Numerical Finite Element Method Research Articles

Numerical simulation of the stress-strain state near the injection well at deep disposal facilities for liquid radioactive waste

Relevance. The need to predict deformations of the earth's surface near injection wells pumping liquid radioactive waste, as well as their stability when pressure changes in the well during injection. Aim. To perform a numerical analysis of the stress-strain state of the structural elements of the injection well and the surrounding rock mass using the finite element method, to determine the magnitude of the deformations of the earth's surface and define the stability of the well and the strength of the cement stone at the maximum injection pressure of liquid radioactive waste. Objects. Near-wellbore zone of one of the injection wells located at the liquid radioactive waste injection site. Methods. Numerical finite element method for calculating the stress-strain state of the near-wellbore zone, taking into account the distribution of the elastic properties of rocks along the simulated section and the main structural elements of the well. Results. The authors have developed the numerical finite element scheme of one of the injection wells, taking into account its main structural elements, as well as allowing you to set the pressure distribution within the exploited horizon during the injection of waste. In the model, the distribution of the elastic properties of rocks along the section was set, taking into account their lithological features. The authors carried out the analysis of the hydrodynamic parameters of the well operation and determined the maximum pressure at the wellhead during the injection of liquid radioactive waste, equal to 1.71 MPa. Numerical modeling of the stress-strain state of the near-wellbore zone was performed in two stages: for the conditions of an idle well and taking into account the pressure distribution at the maximum waste injection pressure. The distribution of vertical displacements at the level of the earth's surface, as well as at the top of the operational horizon at the maximum pressure of liquid radioactive waste injection, is obtained. It is shown that at such a pressure, the largest uplifts will be: on the earth's surface – 4.5 cm, on the top of the production horizon – 11 cm. An assessment of the stability of the well structural elements at a maximum waste injection depth of 280 m, corresponding to the maximum pressure, showed that the stresses in the well and cement stone are much lower than the values that can lead to their violation. For cement stone, the safety factor at a maximum pressure of 1.71 MPa was equal to 7.8.

Numerical Simulations of a Permeability Test on Non-Cohesive Soil Under an Increasing Water Level

With the intensification of global climate change, extreme rainfall events are occurring more frequently. Continuous rainfall causes the debris flow gully to collect a large amount of rainwater. Under the continuous increase in the water level, the water flow has enough power to carry plenty of loose solids, thus causing debris flow disasters. The intensity of the soil is reduced with the infiltration of rainwater, which is one of the key causes of the disaster. The rise in the water level affects the infiltration behavior. There have been few previous studies on infiltration under variable head. In order to understand the infiltration behavior of soils under the action of water level rises, this paper conducted an indoor permeability test on non-cohesive soil under the condition of an increasing water level. A numerical model was established using the finite element analysis software, Abaqus 6.14, and the pore pressure was increased intermittently to simulate the intermittent increase in the water level. Thereafter, the permeability coefficient and seepage length were changed to interpret the changes in the flow velocity and rate in the permeability test of the non-cohesive soil. The results showed that the finite element numerical simulation method could not reflect the particle movement process in the soil. The test could better reflect the through passage and void plugging phenomenon in soil; when the permeability coefficient alone changed, the velocity of the measuring point with higher velocity changed more violently with the permeability coefficient; when the length of soil seepage diameter was uniformly shortened, the velocity of water flow increased faster and faster.

Loaded tooth contact analysis for helical gears with surface waviness error

Meshing characteristics are crucial for the transmission performance of vibration noise and strength of gear systems. Gear transmission error has been acknowledged as a prominent excitation in vibration systems, but the surface waviness deviations that directly affect it in contact analysis are generally ignored. This study proposes a comprehensive model for quasi-static analysis of tooth surfaces with waviness error. The model reconstructs the actual tooth surface in reverse based on the gear Fourier measurement principle. Instead of solving the meshing equations to pre-assume contact position, the problem of normal contact between surfaces with deviations is solved by an innovative multiscale grid and a local iterative numerical algorithm. Combining the finite element numerical method and surface integral of the Boussinesq solution determines gear deformation and develops a loaded contact model. The validity of the model is verified through numerical examples. Furthermore, the proposed model is applied to discuss the tooth surfaces with different waviness amplitudes, frequencies, and distribution angles for the first time. It explains the interaction between local microscale and global scale introduced by waviness error on tooth surfaces and reveals the mechanism of the waviness error on meshing performance.

Dynamic response of pile–slab retaining wall structure under rockfall impact

Abstract. Pile–slab retaining walls, as innovative rockfall protection structures, have been extensively utilized in the western mountainous regions of China. With their characteristics of a small footprint, high interception height, and ease of construction, these structures demonstrate promising potential for application in mountainous regions worldwide, such as the Himalayas, Andes, and Alps. However, their dynamic response upon impact and impact resistance energy remain ambiguous due to the intricate composite nature of the structures. To elucidate this, an exhaustive dynamic analysis of a four-span pile–slab retaining wall with a cantilever section of 6 m under various impact scenarios was conducted utilizing the finite-element numerical simulation method. The rationality of the selected material constitutive models and the numerical algorithm was validated by reproducing two physical model tests. The simulation results reveal the following. (1) The lateral displacement of the pile at the ground surface and the concrete damage under the pile at the impact center are greater than those under the slab at the impact center, implying that the impact location has a significant influence on the stability of the structure. (2) There is a positive correlation between the response indexes (impact force, interaction force, lateral deformation of pile and slab, concrete damage) and the impact velocities. (3) The rockfall peak impact force, the ratio of the peak impact force to the peak interaction force, and lateral displacement of the pile at the ground surface had strong linear relationships with rockfall energy. (4) Relative to the bending moment, shear force, and damage degree, the lateral displacement of the pile at the ground surface is the first to reach its limit value. Taking the lateral displacement of the pile at the ground surface as the controlling factor, the estimated maximum impact energy that the pile–slab retaining wall can withstand is 905 kJ in this study when the structure top is taken as the impact point. In cases where the impact energy of falling rocks exceeds 905 kJ, it is recommended to optimize the mechanical properties of the cushion layer, improve the elastic modulus of concrete, increase the reinforcement ratio of longitudinal tension bars, enlarge the section size of piles at ground level, or add anchoring measures to enhance the bending resistance of the retaining structure.

Simulation study of abdominal hemorrhage based on magnetic induction tomography.

Abdominal hemorrhage is an important clinical disease that can be life-threatening in severe cases. Therefore, timely detection and treatment of abdominal hemorrhage is crucial for the health and safety of patients. Magnetic induction tomography is a non-invasive, nonradioactive, and non-contact electromagnetic imaging technology with potential application value for disease screening and continuous monitoring. In this paper, a simulation model of electrical impedance distribution close to the real human abdominal tissue was constructed, and based on this model, the magnetic induction tomography simulation method of internal bleeding was studied by the finite element numerical method, and the comparison was verified by phantom experiments. The eddy current density distribution inside the abdominal tissue and the magnetic induction phase data at the tissue boundary are solved, and sensitivity analysis of phase differences caused by changes in the radius and position of bleeding volume was conducted, and three sensitivity indicators were proposed. Both the simulation and phantom experiment show that when there are six types of tissues with different conductivity in the abdomen, the radius of bleeding increases from 10 to 30mm, and the radius phase difference sensitivity index Ar increases approximately linearly monotonically. Its radius transformation sensitivity Kr is 3.0961 × 10-5°/cm. When the position of the bleeding volume changes, the sensitivity index Ax of the x-axis displacement phase difference shows a quasilinear monotonic decrease, and the x-axis displacement sensitivity Kx is -6.3744 × 10-6°/cm. The y-axis displacement phase difference sensitivity Ay index shows a quasilinear relationship and monotonically increases, with a y-axis displacement sensitivity Ky of 5.2870 × 10-4°/cm. The results indicate that the phase difference sensitivity before and after the occurrence of bleeding can be used as a quantitative monitoring indicator to monitor the occurrence and trend of intra-abdominal hemorrhage, laying the foundation for the preliminary screening and continuous monitoring of abdominal hemorrhage diseases using magnetic induction imaging.

Verification and Demonstration of One-Dimensional Freezing Model in SAM for Salt-Cooled Reactor Analysis Applications

This work presents the development and implementation of the one-dimensional freezing model in system analysis code SAM (System Analysis Module), code verification using analytical solutions, and code demonstration of a postulated overcooling transient for a fluoride salt–cooled high-temperature reactor (FHR) system and safety analysis applications. This paper first summarizes the freezing model, finite element numerical method, and special numerical treatment for handling transitions between single- and two-phase conditions. Analytical solutions are derived for two cases, with and without solid walls, for code verification purposes. As expected, the numerical results predicted by SAM agree very well with the analytical solution. A code demonstration is then performed on a postulated protected overcooling transient event of a generic reference pebble bed FHR design. The code was found to successfully predict salt freezing during such a postulated event. However, due to the lack of salt freezing testing data, code validation is not performed in this work, but will be pursued in future studies when such data become available.

The analysis of Yunnan Dayao basin effect based on microtremor test and numerical simulation

AbstractMicrotremor tests and finite element numerical simulations were used to analyze the seismic ground motion effects of the Yunnan Dayao sedimentary basin. The results of the microtremor relative to the reference point spectral ratio (HS/HR) method showed that the spectral ratio curves of each observation point in Dayao basin show multipeak characteristics, indicating that the site consists of different soil layers; the predominant frequencies of each observation point mainly are 6~9 Hz in the basin and there are lots of differences in the predominant frequencies of different observation points, which indicate that the site stiffness of each observation point is different; the differences of spectral ratios between the east–west directions (EW) and the north–south directions (NS) reveal the site's anisotropy. The amplification coefficient characteristics of each observation point in the basin obtained by numerical simulation show that the predominant frequency is 6 ~ 9 Hz; the amplification coefficients of each observation point are different; the edge effect and the focusing effect amplify the seismic ground motion in the basin; the different amplification coefficients of the two sub‐basins reflect the significant effect of the basin soil layers' differences on the seismic ground motion, the site is softer and amplification coefficients are larger; the slope degree of basin edges significantly affects the seismic ground motion near the basins edge, the amplification coefficients of the slope steeper and amplification coefficients larger. This study demonstrates that the microtremor test spectral ratio (HS/HR) method has good reliability applied to the analysis of basin effect and combining the finite element numerical simulation method is more effective in revealing the basin effect mechanism.

Blasting safety criterion of existing high speed railway tunnel over tunnel

Drilling and blasting method is still an important method in the current tunnel excavation construction. Controlling the vibration effect of blasting during construction and its influence on the upper span tunnel is the key problem in tunnel construction. Based on Chongqing Science City tunnel excavation blasting project, combined with the tunnel blasting vibration monitoring and testing, this paper analyzes the propagation attenuation law of tunnel blasting vibration along the rock mass, and studies the load characteristics of the explosion stress wave propagating to the existing high-speed railway tunnel. Considering the influence of the buried depth of the blasting source, a mathematical prediction model of the attenuation law of the upper span existing high-speed railway tunnel caused by tunnel blasting is established. Based on the dynamic finite element numerical calculation method, the influence of blasting vibration on the structure of the existing high-speed railway tunnel under construction is analyzed, and the propagation and attenuation law of blasting vibration along the tunnel contour is studied. Based on the ultimate tensile stress criterion, the ultimate shear stress criterion and the Mohr criterion, and compared with the results obtained from the numerical simulation, the blasting safety criterion model of the existing high-speed railway tunnel over the tunnel is established.

Improving mechanical properties of lattice structures using nonuniform hollow struts

In contrast to constant-strut lattices, the introduction of innovative strut designs has the potential to enhance the mechanical properties of lattice structures. This study presents a Bézier curve-based nonuniform section design for body-centered cubic lattices with hollow struts (BCCH). Periodic boundary conditions are applied to the unit cells, and a finite element (FE) numerical homogenization method is employed to assess their elastic properties. A comprehensive dataset is generated through the FE model, which is subsequently divided into training, validation, and testing sets. The coordinates of the Bézier curve control points serve as inputs to deep learning networks, which are trained on the training dataset. Relative density and elastic properties are treated as two distinct networks, with the validation set utilized to prevent overfitting. The objective function consists of two weighted components: one aims to maximize the relative Young's modulus, while the other ensures that the relative density achieves a specified value. An evolutionary algorithm is employed to optimize the objective function, with variations in the control point coordinates constrained to specific ranges. By leveraging the fast inference ability of the deep learning model, the stiffness and orientation-dependent mechanical properties can be efficiently tailored. Our results demonstrate that the optimized structures demonstrate superior stiffness (+92.8 %) and distributed stress field compared to the benchmark lattice. The design method also enables tailoring of specific mechanical properties, including isotropic elasticity. 3D-printed lattice designs were fabricated and compression tests confirmed agreement with simulation results in terms of stiffness. Additionally, the optimized designs exhibit superior strength (+99.6 %) and toughness compared to the benchmark lattices.

Evaluation of acoustic environmental effects and improvement method of ecological fish-nest bricks in the Yangtze River Basin: A model-based case study

With the rapid development of the Yangtze River Basin, the issue of underwater noise pollution has become increasingly severe, which has adversely affected aquatic creatures, particularly fish. Ecological fish-nest bricks (EFNBs), a new type of eco-friendly revetment, can provide a favorable habitat for fish. However, its effects on the acoustic environment remain unclear. The finite element numerical simulation method of acoustic-structure coupling is adopted to explore the acoustic environment of EFNBs, analyzing the impact of sound source frequency (within 300 Hz), structural forms, and arrangement of these bricks on the internal sound pressure level. The sound pressure level distribution of A-EFNBs were also analyzed at a distance of 0–0.5 m from the opening. A method of acoustic environment improvement is proposed, which utilizes porous polyurethane sponge (PPS) sound-absorbing material to establish a conducive acoustic environment for fish in EFNBs. The study results indicate that at low frequencies of sound source (f ≤ 150 Hz), the sound pressure level within EFNBs slightly decreases compared to the adjacent areas without EFNBs. The sound pressure level variation within the bricks increases with sound source frequency. The peak sound pressure increases with the number of openings. Interval arrangements can in general decrease sound pressure by less than 20 dB. At higher frequencies(f＞200 Hz), the sound pressure level at the opening of the A-EFNBs tends to increase. However, the PPS sound-absorbing material substantially reduces the sound pressure level by 15 –55 dB, rendering it an effective method for improving the acoustic environment for fish. The PPS sound-absorbing material is more suitable for habitat improvement of black carp (Mylopharyngodon piceus) and grass carp (Ctenopharyngodon idellus) with relatively low hearing thresholds among the four famous Chinese carps. The research findings can serve as a reference for designing and implementing river ecological restoration projects.

Application of machine learning for film thickness prediction in elliptical EHL contact with varying entrainment angle

This contribution demonstrates the potential of machine learning (ML) algorithms in predicting elastohydrodynamic lubrication (EHL) film thickness in elliptical contact with varying direction of lubricant entrainment, ranging from wide to slender elliptical configurations. The input parameters pertain to worm gear contacts, which are characterized by slender-like elliptical contact between a steel and a soft metal component. The study encompasses generating a database using numerical Finite Element Method (FEM) simulations, training artificial neural network (ANN) models, and evaluating their performance in terms of bias and variance. Key outcomes include the successful training of the ANN models, detailed analysis of the impact of tailored architecture on the ANN models' performance, and the superiority of the ANN compared to other ML regression algorithms. The study further identifies key input parameters that influence prediction accuracy and introduces a strategic dataset augmentation procedure to increase local and overall prediction accuracy. This strategic dataset augmentation enhances model robustness and precision while providing insights for expanding databases collaboratively. It holds potential for broader applications of ML for performance prediction of tribological contacts, thus paving the way for advanced ML models that consider additional factors and collaborative databases refined by multiple research groups.

Microwave Ablation Therapy for Hepatocellular Carcinoma: The Effect of Metabolic Heat on Temperature Distribution

Hepatocellular carcinoma is the main cause of liver cancer and one of the most occurring cancers worldwide. Microwave Ablation (MWA) is a method to destroy cancer cells by heating tumors above 50°C. Cancerous tissues can have high metabolic heat rates and affect temperature gain and distribution in thermal therapies. This research clarifies the metabolic heat effects in MWA therapy of liver cancer. Using Pennes Bioheat transfer equation with finite element numerical method, this research simulates temperature distribution with metabolic heat value ranging from 368,1 W/m3 to 29000 W/m3. The heat generated by metabolic heat is lower than the MWA heat source. However, the temperature increase should be considered as it can increase healthy surrounding tissue temperature to dangerous levels.

Analytical Solution of the Two-Dimensional Steady-State Seepage Field of a Seepage Anisotropy Pit Considering the Free Surface

An anisotropic foundation pit steady-state seepage field under a suspended waterproof curtain support considering the position of the free surface is studied analytically, and an analytical solution for the free surface position is given. The head distribution in the three zones is expressed as a series solution using the separation of variables method, and the explicit solution for the extent of the seepage field in each zone is obtained by combining the continuity condition between zones and the series orthogonality condition. The free surface position is determined according to the condition that the total head of the free surface is equal to the position head. A comparison of the calculation results of the analytical method and the indoor test and finite element analysis results verifies the correctness of the analytical solution, and the analytical method has more calculation efficiency than the finite element numerical method. Employing the aforementioned methods to analyze the influence parameters of the free surface position, the results show that drawdown increases as the ratio of the vertical permeability coefficient to the horizontal permeability coefficient increases; the greater the ratio of pit width to depth, the more significant the drawdown, but when the ratio continues to exceed 1.5, the drawdown is negligible.

НЕЛИНЕЙНАЯ ДЕФОРМАЦИОННАЯ МОДЕЛЬ СП 63.13330 В СТАДИЙНОЙ ПОСТАНОВКЕ

Normative documents in the field of reinforcement of reinforced concrete structures and the design of prefabricated monolithic structures fairly prescribe consideration of the initial stressstrain state of structures before reinforcement. The calculation can be performed using a normalized nonlinear deformed model according to SP 63.13330. At the same time, it does not explicitly provide for a calculation in several stages. The aim of the study is to develop a calculation method based on a normalized nonlinear deformation model in a staged formulation with minimal differences from the provisions of SP 63.13330. To achieve the goal, the following tasks are set: development of a calculation method, implementation of the method in the form of a universal program and verification of the developed program. The article presents a universal nonlinear deformation model in a staged formulation, which allows, within the framework of certain ratios, to calculate the strength and crack resistance of structural sections at an unlimited number of work stages, taking into account reinforcement, prestressing, initial stresses and cyclic loading (unloading and reloading). The method is implemented as a program in the Python programming language and verified on full-scale and numerical (finite element method) experiments. If we assume the initial stresses and deformations to be zero and calculate in one stage, then the proposed model is reduced to the SP 63.13330 model. For this reason, changing the norms according to the proposed method will not affect the current algorithms for calculating structures in one stage, however, it will significantly increase the scope of the model for calculating prefabricated monolithic, steel-reinforced concrete and reinforced structures. In addition, the accuracy of calculations of prestressed structures will increase, and it will be possible to calculate the cyclic loading of the section.

The thermal conductivity properties of porous materials based on TPMS

In this study, the effective thermal conductivity of materials based on a porous TPMS structure is investigated. The resulting structure is similar to a matrix and consists of identical pore cells that are strictly periodic in all directions. These pores have several characteristic sizes, and by altering them, materials with predictable effective thermal conductivity can be created. This work investigated materials based on Triply Periodic Minimal Surface (TPMS) of Schwarz P, Schoen IWP and Neovius. The calculation of thermophysical properties was performed using the numerical finite element method in the Ansys software package. Heat transfer in the structures was studied both with and without considering air. The empirical coefficient “n” for the Aivazov–Domashnev formula is expressed analytically. This relationship allows for the creation of materials with predictable thermophysical properties, taking into account the thermal conductivity of non-porous materials. The results of numerical modeling are validated by analytical Austin’s models and experimental data. The samples for the experimental study were made using additive technologies from PETG, ABS, PLA plastic and photopolymer resin. The study has scientific and applied significance, since a method is proposed for predicting the thermal conductivity of materials with an ordered structure. Several solid-state samples of elementary cells were made publicly available for designing materials with predictable thermal conductivity. The novelty of the work lies in obtaining the dependence of effective thermal conductivity on the geometric parameters of the ordered structure for materials with thermal conductivity in a wide range from 0.12 to 400 W/(m°C).

Fatigue Life Data Fusion Method of Different Stress Ratios Based on Strain Energy Density.

To accurately evaluate the probabilistic characteristics of the fatigue properties of materials with small sample data under different stress ratios, a data fusion method for torsional fatigue life under different stress ratios is proposed based on the energy method. A finite element numerical modeling method is used to calculate the fatigue strain energy density during fatigue damage. Torsional fatigue tests under different stresses and stress ratios are carried out to obtain a database for research. Based on the test data, the Wt-Nf curves under a single stress ratio and different stress ratios are calculated. The reliability of the models is illustrated by the scatter band diagram. More than 85% of points are within ±2 scatter bands, indicating that the fatigue life under different stress ratios can be represented by the same Wt-Nf curve. Furthermore, P-Wt-Nf prediction models are established to consider the probability characteristics. According to the homogeneity of the Wt-Nf model under different stress ratios, we can fuse the fatigue life data under different stress ratios and different strain energy densities. This data fusion method can expand the small sample test data and reduce the dispersion of the test data between different stress ratios. Compared with the pre-fusion data, the standard deviations of the post-fusion data are reduced by a maximum of 21.5% for the smooth specimens and 38.5% for the notched specimens. And more accurate P-Wt-Nf curves can be obtained to respond to the probabilistic properties of the data.

Influence of Subsoil and Building Material Properties on Mine-Induced Soil–Structure Interaction Effect

Soil–structure interaction (SSI) refers to the dynamic interaction between a structure and the surrounding soil on which it rests. The behavior of the soil can significantly affect the response of the building structure. In the context of civil engineering and structural analysis, SSI becomes particularly important when considering the response of structures to dynamic loads such as earthquakes or so-called paraseismic loads, e.g., mining tremors. Several factors contribute to SSI. Soil and building structure material properties, foundation type, and loading conditions are the most important parameters. The article concerns SSI in the case of mining rock bursts in Poland. The influence of changes in site material conditions and building material properties on the SSI phenomenon was investigated. A few variants of different properties of typical construction materials (brick, reinforced concrete, and cellular concrete) in the case of selected representative building structure were considered. The subsoil material properties from the wide range were also taken into account. Numerical three-dimensional finite element method (FEM) analysis was applied. The adopted models of the soil-structure system were verified by data from in situ experimental vibration measurements. A significant influence of the subgrade material and the building structure material on the SSI was demonstrated.

Complex variable solution for ground deformation responses considering the grouting pressure of shallow shield

During shield tunneling in shallow strata, ground deformation is highly sensitive to grouting pressure response. Excessive grouting pressure can cause ground uplift, and an excessively low grouting pressure can cause excessive ground settlement, affecting the surrounding environment. Current studies seldom analyze the influence of shield excavation on ground deformation when the grouting pressure is considered. To ensure micro-disturbance of the surrounding environment during shield tunneling, this study presents a complex variable analysis method for analyzing the influence of grouting pressure on surface settlement. This solution maps the semi-infinite strata outside the segment into circular domains by introducing a complex function conformal mapping method. The nonuniform convergence deformation pattern BC-4 was introduced as the boundary condition for the displacement around the tunnel. The Laurent series expansion of the analytical function considering the grouting pressure in the circular domain was substituted into each boundary condition to solve the analytical function. Subsequently, the accuracy of the analytical method was verified by combining it with a finite element numerical method. Finally, the influence of grouting pressure on ground deformation under different working conditions was analyzed through parameterization. This analytical method can provide a theoretical basis for controlling grouting pressure parameters in shield tunnels.

6σ Robust Lightweight Design of the GIL/GIS Bus Based on Co‐Simulation of Insulation, Current Flow, and Mechanical Stress

GIL/GIS bus is widely used in the field of power transmission and distribution, and the demand for lightweight is becoming more and more prominent. To reduce the weight of the bus and ensure the safety and reliability of the structure, a new 6σ robust design method of the GIL/GIS bus based on electric‐thermal‐mechanical co‐simulation is proposed. Taking a 550 kV/5000A bus as the initial structure, considering the uncertainty of product size and performance, a 6σ robust lightweight model of bus insulation electric field strength, current temperature rise, and mechanical stress multi‐performance co‐simulation is established. The finite element numerical calculation method is used to calculate and analyze the performance parameters of the bus. The Kriging surrogate model is used to form the response surface, and the optimal bus structure is obtained by genetic algorithm. The results show that after the robustness optimization, the performance of the bus meets the design requirements, the weight per meter decreased from 65.11 to 39.12 kg, and the lightweight effect is remarkable. Compared with the traditional deterministic optimization design, the reliability of the structure is improved. The new method of the GIL/GIS bus lightweight design proposed in this study has high feasibility and application prospects, which can provide new ideas for the development of gas‐insulated electrical equipment. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Thermal analysis with high accuracy of multi-beam mask fabrication

For a 7 nm technology node and beyond, multi-beam mask fabrication based on charged particles has attracted attention widely and shows great advantages in terms of throughput. However, the heating effect during mask writing is a serious problem and makes deformation error. To address this issue, an accurate analysis of heating with multi-beam writing is necessary. In this study, the thermal effects of electron beams on a mask during writing time (exposure time and nonexposure time) were simulated with a finite element numerical method. The variation in the temperature field with two writing paths (S-shaped and E-shaped) was analyzed. A comparative analysis of the mask’s deformation under different writing paths was conducted. Numerical research shows that the thermal analysis method in this study provides a guide for optimizing the process parameters of mask fabrication.