Numerical Simulation Model Research Articles

Numerical analysis and experimental study of membrane-type acoustic metamaterial plate with X-shaped pendulum arm and cylindrical mass blocks

Membrane-type acoustic metamaterials have a favorable noise suppression effect. Hence, a membrane-type acoustic metamaterial plate (MAML) with an X-shaped pendulum arm and cylindrical mass blocks (CMB) was proposed in this paper. The theoretical model based on spring–mass systems and numerical simulation models of the membrane-type acoustic metamaterial cell (MAMC) were established under fixed and periodic boundary conditions to reveal the noise attenuation mechanism quantitatively, and the necessity of the CMB is discussed. Based on the results, it can be observed that the normal displacement of the membrane is nearly zero when the noise frequency is at the peak of the sound transmission loss (STL) curve. However, when the frequency is at the valley of the STL curve, the displacement is nonzero and fluctuates significantly. Meanwhile, by comparing the STL curves with and without the CMB, it was found that the MAMC performance is improved effectively by the CMB at low frequencies. The effective mass density of MAMC was found to be negative. To verify the accuracy of numerical calculations, an impedance tube experiment was conducted. Finally, orthogonal experiments were designed to describe the effects of the structural parameters a, l, and t on the effective bandwidth [Formula: see text], peak frequency [Formula: see text], and comprehensive index [Formula: see text] and to obtain the optimal structural parameter combinations for different indexes. This work further contributes to applying and developing the membrane-type acoustic metamaterial.

Mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces

Establishing multi-component phase field models on dynamic surfaces, and exploring the similarities and differences in phase field evolution between evolving and static surfaces, are interesting studies in multi-phase flow problems. This paper focuses on mathematical modeling and numerical simulation of the N-component Cahn-Hilliard model on evolving surfaces. In the modeling process, the evolution of the energy functional, componential mass conservation, and point-wise mass conservation (hyperplane link condition) are considered. On an evolving surface, the energy dissipation law does not hold because the surface velocity can be viewed as an external force in the system. Meanwhile, due to the velocity, the surface area may change, the componential mass conservation property and the hyperplane link condition can not be satisfied simultaneously. From the point of view of preserving these two physical properties of mass conservation, three types of N-component Cahn-Hilliard model are established on the evolving surface: componential mass conservation, point-wise mass conservation, and both componential and point-wise mass conservation. For the numerical simulation, the evolving surface finite element method is considered for the space-time discretization of the proposed model. In order to obtain a linear, decoupled, high-accurate, and stable scheme for long time numerical simulations, the stabilized semi-implicit method is integrated into the framework of the evolving surface finite element method. Through several numerical examples, the rationality of the model and the efficiency of the numerical method are shown. Additionally, three- and four-component phase separation phenomena are shown to investigate the N-component Cahn-Hilliard dynamic on various evolving surfaces.

Research on optimization of engineering parameters of effective action distance of multi-stage alternating injection acid etching

This study calibrated the numerical simulation model by using indoor experiments to measure experimental data related to conductivity, acid rock reaction kinetics and acid fluid loss, and combined it with the numerical simulation model to calculate the multi-condition acid flow under multi-physics coupling . The effective action distance of the acid liquid is finally formed, which can be used at 200℃ and 250℃. The effective action distance of the acid liquid is related to the amount of acid liquid and the number of acid liquid injection stages. A set of quick diagrams that can be quickly applied to multi-stage Alternate injection process design and optimized workflow. After calculation, it is concluded that: for the 200℃ formation, it is recommended that the total amount of acid used in the level 3 injection process should be more than 400m3; if level 2 injection is used, taking into account both cost and benefit, the total acid amount of 300m3 can be close to the same amount of acid in level 3 The effective range of the injection. For the 250℃ formation, it is not recommended to use a solution with small liquid volume and multiple stages. If level 3 injection is used, it is recommended that the acid dosage be more than 500m3; if level 2 injection is used, taking into account both benefits and costs, it is recommended to use 400m3 acid liquid . Injection can obtain an effective distance similar to that of level 3 injection with the same amount of acid.

Comparative Study between Thermo-Mechanical and Inherent Strain Method in Analysing Part Distortion of WAAM Component Using Numerical Simulation

This research investigates the part distortion of WAAM process by utilizing advanced numerical simulation. The WAAM component is made of a stainless steel SS316L deposition layer that is deposited on top of a mild steel S235 substrate plate to create a hollow, rectangular structure with a thin wall. In this study, Goldak's double-ellipsoid was used as the heat source model, and an isotropic hardening rule based on the von-Mises yield criterion was used. MSC Marc/Mentat is utilized as the numerical FE software for this research. The commercial S235 mild steel for substrate and the evolved SS316L was scanned by JMATPRO as the input for material modelling. In order to reduce the computational time of the numerical WAAM process, an Inherent Strain Method (ISM) is proposed for a numerical WAAM simulation in Marc. There are two ISM methods proposed for this study, the first is the analytical ISM based on the calculations and second is the calibration-based ISM using Virtual Calibration Test (VCT). On obtaining the ISM value based on the result of VCT, the mathematical software MATLAB were utilized to find the optimized ISM value. This research has a final purpose to determine which numerical simulation model that has a clear advantage on predicting the component deformation result in term of result accuracy as well as computational time. The expected final outcome of this study is the implementation of ISM method on numerical WAAM simulation is able to predict a part distortion in an accurate manner similar to TMM model with significantly faster computational time. Keywords: WAAM, Part Distortion, Numerical Simulation, Inherent Strain Method, Computational Time.

Interaction characteristics between the large ship-rubber fenders-wharf structure in deep-water considering the flexibility of the wharf structure

High pile-supported wharf structures in offshore deep water have significant flexibility due to long free ends and large slenderness ratios of the pile bodies, resulting in substantial deformation of the pile body under kinds of loads. In the design of this new type of wharves, it is expected to consider the characteristic of elastic deformation of pile body absorbing a portion of the ship impact energy reasonably. However, the existing calculation method still adopts the theoretical formulas of traditional wharf structures, failure to incorporate this advanced design concept fully. In order to solve this, firstly, a comprehensive three-dimensional numerical simulation model encompassing large ship, rubber fenders and wharf structure, was developed using Ansys/LS-Dyna, and the calculation model was validated against the existing research results. Subsequently, dynamic response characteristics of wharf structures during the normal berthing of ships were examined meticulously, and the variations in absorption energy and reaction forces of rubber fenders and wharf structures were analyzed systematically. And then the analysis results were compared with previous research, the limitations of the existing design code for wharf structures were discussed as well. Finally, the findings demonstrate that peak values of absorption energy and energy transfer times increase with the increase of ship loading capacities. And the elastic deformation of the wharf structure indeed absorbs considerable partial of the impact energy effectively, with about 30 % for conditions in this study, leading to lower impact forces acted on the wharf structure. Moreover, the maximum pile top displacement of the wharf structure is also smaller than that reported in the existing literature in the same load condition, indicating that considering the structural flexibility in the design of this new type of wharf structure is more in line with reality, and it is more reasonable and economical as well.

Numerical simulation and experimental investigation of the molten pool evolution and defects formation mechanism of Selective laser melted CuSn20/Diamond composites

Some defects such as small pores, thermal damage of diamond particle and micro-cracks between diamond and metal matrix existed in SLM-fabricated metal-bonded diamond tools. For further application, it is vital to understand the formation mechanism of such defects by SLM-fabricated parameters. In this work, a multiphysics field numerical simulation model based on computational fluid dynamics (CFD) was developed to investigate molten pool evolution and defects formation mechanism for SLM-fabricated CuSn20-bonded diamond composites. From simulation results, the metal particles melt and flow forward under the action of the laser. Also, the presence of diamond particles can obstruct the normal flow of melted CuSn20 fluid. Increasing the laser power can widen and stabilize the molten pool, however, exacerbate the thermal damage of diamond particles. Specially, the migration and marginalisation of the diamond particles during the formation of molten pool were found by simulation and experimental results. Unavoidably, there are obvious gaps in the interfacial bonding region of diamond and CuSn20 due to the comprehensive reasons of thermal gradient, differences in thermophysical properties of two materials and undergo continuous migration and rotational behavior of diamond particles. These findings have potential value for understanding and optimizing the process of SLM-fabricated metal-bonded diamond tools.

Exploring time-series transformers for spatio-temporal prediction of microstructural evolution of polycrystalline grain

This study introduces a novel microstructure prediction model (polycrystalline grain transformers: PGTs) for metal solidification processes, leveraging the capabilities of transformer networks. The model’s primary purpose is to predict the dynamic evolution of polycrystalline microstructures within additive manufacturing conditions. To facilitate the training of the PGTs model, we generated a comprehensive dataset through a two-dimensional multi-phase field numerical simulation model. The inherent strength of transformer networks lie in its multi-head attention mechanism, which enables the PGTs model to autonomously identify crucial feature information within the input sequence, particularly related to structural evolution. Our research outcomes underscore the robustness of the PGTs model, as it closely aligns with predictions obtained from conventional phase-field calculations. Importantly, this model exhibits a remarkable improvement in computational efficiency, surpassing traditional phase-field methods by several orders of magnitude. This breakthrough opens up new avenues for research, offering an efficient and cost-effective strategy for delving deep into the intricate relationship between solidification processes and material mechanical properties. Notably, we mark this study as the pioneering application of transformer networks in numerical simulations of the metal solidification process, showcasing its immense potential across various domains, including material design.

Finite-Element Analysis of Temperature Field and Effect on Steel-Concrete Composite Pylon of Cable-Stayed Bridge without Backstays

The backless cable-stayed bridge has the advantages of beautiful shape and reasonable force, but due to the low overall stiffness of the bridge pylon during cantilever construction, it is susceptible to the effect of solar temperature. To reveal the temperature deformation laws and achieve accurate alignment prediction during the installation process of steel–concrete composite pylons in complex environments, a refined numerical simulation model for the 3D bridge temperature field was established based on the proposed automatic sunshine-shadow recognition method. Subsequently, the optimal time periods for construction control are provided. The results of the study show that, during the cantilever construction of the bridge pylon, one pylon column will shade the other pylon column, resulting in asynchronous deformation that can reach 7.6 mm. The effect of solar temperature on the displacement of the bridge pylon is significant, where the maximum daily change in transverse displacement in the cantilevered state of the pylon can reach 33.6 mm, and the maximum change in cable force value can reach 52 kN. In order to mitigate the effect of solar radiation, the best construction time for the bridge pylon is 19:30~9:30, while the tensioning and measurement of the cable should be avoided from 6:00~18:00. This strategy ensures that the control of the pylon top displacement is maintained within 1/4000 of the pylon height, and the error in cable force is kept within 5%.

Влияние динамических характеристик процесса резания на шероховатость поверхности детали при токарной обработке

Introduction. The formation of the surface of a part when processing it on a metal-cutting machine is based on properly selected cutting modes. Complex methods of ensuring the specified quality of the part surface also take into account the tool geometry, its condition, and include corrections for tool deviation from the trajectory set by the CNC system under the influence of kinematic disturbances and spindle wavering. Subject. The paper analyzes the relationship between cutting modes and dynamic characteristics of the turning process, and its mapping into surface roughness. The aim of the work is to evaluate the influence of technological cutting modes taking into account the vibration activity of the tool on the roughness of the machined surface by means of simulation modeling. Method and methodology. Mathematical simulation of the dynamics of the cutting process is given, on the basis of which a digital simulation model is built. A methodology of using the simulation model for determining optimal cutting modes and predicting surface roughness taking into account tool vibrations is proposed. By means of experiments and analysis of the frequency characteristics of tool vibrations, the created model is validated, parameters of the cutting forces model subsystem and dynamic tool subsystem are specified, and geometrical topologies of the part surface are constructed. The calculated cutting forces are compared with experimental forces, and similar patterns and levels of characteristics are observed. An assessment of the optimality of the selected cutting modes is proposed based on the analysis of the tool vibration spectrum relative to the workpiece and the results of the numerical model simulation. Results and Discussion. A comparison of the results of digital modeling of the geometrical surface of the workpiece and the real surface obtained during the field experiment is given. It is shown that the roughness of the real surface obtained by machining with constant cutting modes varies relative to the surface roughness of the simulation model within the limits of not more than 0.066 µm.

Soil and unsaturated zone as a long-term source for pesticide metabolites in groundwater

Pesticide metabolites are frequently detected in groundwater, often exceeding the concentrations of their parent pesticides. Ceasing the application of certain pesticides has often not led to the expected decrease in metabolite concentrations in groundwater, which is potentially caused by residues in soil. Whereas pesticide residues in soils are well-documented, there are only few studies about metabolite residues. We investigated if the soil/unsaturated zone can act as a long-term source for metabolites in groundwater by combining soil analysis, groundwater analysis and numerical modelling. The field study focused on the herbicide chloridazon (CLZ) and its frequently detected metabolites desphenyl-chloridazon (DPC) and methyl-desphenyl-chloridazon (MDPC) while in the model additional pesticides and metabolites were considered. In soil samples from an agricultural area, where the last CLZ application was 5 to 10 years ago, we observed 10 times (DPC: 0.22 – 7.4 µg kg−1) and 6 times (MDPC: 0.12 – 3.1 µg kg−1) higher metabolite concentrations compared to CLZ (< 0.050 – 1.0 µg kg−1). Calculations suggested that the majority of the metabolites (DPC: 63 - 96%, MDPC: 74 – 97%) were sorbed despite their lower sorption tendency. The metabolite retention was in particular related to the organic carbon content. The calculated pore water concentrations were highest in the deepest part of the soil profile (75 – 100 cm) with median concentrations of 3.6 and 1.7 µg L−1 for DPC and MDPC, respectively. The groundwater concentrations of DPC and MDPC were 3 to 3.5 times higher in monitoring wells downgradient from the agricultural zone than upgradient of it. This increase highlights the potential of soil and unsaturated zone as a long-term metabolite source after the application stop of pesticides, consistent with the calculated elevated pore water concentrations. Numerical flow and transport model simulations suggested that this input from soil and unsaturated zone can cause elevated metabolite concentrations (> 0.1 µg L−1) in groundwater over more than one decade. The study highlights that soil and unsaturated zone can act as a long-term source of pesticide metabolites even if they have much higher mobility than the parent compound.

Biorealistic Neuronal Temperature-Sensitive Dynamics within Threshold Switching Memristors: Toward Neuromorphic Thermosensation.

Neuromorphic nanoelectronic devices that can emulate the temperature-sensitive dynamics of biological neurons are of great interest for bioinspired robotics and advanced applications such as in silico neuroscience. In this work, we demonstrate the biomimetic thermosensitive properties of two-terminal V3O5 memristive devices and showcase their similarity to the firing characteristics of thermosensitive biological neurons. The temperature-dependent electrical characteristics of V3O5-based memristors are used to understand the spiking response of a simple relaxation oscillator. The temperature-dependent dynamics of these oscillators are then compared with those of biological neurons through numerical simulations of a conductance-based neuron model, the Morris-Lecar neuron model. Finally, we demonstrate a robust neuromorphic thermosensation system inspired by biological thermoreceptors for bioinspired thermal perception and representation. These results not only demonstrate the biorealistic emulative potential of threshold-switching memristors but also establish V3O5 as a functional material for realizing solid-state neurons for neuromorphic computing and sensing applications.

Application of a Bayesian-Based Integrated Approach for Groundwater Contamination Sources Parameter Identification Considering Observation Error

Groundwater contamination source (GCS) parameter identification can help with controlling groundwater contamination. It is proverbial that groundwater contamination concentration observation errors have a significant impact on identification results, but few studies have adequately quantified the specific impact of the errors in contamination concentration observations on identification results. For this reason, this study developed a Bayesian-based integrated approach, which integrated Markov chain Monte Carlo (MCMC), relative entropy (RE), Multi-Layer Perceptron (MLP), and the surrogate model, to identify the unknown GCS parameters while quantifying the specific impact of the observation errors on identification results. Firstly, different contamination concentration observation error situations were set for subsequent research. Then, the Bayesian inversion approach based on MCMC was used for GCS parameter identification for different error situations. Finally, RE was applied to quantify the differences in the identification results of each GCS parameter under different error situations. Meanwhile, MLP was utilized to build a surrogate model to replace the original groundwater numerical simulation model in the GCS parameter identification processes of these error situations, which was to reduce the computational time and load. The developed approach was applied to two hypothetical numerical case studies involving homogeneous and heterogeneous cases. The results showed that RE could effectively quantify the differences caused by contamination concentration observation errors, and the changing trends of the RE values for GCS parameters were directly related to their sensitivity. The established MLP surrogate model could significantly reduce the computational load and time for GCS parameter identification. Overall, this study highlights that the developed approach represents a promising solution for GCS parameter identification considering observation errors.

Study on the Application of Finite Difference in Geological Mine Fault Groups: A Case Study

Fault structures can cause a bad mining environment and increase the stress of surrounding coal pillar faults. The study investigates the stress evolution characteristics within fault structure groups and their surrounding coal pillars and explores the extent to which these fault structure groups influence the stress distribution in coal pillars. Based on three-dimensional modeling technology, a transparent geological model of the geological environment of fault structure groups was constructed and finite difference software was used to generate a numerical simulation model. Two survey lines and four survey points were arranged to analyze the stress distribution of a coal pillar fault. The results show that the fault structure groups have obvious stress barrier effects. There is a 35 m stress reduction zone in the hanging wall of the fault and a 30 m stress increase zone in the footwall of the fault. Both FL-1 and FL-3 faults have a stress barrier effect in the hanging wall. The obvious stress increases in the footwall of the fault are 37.7 MPa and 33.5 MPa, respectively. The stress of the FL-2 fault as a whole appears to be a more obvious superposition at the end of mining, and the peak stress reaches 41.5 MPa.

Analyzing the gain and noise characteristics of the Bi/Er co-doped fiber amplifier

In this paper, we present the energy levels, hopping configurations, and numerical models of the Bi/Er co-doped fiber amplifier. Numerical simulations are utilized to solve the rate and power transfer equations of the model. The gain and noise characteristics of the Bi/Er co-doped fiber amplifier are comprehensively compared and analyzed. The results show that providing lower signal power and sufficiently high pump power is beneficial to improving the gain of the Bi/Er co-doped fiber amplifier, and the gain is independent of the pump direction in this case. The forward pump design has the lowest noise figure, followed by the bidirectional and thebackward. Gain spectra in the range of 1360 nm to 1560 nm are predicted. In addition, we have verified the feasibility of the numerical simulation model by comparing it with the experimental data. This analysis provides specific references and guidance for the design and optimization of the Bi/Er co-doped fiber amplifier.

Two-interface and thin-filament approximation in Hele-Shaw channel flow

When a viscous fluid partially fills a Hele-Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman–Taylor instability. We consider the evolution of a fluid region of finite extent, bounded between two interfaces, in the limit that the interfaces are close, that is, when the fluid region is a thin liquid filament separating two gases of different pressure. In this limit, we derive a second-order ‘thin-filament’ model that describes the normal velocity of the filament centreline, and evolution of the filament thickness, as functions of the thickness, centreline curvature and their derivatives. We show that the second-order terms in this model, that include the effect of transverse flow along the filament, are necessary to regularise the instability. Numerical simulation of the thin-filament model is shown to be in accordance with level-set computations of the complete two-interface model. Solutions ultimately evolve to form a bubble of rapidly increasing radius and decreasing thickness.

Numerical simulation of the development of hydrate-bearing layers by depressurization of radial wells

A perpendicular bisector unstructured grid was used for meshing a model with radial wells, and the non-orthogonal correction of the flux calculation was implemented in the Tough+Hydrate software. A numerical simulation model was established based on the geological parameters of hydrate-bearing layers (HBLs) in the Shenhu area of the South China Sea. Gas and water production from the HBL, developed through depressurization of radial wells, was studied, and factors influencing gas production were analyzed. The findings indicate that employing radial wells in both hydrate and mixed layers significantly accelerated gas and water production in the HBL, facilitating rapid depressurization. Faster depressurization, in turn, promoted the dissociation of natural gas hydrate (NGH) and increased gas production. Cumulative gas production using radial wells in double layers increased by 110.03% compared with a horizontal well. In the later stage of depressurization development, NGHs in the mixed layer were almost entirely dissociated, whereas nearly three-quarters of NGHs in the hydrate layer remained undissociated. The combined method of depressurization and thermal stimulation is expected to further promote NGH dissociation and enhance gas production. Analysis of influencing factors revealed that higher gas production was associated with a greater number of laterals and larger lateral length, whereas the layout of the laterals had little effect on performance.

Numerical simulation of Buongiorno's model on Maxwell nanofluid with heat and mass transfer using Arrhenius energy: a thermal engineering implementation

The thermal features of nanoparticles owing to progressive mechanisms are a fascinating phenomenon due to their applications in energy production, cooling procedures, heat transmission devices. Therefore, in the present study, the magnetohydrodynamic combined convection of Maxwell nanofluid and characteristics of heat transport in the presence of thermal radiation with a nonlinear relationship for modifications in the energy equation have been examined. Moreover, the features of activation energy in the presence of swimming microorganisms are considered. For motivation, the influence of bioconvection, magnetic field, and thermophoresis with convective boundary conditions are part of this investigation. The governing PDEs connected with momentum, energy, concentration, and density are converted into ODEs by using similarity functions. A transformed, dimensionless, nonlinear set of ODEs is tracked via a shooting scheme. The numerical results of prominent parameters have been analyzed in the form of graphs and tables using the computational software MATLAB. A significance improvement in the velocity profile is noted for the increasing value of Maxwell parameter. With rise of mixed convection parameter, both energy and volumetric friction field deteriorated. The determination of Biot number that is associated with the coefficient of heat transfer is more effective for growing the temperature and volumetric friction distribution. These conclusions may be appreciated in improving the efficiency of heat transfer strategies.

Three-dimensional numerical simulation and theoretical model of a hollow droplet impacting on a solid surface

The phenomenon of a hollow droplet impacting on a solid surface is widely found in various fields. The dynamic characteristics of hollow diesel droplets impacting on a solid surface are studied by combining numerical simulation and theoretical analysis. The dynamic contact angle model presented in this paper couples the advantages of existing dynamic contact angle models for simulating both the spreading and retracting stages. It also considers the continuous variation of the contact angle during the maximum spreading state. Compared to existing models, the maximum error has been reduced from 14.9% to 4.6%. The effects of impact velocity, impact angle, and volume ratio of a hollow droplet on the spreading and jetting characteristics are investigated by three-dimensional numerical simulations. It is found that air entrainment occurred in the counter-jet, and the presence of the impact angle increased the asymmetry of the counter-jet and spreading liquid film, promoting fingerlike splashing at the front liquid film. Based on energy conservation law, the theoretical prediction models of the maximum spreading coefficient of the hollow droplet impacting on the surface and the velocity of the counter-jet at the maximum spreading state are established using the multi-regional modeling method and the energy distribution principle. Compared with existing hollow droplet theoretical models, the proposed theoretical models exhibit a more concise expression, higher accuracy, and wider applicability range.

Radar Signatures and Surface Observations of Elevated Convection Associated with Damaging Surface Winds

Abstract Identifying radar signatures indicative of damaging surface winds produced by convection remains a challenge for operational meteorologists, especially within environments characterized by strong low-level static stability and convection for which inflow is presumably entirely above the planetary boundary layer. Numerical model simulations suggest the most prevalent method through which elevated convection generates damaging surface winds is via “up–down” trajectories, where a near-surface stable layer is dynamically lifted and then dropped with little to no connection to momentum associated with the elevated convection itself. Recently, a number of unique convective episodes during which damaging surface winds were produced by apparently elevated convection coincident with mesoscale gravity waves were identified and cataloged for study. A novel radar signature indicative of damaging surface winds produced by elevated convection is introduced through six representative cases. One case is then explored further via a high-resolution model simulation and related to the conceptual model of up–down trajectories. Understanding the processes responsible for, and radar signature indicative of, damaging surface winds produced by gravity wave coincident convection will help operational forecasters identify and ultimately warn for a previously underappreciated phenomenon that poses a threat to lives and property. Significance Statement We identified unique radar and observational signatures of thunderstorms that produce damaging surface winds through a recently discovered mechanism. The radar and observational signatures can be used to issue warnings to protect lives and property in situations where damaging winds were previously unexpected. Key observational signatures include associated increases in surface pressure, sustained wind, and wind gust magnitudes, as well as little to no change or an increase in surface temperature. In addition, base radar data exhibit a divergence signature, including in regions of little or no detectable precipitation. Additional study is needed to answer why some atmospheric environments are supportive of the unique damaging-wind-producing mechanism while others are not.

Optimization design method of 2D + 3D slope shape for landslide prevention in open-pit coal mine

In order to improve the stability of the slope and prevent the occurrence of landslide disasters, taking the east slope of the first mining area of Zhundong Open-pit Coal Mine as the engineering background, a combination of the 2-Dimensional (2D) limit equilibrium method and 3-Dimensional (3D) numerical simulation is used to optimize the shape of the east slope. By selecting a typical calculation profile based on the Bishop method and the residual thrust method in the 2D rigid body limit equilibrium method, the stability analysis of the profile slope is carried out, and the slope shape of the profile position meeting the requirements of the safety reserve coefficient and stripping ratio is preliminarily designed. Based on the 3D finite element strength reduction method, aiming at the slope shape that does not meet the requirements of safety reserve coefficient and stripping ratio, the width of the transport plate is reasonably changed, and a 3D numerical simulation model of various schemes is established. The influence of different tracking distances and slope angles on slope stability is studied. The 3D stability of the slope under different spatial forms is calculated, and the optimal tracking distance and optimal slope angle are determined. The slope stability and stripping ratio are further optimized. The results show that when the width of the transport plate of the DBS3 section slope is 8 ​m, it does not meet the requirements of safety reserve coefficient 1.2. When the width of the transport plate is set to 24 ​m, it meets the requirements of a safety reserve coefficient of 1.2 and an economic stripping ratio of not more than 8.0 ​m3/t. The 3D numerical simulation results show that the optimal tracking distance on the east side is 50 ​m, and the optimal slope angle is 35°. After the optimization design of a 2D and 3D slope shape, 2.456 million tons of coal resources were mined, creating a profit of about 21.1268 million yuan. While preventing landslide disasters, the recovery rate of coal resources was further improved.