Numerical Analysis Method Research Articles

Corrosion evolution and mechanical property deterioration of Q355NH weathering steel in long-term neutral salt spray environment

To investigate the morphology and mechanical behavior of Q355NH steel after long-term corrosion, neutral salt spray accelerated test were conducted for up to 180 days, with Q355 steel as the control group. By macro and micro observations, the evolution of rust layers and cracking mechanisms was elucidated. The corrosion thickness loss was divided into depth of uniform corrosion and pitting depth, and their relationships with corrosion time were established, respectively. Corrosion kinetic equations were also established, revealing no significant differences between two types of steel when the corrosion period was less than 65 days. However, as the corrosion period exceeded the critical time, Q355NH steel gradually exhibited better corrosion resistance. Additionally, corrosion rate for Q355NH and Q355 steel in various environments were compared, the average thickness loss rate of Q355 steel was revealed higher in intermittent neutral salt spray than continuous neutral salt spray. However, Q355NH steel exhibited the opposite trend due to the formation of the protective rust layer. Degradation equations were developed for the relationships between strengths, strains and mass loss rate in both Q355NH and Q355 steel, and constitutive models were also established for these corroded steels. Furthermore, based on the pitting evolution model, a numerical analysis method for evaluating the mechanical properties of corroded weathering steel was proposed and validated. Through parametric analysis, strength degradation formulas for double-sided non-uniform corrosion were established. It is demonstrated that the pit aspect ratio did not affect the strength. However, the strength significantly decreased when the initial thickness was small. For engineering applications involving uncoated weathering steel, a minimum thickness of 6 mm is recommended, preferably greater than 10 mm.

FLAC3D-based slope stability analysis and calculation

Slope stability is related to the normal operation of the project and operational safety, and there have been various methods for evaluating slope stability for a long time, among which the numerical analysis method is the most popular and comprehensive analysis and evaluation method nowadays. In this paper, the numerical simulation is carried out by FLAC3D software to solve the safety coefficient of the slope and the slope stability analysis in combination with the slope of the inverted siphon entry road section at the beginning of Xiaoyuiba, and the conclusions are in line with the actual situation, which shows that FLAC3D software can carry out scientific analysis and evaluation of slope stability and make comprehensive judgement.

Experimental and numerical investigation on low‐velocity impact response of sandwich structure with functionally graded core

AbstractThe present research investigates optimizing the impact resistance of functionally graded sandwich structures using experimental and numerical approaches. The low‐velocity impact (LVI) responses of functionally graded sandwich composite (FGSC) with different configurations with skin material jute/rubber/jute (JRJ) and core material having epoxy and sea sand by volume fraction of sea sand at 0%, 10%, 20%, and 30%. Sandwich structures were impacted with LVI (5.89, 10.92, and 15.18 m/s), with the impactor dropped from heights of 0.5, 1, and 1.5 m with precompressed spring loads. FGSC samples are considered a deformable body, and the impactor is modeled as a rigid body using commercially accessible dynamic explicit software. The burn‐out test and weight method were used to test the core's gradience; both methods' results substantially matched, and the variance in gradation could be observed. The proposed sandwich structure characteristics are examined by energy absorption, peak force, energy loss percentage, and coefficient of restitution. Results showed that SC30S provides greater energy absorption and superior damage resistance when tested on LVI. To evaluate the accuracy of experimental findings in predicting the indentation behavior of the sandwich structure, the finite element analysis was used to compare with the experimental results. According to the examination of these proposed FGSC overall performance, they could potentially be employed as sacrificial materials for LVI applications like claddings to shield major structural components. The systematic approach used in this work serves as a standard for choosing and using FGSC effectively for LVI applications.Highlights Low‐velocity impact behavior of sandwich structures was investigated. Combining flexible skin and epoxy core enhances energy absorption. Based on impact energy levels, impact damage areas were determined. Examined sandwich structure advantages in structural and aerospace uses. In terms of time and cost, the numerical analysis method would be useful.

Numerical analysis of discs based on carbon-nanofiber/Al2O3ZrO2 nanocomposite materials

In this study, the behavior of three different discs consisting of AS4 carbon fiber, T-300 carbon, and Al2O3ZrO2 (nanocomposite) materials at constant temperature was investigated by the numerical analysis method. Nanocomposites are formed by the dispersion of nanometer-sized particles in a matrix. With the advantages that nanocomposites bring to the material, they increase heat resistance in general. Carbon fibers, on the other hand, are preferred in the aerospace industry and aircraft industry due to their high strength properties. In this study, it was assumed that the modulus of elasticity does not change with temperature. The temperatures applied to the discs are 45 ℃, 60 ℃, 75 ℃, 90 ℃, and 105 ℃, respectively. It has been observed that the radial and tangential stress values obtained at high temperatures are higher than at low temperatures. The Al2O3ZrO2 nanocomposite materials have found that the stresses occurring in the Al2O3ZrO2 (nanocomposite) disc are higher than the stresses occurring in the AS4 carbon fiber disc. The stresses obtained on the AS4 carbon fiber disc are T-300 carbon discs.

Flow development region in the boundary layer: two-component molecular viscosity and partial slip

The subject of this study is the flow development region of laminar incompressible fluid flow in the boundary layer. This flow is an example where a direct application of the Navier-Stokes equations of gradient-free laminar incompressible fluid flow, in which the molecular viscosity is assumed to be a constant value independent of spatial coordinates, leads to a redefinition of the mathematical model. It is about the fluid boundary layer in the region of flow establishment in the motion problem of a semi-infinite plane, where the pressure gradient is zero. There is a situation when the number of equations is equal to three (two equations of momentum conservation and the equation of continuity), and the number of unknowns is equal to two - the number of the speed component. As a logical solution to the obtained inconsistency, it is proposed, as was already done for the problem of stationary motion of a plane and the problem of acceleration of a plane, to depart from the false statement about the constancy of molecular viscosity in the gradient-free boundary layer of an incompressible flow and consider molecular viscosity as a function of spatial coordinates. The need to consider the variable nature of molecular viscosity led to the discovery of another flaw in the Navier-Stokes theory. This non-trivial flaw was discovered during the application of the original numerical analytical method for solving the flow development region problem. The Navier-Stokes equations are supplemented by boundary conditions. The most important condition is the condition of fluid non-slipping on the surface of a solid body, which, by the way, does not follow any physical law. As a result, on the surface of a half-plane (or a moving body), the component of the velocity, which coincides with the direction of motion, has a constant value equal to the velocity of the body. It immediately follows from the continuity equation that the normal derivative of the normal component of the velocity must be equal to zero along the surface of the plane (body), since the longitudinal derivative of the velocity becomes zero. However, it is quite obvious that the velocity component normal to the surface of the plane (body) changes across the boundary layer in the region of current development, which indicates the presence of a normal gradient (both components) of the velocity. The conflict or contradiction is overcome by moving away from the generally accepted condition of non-slipping to the condition of partial non-slipping, or essentially the presence of sliding. Even with the sudden braking of any vehicle, the complete stop does not occur instantly, but after some finite time and distance, so in the case of the motion of a body in a stationary fluid, there is not an instant sticking, but a gradual one - from complete sliding, when a particle of liquid has just met a moving plane (body), to complete non-slipping at the end (and further) of the flow development region. Research methods. This work uses purely theoretical methods based on the use of calculus of variations, laws of physics, and ideas from everyday life. Conclusions. An improved model of a viscous Newtonian fluid in the area of flow development in the boundary layer was derived. On the basis of assumptions about the variable nature of the molecular viscosity, which already has two components, and the departure from the non-slipping condition, analytical solutions for both components of the velocity and both components of the molecular viscosity were obtained. A comparison of the obtained results with the results of other studies is presented.

A Design Strategy for Surface Nanostructures to Realize Sensitive Refractive-Index Optical Sensors.

Refractive-index optical sensors have been extensively studied. Originally, they were surface plasmon resonance sensors using only a flat gold film. Currently, to develop practically useful label-free optical sensors, numerous proposals for refractive index sensors have been made using various nanostructures composed of metals and dielectrics. In this study, we explored a rational design strategy for sensors using surface nanostructures comprising metals or dielectrics. Optical responses, such as reflection and transmission, and resonant electromagnetic fields were computed using a numerical method of rigorous coupled-wave analysis combined with a scattering-matrix algorithm. As a result, good performance that almost reached the physical limit was achieved using a plasmonic surface lattice structure. Furthermore, to precisely trace the refractive-index change, a scheme using two physical quantities, resonant wavelength and reflection amplitude, was found to be valid for a 2D silicon metasurface.

Periodic motion and optimization design of non‐stacked particle damper based on the double inert mass equivalent model

AbstractTo promote the application of non‐stacked particle damper (NSPD) in civil engineering, a design methodology was suggested on the basis of the double inert mass equivalent model. NSPD single‐story steel frame model is selected as the research object in this paper. First, the analytical solution for the periodic motion with symmetric two impacts was discussed. The shaking table test was performed to verify the rationality of the analytical solution under harmonic excitation. Subsequently, based on the analytical solution, the influence of equivalent connection stiffness on the vibration reduction effect and mechanism was analysed under resonant and non‐resonant harmonic excitation. The numerical analysis methods of the optimal equivalent connection stiffness were obtained accordingly. Finally, the effectiveness and generalization of the proposed optimal equivalent connection stiffness were discussed numerically under harmonic excitation and seismic ground motion. An optimal design process for the NSPD was proposed accordingly. Based on this, the vibration reduction performance analysis of NSPD under far‐field records, near‐fault pulse‐like records and near‐fault non‐pulse records was further conducted in the end. The results show that the time‐dependent frequency behaviour of the uncontrolled structure has a significant impact on the performance of the NSPD. The proposed optimization method is effective, which can be used as the foundation for the optimization of NSPD under earthquakes.

Lateral and vertical diffusion of magnesium in ion-implanted Halide Vapor Phase Epitaxy gallium nitride

In the present study, the diffusion of magnesium in gallium nitride was investigated. In order to ensure high structural quality and purity of the analyzed material, bulk crystals, grown by Halide Vapor Phase Epitaxy on ammonothermal native seeds, were used. Samples of polarity (0001), (10-10) and (11–20) were prepared from them and implanted with magnesium ions with fluence of 1 × 1016 cm−2 and 230 keV energy. X-ray diffraction was used to assess the structural quality of the samples at each stage of the study. Ultra-high-pressure annealing was carried out in the temperature range of 1250–1450 °C to activate the dopant and remove post-implantation damage. Diffusion of the implanted species was a consequence of the annealing process. Secondary ion mass spectrometry was used to assess the in-depth concentration of magnesium in the annealed samples. Strong diffusion anisotropy was observed for the crystallographic directions analyzed, with [000–1] being the most susceptible to diffusion and [10-10] being the most resistant. Using the finite element method for numerical analysis of the measured profiles, the diffusion coefficients were determined. Substitutional diffusion involving gallium vacancies was found to be the dominant mechanism in the analyzed samples. The temperature-independent diffusion coefficient was calculated. Its value was 1.7 × 10−4 cm2/s for the [0001] direction and one order of magnitude less for non-polar directions. The activation energy was similar for all cases studied and ranged from 2.26 eV to 2.38 eV.

Expanding the Scene of Tunnel Behaviour Through the DEM Model: a Case Study from ZaB-Zentrum Am Berg

The displacement of a tunnel plays a crucial role in conventional tunneling methods, serving as a key parameter for support requirement. Therefore, analyzing tunnel displacement is important for ensuring safety and optimizing costs by determining the appropriate level of tunnel support and installation time. Numerical analysis methods are commonly employed for assessing tunnel displacement, and two widely recognized approaches used worldwide are the continuum and discontinuum methods. While previous studies have highlighted differences in the analysis results obtained from these two methods, the magnitude of such disparities has not been extensively explored. Hence, the objective of this study is to quantify the extent of variation between the two methods through various scenarios, encompassing unsupported and supported excavated ground. Specifically, the focus is on tunnel displacement and the tensile force generated on axial tunnel supports, such as rock bolts. To facilitate this investigation, three tunnel sections from the Zentrum am Berg, tunnel research centre located in Austria, are utilized. The results show that discontinuum models exhibit higher displacements and higher tensile loads on axial support than continuum numerical models of the same tunnel geometry and equivalent rock masses. We show that discontinuum models can also capture asymmetric behaviour, and thus should be preferentially used in fractured rock masses where displacement of rock blocks dominate the rock mass behaviour.

Studying the bending behavior of polymer-based composites reinforced with wires of different geometric shapes by numerical analysis method

Studying the bending behavior of polymer-based composites reinforced with wires of different geometric shapes by numerical analysis method

The Influence of Different Sublevel Heights on the Stability of Faults under Sublevel-Filled Synergistic Mining

At present, when addressing the problem of fault stability in mines, most attention is paid to the study of the impact of a single mining method on faults. In order to study fault stability in mines more comprehensively, this paper researches the effect of coordinated mining using multiple mining methods. For example, the sublevel caving method without the sill pillar and the lower-layer filling method of coordinated mining can be used to analyze the dynamic response law of the fault, as well as the stability of the fault in different mining conditions. In this paper, the stress field, displacement field and sliding trend index of the fault plane and orebody near the fault are obtained via numerical simulation and theoretical analysis methods, and the main factors affecting fault stability under different mining conditions are analyzed. The results show that under the influence of cooperative mining, the shear stress fluctuation of the fault surface and the ore body near the fault increase gradually with the sublevel height of the sublevel caving method without the sill pillar and the lower-layer filling method, and the indexes of slip tendency become larger, which may be a precursor of fault activation. In particular, the fault surface of the sublevel caving method without the sill pillar reflects the drastic change in the shear stress with the larger displacement, and the instability brought to the fault by the sublevel caving method without the sill pillar is greater than that brought to the fault by the lower layer filling method under the premise of only changing the height of the sublevel.

Mechanism of Tire / Road Noise Emission and Reduction Technology

The significant noise reduction has been brought by recent electrification of power train of vehicles. More concern about impact on the health due to the environmental noise, especially road traffic noise, requires further reduction of tire / road noise emission caused by the contact between the tire and road surface. The tire / road noise emission mechanism can be described by three different systems such as the excitation, the response, and the propagation. The excitation is composed of the road excitation, the tread excitation, the air-pumping and the friction. The tire structural response and the acoustic response in the void formed inside contact patch are respectively excited by those sources. The recent technology development in numerical analysis and test methods allow us to investigate the detailed behavior of tire in various rolling condition. The present article gives progresses on the mechanism understanding of tire / road noise emission and some reduction technologies.

Optimum design of TMDs for reduction of floor vibration using evolutionary computation

Perceptible floor vibration can arise due to human activities such as walking, especially in steel-framed buildings. A general strategy to reduce floor vibration is to install tuned mass dampers (TMDs) between the floor slab and a raised OA floor. For the TMDs to act effectively, two parameters must be designed properly depending on the dynamic characteristics of the target floor: eigenfrequency and damping ratio. Conventionally, even when installing multiple TMDs in a floor, design has been carried out using fixed-point theory, which was originally used to design a single TMD. With the purpose of improving the performance of multiple-TMD installations, this paper describes the use of evolutionary computation (EC), a mathematical optimization method, to design the parameters for multiple TMDs. The new technique is first verified by implementing a numerical simulation using the spectral element method, a high-efficiency numerical analysis method. TMDs designed with EC are shown to suppress floor vibration more efficiently than those designed with fixed-point theory. Next, in experiments with an actual steel-framed building, sufficient vibration suppression performance is achieved with fewer EC-designed TMDs.

SOLUTIONS OF NONLINEAR BOUNDARY SYSTEM WITH COUPLED INTEGRAL BOUNDARY CONDITIONS

This article presented some theorems on a novel non-linear multiple Integro-differential equations of boundary T-system. It has been studied the numerical-analytic method and Banach fixed point theorem for the existence and approximation of the solutions over considered boundary system in compact space. In this work, we demonstrate that the mention methods can be discussed and analyzed for the existence and uniqueness, of a solution for the vector system. The paper satisfies the Hölder condition.

Stress Test of Precast Concrete Materials for Prefabricated Buildings by Numerical Analysis

There are serious environmental pollution problems in traditional construction operations. To improve China's construction industry, precast concrete has become one of the important environmental protection materials. Therefore, the stress of precast concrete is deeply analyzed. Based on the numerical analysis, prefabricated concrete buildings and other theories, numerical analysis and finite element method are taken as the research methods to analyze the mechanical properties of precast concrete materials and of steel bars. Finally, the situation and level of the DW1 specimen and DW2 specimen after the influence of the sliding and rotation of the ground beam on the horizontal displacement of the vertex are expounded from various aspects. The research results show that in terms of the mechanical properties of precast concrete materials, the performance data of prefabricated wallboards are all above 37, which is higher than the average strength. In the analysis of mechanical properties of steel bars, the steel bar with a diameter of 8 has a yield strength of 456.4 Mpa, an ultimate strength of 617.3 Mpa, and an elongation of 25.6%. The steel bar with this diameter has the best properties. In DW1 specimen and DW2 specimen, with the continuous progress of the loading process, the overturning moment caused by horizontal loads is also gradually increasing. In the horizontal level of prefabricated building materials, the increase of the axial compression ratio increases the anti-overturning moment of the specimen, and the peak bearing capacity of the specimen increases significantly, but the ductility decreases significantly. In the bearing capacity, there is little difference between the measured bearing capacity and the calculated bearing capacity of each specimen with vertical force applied. Therefore, the force test of precast concrete materials in prefabricated buildings is deeply studied based on numerical analysis, which has an important guiding significance for the construction industry to improve business performance and market competitiveness.

Analysis of Deformations of the Tunnel Excavation Face via Simplified Calculation Methods

The stability of the excavation face during the excavation of a tunnel is necessary to safeguard the lives of workers and to guarantee regular and rapid progress of the works. In this paper, the stability conditions of the tunnelling face were analysed using simplified numerical calculation methods (one-step approach) and analytical methods, in order to evaluate the extrusion of the tunnelling face as a representative quantity of the mechanical behaviour of the rock ahead of it. A comparison between the numerical method and the hemispherical method was illustrated, which was able to demonstrate how the latter can be used with high reliability in this type of study. An extensive parametric analysis of the typical conditions encountered in the excavation of tunnels in weak rock made it possible to determine the extent of the face extrusion and the effect on it of the main considered geometric and geomechanical parameters. Thanks to the comparison of the extrusion values obtained from the calculation with the limit value indicated by the scientific literature, it is possible to arrive at a rapid assessment on the stability of the face. A specific study on the role of the pressure applied to the face on the extent of the extrusion then made it possible to understand how to proceed to define the intensity of the main stabilisation systems (TBM thrust and longitudinal fiberglass bolts) to avoid the risk of collapse of the excavation face.

A numerical study of the multicriteria parametric optimization of the displacement and weight of a two-connected conical shell of minimal surface under thermal and power loading

Various methods and approaches are used to solve the problem of optimal design. Problems of this type are used for the optimal design of spatial coverings, which in modern architecture are progressive structures that are of interest to the whole world. Spatial coatings allow to give the building architectural expressiveness, cover large spans and combine load-bearing and enclosing functions.
 The hulls of minimal surfaces are the hulls of negative Gaussian curvature. In general, the geometry of minimal surfaces cannot be described analytically. To solve this problem, which is associated with solving the differential equation that describes the minimal surface in general, under appropriate boundary conditions, one has to use methods of numerical analysis. This approach allows us to build a point frame of the shell, which is a matrix of discrete solutions of functions that searches for a given minimum surface. In view of this, its geometric characteristics can be obtained only in numerical form.
 The basic relations of the linear theory of thin elastic shells of minimal surface are highlighted in the numerical study of parametric optimization. The mathematical justifications of how the external load is perceived and the process of creating the stress-strain state of the shells of minimal surfaces are highlighted.
 For the numerical implementation of the multicriteria parametric optimization of a double-connected conical shell of minimal surface, a finite element model was built from plate finite elements in the amount of 4824 pieces and 4896 nodes. The perimeter is rigidly clamped to the ground disk. The thermal force load is set, which consists of a combination of static and temperature loads.
 The developed methodology shows quite good results that coincide with the works of other authors and makes it possible to use two types of optimization for one research object simultaneously. The first stage is shape optimization, and the second stage is multicriteria parametric optimization.
 This methodology makes it possible to perform optimization processes in an automated mode, which is an important applied task for construction and applied mechanics.

Review of “Numerical Methods in Environmental Data Analysis” by Moses Eterigho Emetere

Review of “Numerical Methods in Environmental Data Analysis” by Moses Eterigho Emetere

New geometry-inspired numerical convex analysis method for yield functions under isotropic and anisotropic hardenings

Convexity of a yield function must be guaranteed to ensure unique relationship between plastic strain increments and stress components. A geometry-inspired numerical convex analysis (GINCA) approach is developed to analyze the convexity of a yield function. The numerical approach is verified by the computation of convex domains for several typical yield functions of Drucker, Cazacu-Barlat2004, Hu2017, Cazacu2018 and a newly proposed function for differential-anisotropic hardening. The verified GINCA is applied to analyze the convexity of the Gao2011 yield function since it was not determined yet. The numerical approach is also used to determine the convex domain evolution with respect to plastic deformation in an anisotropic hardening function. It is also applied to investigate the convexity of polynomial yield functions for strong anisotropic metals. The result shows that the GINCA can effectively and correctly compute the convex domain for different yield functions. Besides, the numerical approach only needs to compute the effective stress from a yield function without any computation of the first- and second-order partial derivatives, compared to the complicated convex analysis by the Hessian matrix. Therefore, the proposed GINCA is user-friendly, effective and accurate to analyze the convexity of a yield function both for isotropic hardening and anisotropic/differential hardening. The Matlab codes are shared as electric attachments for scientists and engineers to check the convexity of a yield surface under biaxial loading, plane stress with shear stress and triaxial loading conditions.

Opening-dependent phase field model of hydraulic fracture evolution in porous medium under seepage-stress coupling

In this paper, a seepage-stress coupling numerical analysis method is developed to simulate complex hydraulic fracturing in porous medium, in which the characteristics of hydraulic fracture evolution in porous medium under seepage-stress coupling are revealed. The classical Biot's poroelasticity theory is applied to couple the stress and fluid fields, and the crack propagation path of hydraulic fracturing is described by an opening-dependent phase field model. Potential energy caused by fluid pressure is also coupled into the governing equation of phase field evolution. The system of fracture opening affecting fluid flow is established. Staggered iterative scheme is applied to solve the above three-field coupled problem based on Newton–Raphson iterative algorithm. Three classical cases are presented to validate the proposed method: the first one is an analytical solution of pressure distribution in a fixed opening crack and the second one is a benchmark case of Sneddon analytical solution for a pressurized pre-crack and the third one is the KGD problem for hydraulic fracture propagation. Moreover, numerical simulations of hydraulic fracturing in shale block, multi-layer and natural fractures are also investigated. The numerical results agree well with the results in published literatures. It is indicated that hydraulic fracture evolution under seepage-stress coupling can be forecasted by the proposed method. The proposed method not only provides a powerful analytical tool for the oil or gas production, but also provides assessment tools for the stability of geotechnical engineering in water rich environments.