation of the latter is based on the development of a technique by subdividing the upper part of the section into adjacent common triangles at one point for the full solid section or by segments on the boundary for the thin-walled section. To speed up the process of numerically calculating this integral with high precision and reduced time, Gauss Legendre quadrature of order 40 is used. The calculation of the distribution of the tangential stress as well as its maximum value is determined. A shear shape coefficient is therefore determined. In the second part of this work, an application is made for the static calculation by the FEM of a hyper static beam with a view to determining the influence of this coefficient on all the parameters of resistance and bending stiffness as a correction of the classical model of bending by the FEM. A study of the error made by the classical bending model on our shear effect model is presented. A coefficient of efficiency of a section is presented.

Study on the evolution law of rock joint shear stiffness during shearing process through loading-unloading tests

Tunnels are usually located in highly jointed rock masses and most of them are in the area with frequent seismic activities. The joints have a great impact on the strength and failure mode of the rock mass. The jointed rock mass is subjected to frequent loading and unloading under complex geological and engineering conditions. Shear stiffness is a key parameter to reflect the shear deformation properties of the discontinuities. It is usually considered a constant value in the traditional calculation, but this assumption may not conform to engineering practice in practical engineering. Loading-unloading shear tests were conducted to study the evolution law of rock joint shear stiffness during the shearing process. The rock-like specimens with different joint roughness coefficients were used to simulate the natural rocks. The results show that the shear stiffness will gradually decrease with the increase of shear displacement. The shear stiffness of rock joints increases with the increase of joint roughness coefficient. According to the test results, a shear stiffness prediction model related to shear strain was derived. The prediction results were in close agreement with the laboratory test results, and the error range was within 12%. Which indicated that the established prediction model can better reproduce the shear stiffness change behavior of rock joints in different shear stages. In tunnel engineering design, the evolution of the shear stiffness of rock joints needs to be considered. More accurate results can be obtained by inserting the prediction model into the numerical simulation programs.

Study of dynamic debris impact load on flexible debris-resisting barriers and the dynamic pressure coefficient

The use of steel flexible barriers to mitigate landslide risk on natural hillsides is becoming common in the past decade in Hong Kong. The current design approach for this kind of barrier structure involves the adoption of the hydrodynamic load model to predict dynamic impact forces, followed by non-linear structural analyses of flexible barriers using numerical programs based on the pseudo-static force method. From local design guidelines, the dynamic pressure coefficient, a critical input parameter in the hydrodynamic load model, is taken as 2.0. This empirically considers the effect of impacts from boulders up to 2.0 m in diameter. With a view to rationalising the design approach, a series of physical impact tests and numerical analyses was conducted to investigate the dynamic debris impact on flexible barriers and the resulting barrier response. The physical impact tests involved up to 9 m3 of debris resisted by a 1.5 m high steel ring-net barrier. The tests were conducted in the 28 m long large-scale flume facility at the Kadoorie Centre in Hong Kong. Numerical modelling using computer programs LS-DYNA and NIDA-MNN was conducted to analyse the dynamic response of flexible barriers with different structural forms. The study aims to evaluate the dynamic pressure coefficient and to verify the current design approach based on the suggested dynamic pressure coefficient from this study. Results indicate that a dynamic pressure coefficient of 1.0 is, in general, appropriate for design purposes if the debris comprises primarily water and fine-grained particles.

Analytical method for predicting pile running during driving

Most offshore structures, such as conventional oil and gas jacket platforms or wind turbines, are typically supported by driven large-diameter steel piles. The piles resist the loads of the superstructure and environmental wind and wave forces. Pile running is a major hazard associated with the installation of driven piles in a layered seabed. An analytical method based on Newton's second law of motion is proposed to predict pile running. Two methods are used to calculate the soil resistance to dynamic penetration: (1) the conventional American Petroleum Institute (API) method, where the strain rate dependency and remoulding of the surrounding soil are considered, and (2) the Cone Penetration Test (CPT)-based method, which accounts for friction fatigue. The drag resistance in the context of fluid mechanics has also been considered for pile running. The velocity at the start of pile running was determined by the energy delivered by the piling hammer. A numerical programme was implemented and validated, and then used for three case studies; the results obtained were in good agreement with field measurements. The method presented in this study is dependable for analysing pile running and can provide significant support for pile installation assessment and risk management in offshore engineering design.

Local buckling and capacity of press-braked ferritic stainless steel channel sections under minor-axis combined loading

This paper presents experimental and numerical studies of the local buckling behaviour and cross-section resistances of press-braked ferritic stainless steel channel sections under combined compression and minor-axis bending. An experimental programme was firstly conducted and included material testing, initial local geometric imperfection measurements and ten eccentric compression tests. Following the experimental programme, a numerical modelling programme was conducted, where finite element models were developed to replicate the test observations and then used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. The obtained test and numerical data were then used to assess the relevant design interaction curves for press-braked ferritic stainless steel channel sections under minor-axis combined loading, as set out in the European code and American specification. The assessment results revealed that the codified design interaction curves result in conservative and scattered resistance predictions, mainly owing to the conservative bending end point and inefficient linear shape. Finally, new design interaction curves were developed and shown to provide a higher level of design accuracy and consistency than the codified design interaction curves.

Experimental and numerical study of stainless steel channel-to-gusset plate connections

With the advantages offered by stainless steel in terms of sustainability, mechanical performance and superiorserviceability, structural application of stainless steel is prevalent. This paper presents experimental and numerical studies of stainless steel channel-to-gusset plate connections failing by net section fracture. The experimental programme was carried out on 16 stainless steel channel-to-gusset plate connections, with each consisting of a channel section member bolted to two gusset plates by web or flange. The test setup and procedures as well as the key test results, including the failure loads, load–elongation curves, failure modes and strain distribution at critical cross-sections, were reported in detail. The effects of connection length, out-of-plane eccentricity and in-plane eccentricity on net section efficiency were discussed. Following the experimental programme, a numerical modelling programme was performed, where finite element models were firstly developed to replicate the tests and then employed to conduct parametric studies to generate further numerical data over a wide range of cross-section dimensions and connection lengths. Based on the test and numerical data, the existing design rules for stainless steel channel-to-gusset plate connections failing by net section fracture, as given in the European code and American specification, were evaluated. Generally, the European code yields excessively conservative and scattered failure load predictions, while the American specification leads to unsafe and scattered failure load predictions. An improved design approach was proposed and shown to provide substantially improved failure load predictions over the design codes.

S960 ultra-high strength steel slender welded I-section beam–columns: Testing, numerical modelling and design

This paper presents experimental and numerical investigations of the buckling behaviour and resistance of S960 ultra-high strength steel slender welded I-section beam–columns under combined compression and minor-axis bending moment. An experimental programme, including initial geometric imperfection measurements and eight beam–column tests, was firstly conducted. The test procedures, setups and results were fully reported. Following the experimental programme, a numerical modelling programme was carried out, with finite element models initially developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data. On the basis of the test and numerical data, the relevant design interaction curves, as provided in the European code, Australian standard and American specification, were evaluated for their applicability to S960 ultra-high strength steel slender welded I-section beam–columns. The evaluation results revealed that all three codified design interaction curves lead to conservative resistance predictions, mainly owing to the conservative end points (i.e. column buckling strength and cross-section minor-axis bending resistance). Finally, a revised Eurocode design interaction curve, with improved compression end point determined from more accurate column buckling curve and bending end point determined from the direct strength method, was finally proposed, and shown to result in more accurate resistance predictions for S960 ultra-high strength steel slender welded I-section beam–columns than the codified design interaction curves.

Experimental and numerical study of press-braked S690 high strength steel slender channel section columns prone to local–flexural interactive buckling

This paper reports an experimental and numerical investigation into the local–flexural interactive buckling behaviour and resistance of press-braked S690 high strength steel slender channel section columns. An experimental programme was firstly conducted and included initial geometric imperfection measurements and twelve pin-ended column tests. Interaction between local buckling and flexural buckling was observed for all specimens upon testing and discussed in detail. The experimental programme was accompanied by a numerical modelling programme, where finite element models were developed and validated against the test results and then employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and member effective lengths. The obtained test and numerical data were used to assess the accuracy of the codified design rules for press-braked S690 high strength steel slender channel section columns failing by local–flexural interactive buckling, as set out in the European code, North American specification and Australian/New Zealand standard. The assessment results revealed that the European code leads to excessively conservative and scattered resistance predictions, while the North American specification and Australian/New Zealand standard result in a higher level of design accuracy and consistency, but still with many conservative resistance predictions for columns with short to intermediate lengths. Finally, a new design approach was proposed and shown to yield substantially more accurate and consistent resistance predictions for press-braked S690 high strength steel slender channel section columns over the design codes.

Simulating hydrogen embrittlement fracture based on phase field method

The phase field hydrogen embrittlement fracture model is improved by introducing tension-compression split of strain energy. The numerical formulas of the model are provided, besides, the coupling term of concentration field and displacement field is deduced. The matlab software is used to compile the numerical program of phase field hydrogen embrittlement fracture. The modes I and II cracks of hydrogen embrittlement are simulated respectively. The simulation results show that hydrogen ions concentrate at the crack tip where stress concentration happens, and that the hydrogen concentration reduces the critical failure load of the square plate. Compared with the numerical results of the existing models, the improved model can accurately calculate the critical failure load in the mode I crack and capture the embrittlement fracture phenomenon when the phase field and the concentration field are accumulated near the crack tip. Moreover, the improved model can effectively simulate the mode II crack with hydrogen embrittlement.

Fiducial perturbative power corrections within the mathbf{q}_T subtraction formalism

We consider higher-order QCD corrections to the production of high-mass systems in hadron collisions within the transverse-momentum (q_T) subtraction formalism. We present a method to consistently remove the linear power corrections in q_T which appears when fiducial kinematical cuts are applied on the final state system. We consider explicitly the case of fiducial cross sections for Drell–Yan lepton pair production at the Large Hadron Collider up to next-to-next-to-next-to-leading order (N^3LO) in QCD. We have implemented our method within the DYTurbo numerical program and we have obtained perturbative predictions which are in agreement at the permille level with those obtained with local subtraction formalisms up to the next-to-next-to-leading order (NNLO). At the N^3LO we are able to provide predictions for fiducial cross sections with numerical accuracy at the permille level.

Impacts of Gravitational Mass Movements on Protective Structures—Rock Avalanches/Granular Flow

Rock avalanches and landslides lead to gravitational flow into their runout areas, which poses increasing danger to settlement areas and infrastructure in the Alpine region as a result of climate change. In recent years, a significant increase in extreme events has been registered in the Alps due to climate change. These changes in the threat to settlement areas in the Alpine region have resulted in the need for the construction of sustainable protective structures. Many structures are rigid, but others are now also increasingly flexible, e.g., net and dam structures, which are mainly earth dams with geogrids. In this study, empirical model experiments and numerical simulations were carried out to estimate the flow depth, the deposition forms and the effects on protective structures. Numerical programs usually require unknown input parameters and long computation times for a realistic simulation of the process. This study shows the results of model tests with different granular materials. Furthermore, different design approaches of different authors are presented. Finally, a design model based on the model tests of the University of Innsbruck for rigid barriers, nets and dams due to rock avalanches is presented.

Column Penetration and Diffusion Mechanism of Bingham Fluid Considering Displacement Effect

The diffusion progress of grout is hindered by groundwater, which means the diffusion distance cannot reach the designed values required in engineering for water plugging or reinforcement. In this study, based on the generalized Darcy’s law and the continuity equation of steady column penetration, a column diffusion mechanism for Bingham fluid, considering the displacement effect of grout on groundwater, is proposed. This diffusion mechanism is then validated by the penetration grouting experiments that have been previously performed. The influences of the grouting pressure, groundwater pressure, water–cement ratio and penetration coefficient of porous media on the diffusion radius are analyzed. Based on the Comsol Multiphysics platform, a three-dimensional numerical simulation program for this mechanism is developed using computer programming technology. Numerical simulations of the penetration and diffusion morphology of Bingham cement grout in porous media are then carried out. The results show that the theoretical calculation values of diffusion radius obtained from this mechanism are closer to the experimental values than those obtained from the column penetration grouting theory of Bingham fluid, without considering the displacement effect. The results of this study can provide theoretical support for practical grouting engineering.

Inertial Modification Using Self-Adaptive Subgradient Extragradient Techniques for Equilibrium Programming Applied to Variational Inequalities and Fixed-Point Problems

Equilibrium problems are articulated in a variety of mathematical computing applications, including minimax and numerical programming, saddle-point problems, fixed-point problems, and variational inequalities. In this paper, we introduce improved iterative techniques for evaluating the numerical solution of an equilibrium problem in a Hilbert space with a pseudomonotone and a Lipschitz-type bifunction. These techniques are based on two computing steps of a proximal-like mapping with inertial terms. We investigated two simplified stepsize rules that do not require a line search, allowing the technique to be carried out more successfully without knowledge of the Lipschitz-type constant of the cost bifunction. Once control parameter constraints are put in place, the iterative sequences converge on a particular solution to the problem. We prove strong convergence theorems without knowing the Lipschitz-type bifunction constants. A sequence of numerical tests was performed, and the results confirmed the correctness and speedy convergence of the new techniques over the traditional ones.

Structural Behavior of RC Beams Containing Unreinforced Drilled Openings with and without CFRP Strengthening.

Construction deficiencies can cause serious problems that significantly decrease the design strength of concrete structures, such as the unreinforced drilled openings. With the absence of sufficient reinforcement, the stress concentrations generated around the opening corners produce cracks in the beams. The size and location of the opening significantly affect the behavior of the beam under static and dynamic load. In this work, an experimental and numerical program was performed to investigate the behavior of drilled reinforced concrete beams with and without strengthening using CFRP sheets. Energy absorption and SDOF analyses were performed to preliminary assess the behavior of the beams under the dynamic load, such as blast. One control beam without any openings, six beams with tension-zone openings, and six beams with shear-zone openings were tested. It was found that the samples with tension-zone openings were slightly affected by the opening, where the reduction in the ultimate strength was approximately 7 to 14%. The beams were able to recover up to 46% of the lost strength by CFRP strengthening. On the other hand, the shear-zone opening significantly decreased the strength and energy absorption and increased the blast response. It can be concluded that it is not recommended to drill any opening at the shear zone as strength loss can reach 57% even with the strengthening, especially for blast resisting structure; in addition, the strength recovered from approximately 11.95 to 32.46% only. The finite element model was able to predict the strength of the beams. The results were closer in the case of tension-zone opening than those in the case of the shear-zone opening. Shear cracks were observed at the corners of the openings even if the opening exists at the tension zone. A reduction in the density of cracks can be observed after the strengthening, where the FRP sheet decreases the stress in the concrete.