Three-dimensional Analytical Model Research Articles

TOPOLOGY OPTIMIZATION DESIGN AND MECHANICAL ANALYSIS OF A PERSONALIZED LUMBAR FUSION DEVICE

Objective: To reduce the shielding effect caused by the large elastic modulus of metal fusion devices after osteotomy for the treatment of scoliosis. Methods: A personalized fusion device was designed using reverse engineering techniques, three-dimensional modeling, topology optimization, and finite element analysis. A finite element model of the lumbar spine after orthopedic surgery was established from an actual case. A fusion device was implanted into the lumbar spine before and after the optimized design for simulation calculations, respectively. The similarities and differences in the mechanical properties of the different fusion devices and vertebrae were compared. Based on the topological optimization of the mechanical properties of the fusion system, a lightweight fusion device was designed and the stress-shielding effect on the lumbar vertebrae was improved. Results: The topologically optimized fusion device described in the current case was 60% lighter while maintaining the strength of the fusion. After optimization, the average strain of the fusion was increased by up to 200% and the stiffness was significantly decreased. The average equivalent stress of cancellous bone was increased by up to 9.55% for the PEEK fusion device. In contrast, the topologically optimized fusion can increase the average equivalent stress of cortical bone by 5.63% and reduce the stress-masking effect of vertebrae. Conclusion: Topologically optimized titanium alloy fusion devices can significantly reduce the mass of the implant as well as reduce fusion stiffness. Additionally, a topology-optimized titanium alloy fusion device can effectively improve the stress-shielding effect of cortical bone.

Virtual Three-Dimensional Model Analysis in the Assessment of the Maxillary and Mandibular Donor Sites on Cone-Beam Computed Tomography Images.

Using the Mimics software to assess the maxillary and mandibular donor sites on cone-beam computed tomography (CBCT) images. This cross-sectional study was conducted on 80 CBCT scans. Data in DICOM format were transferred to the Mimics software version 21, and a maxillary and a mandibular mask according to cortical and cancellous bones were virtually created for each patient based on Hounsfield units (HUs). Three-dimensional models were reconstructed, and boundaries of donor sites, including mandibular symphysis, ramus, coronoid process, zygomatic buttress, and maxillary tuberosity, were defined. Virtual osteotomy was conducted on the 3D models to harvest bone. The volume, thickness, width, and length of harvestable bone from each site were quantified by the software. Data were analyzed by independent t-test, one-way ANOVA, and Tukey's test (alpha = 0.05). The greatest harvestable bone volume and length differences were observed between ramus and tuberosity (P < 0.001). The maximum and minimum harvestable bone volumes were found in symphysis (1753.54 mm3) and tuberosity (84.99 mm3). The greatest difference in width and thickness was noted between the coronoid process and tuberosity (P < 0.001) and symphysis and buttress (P < 0.001), respectively. Harvestable bone volume from tuberosity, length, width, volume from symphysis, and volume and thickness from the coronoid process was significantly greater in males (P < 0.05). The harvestable bone volume was the highest in symphysis, followed by ramus, coronoid, buttress, and tuberosity. The harvestable bone length and width were the highest in the symphysis and coronoid process, respectively. Maximum harvestable bone thickness was found in symphysis.

A three-dimensional analytical model for transient tool temperature in cutting processes considering convection

A three-dimensional analytical model for transient tool temperature in cutting processes considering convection

Diagnostics of Transmission Bearing Units Based on Thermal Load Study

Abstract. The operating temperature of the transmission unit is noted to affect its reliability and can serve as a diagnostic criterion. It is proposed to diagnose the transmission unit technical condition by the temperature in the friction zone in order to take into account the influence of air temperature, solar radiation heating and adjacent heat-producing objects. (Research purpose) To ensure the bearing unit controllability based on the thermal load study. (Materials and methods) The study uses the results of calculating the nominal and operational load of the rear power take-off shaft of the Belarus-82.1 tractor. The study uses the three-dimensional modeling and finite element analysis of the temperature distribution under steady-state thermal conductivity conditions. To establish the functional relationship between the temperature in the friction zone and the diagnostic temperature, the method of finite element analysis is used under steady-state thermal conductivity conditions. (Results and discussion) The maximum load modes and temperatures in the friction zone were determined for the 60310A bearing of the power take-off shaft gearbox during aggregation with different agricultural machines such as 4300 Newtons and 2.4 degrees Celsius for FS-2.0U garden cutter (540 revolutions per minute); 4126 Newtons and 40.7 degrees Celsius for Rovatti T3K80/90/2 (540 revolutions per minute) irrigation pump; 956 Newtons and 13.0 degrees Celsius for ROU-6 (1000) manure spreader; 2615 Newtons and 36.6 degrees Celsius for KPRN-3.0A (1000) mower-conditioner. The maximum temperatures as a diagnostic criterion are established in the friction zone, which equal to 41.7 degrees Celsius at 540 revolutions per minute engine speed and 31 degrees Celsius at 1000 revolutions per minute. (Conclusions) Since the direct measurement of the temperature in the friction zone is hardly possible without changing the bearings design, it is proposed to measure the diagnostic temperature on the unit used for mounting the temperature sensor. The coefficient of proportionality k=0.53 of the finite element model is determined. In order to implement diagnostics in an automatic mode, an algorithm is developed for a digital transmission malfunction recorder. Its design is based on the ATmega328 programmable microcontroller and TMP36 temperature sensors. It is found that the digital transmission malfunction recorder provides automatic control of up to seven different transmission units simultaneously, taking into account the ambient temperature.

Developing a three-dimensional urban surface model for spatiotemporal analysis of thermal comfort with respect to street direction

Understanding the urban heat problem, which is intensifying owing to urbanization and climate change, has become a great challenge. Evaluating the thermal environment of urban spaces and predicting changes based on urban planning are essential for developing optimal urban cooling plans. This study addresses the pressing challenge of urban heat by developing a three-dimensional urban surface model (3D-USM) and conducting spatiotemporal thermal comfort simulations, providing valuable insights for the development of effective urban cooling strategies in the face of urbanization and climate change. Mean radiant temperature (MRT), the key element of thermal comfort of humans by reflecting complex urban environments was simulated in east-west streets which are vulnerable to heat, and results demonstrate that a small change of street angle has a significant effect on pedestrian thermal comfort. Specifically, at 0900 LST, the southern sidewalk of the street rotated by 12.5° was more vulnerable than the northern sidewalk. This resulted in a shift in the optimal location of trees that provide effective cooling, highlighting the importance of considering street orientation in the placement of urban greenery. This suggests that spatiotemporal thermal comfort simulations considering urban form in detail are necessary to efficiently cool the city. The proposed 3D-USM, capable of accurately and efficiently simulating the thermal environment and MRT thermal comfort in complex urban environments using simple input data, holds great potential for guiding the development of efficient cooling strategies to foster sustainable cities.

A retrospective study of the accuracy of Invisalign Progress Assessment with clear aligners

The objective of this study was to detective the accuracy of model superimposition and automatic analysis for upper and lower dentition width in Invisalign Progress Assessment during the process of clear aligners. 19 cases were included in this study. Pre-treatment dental cast (T0) and post-treatment dental cast after staged treatment (T1) were available for three-dimensional model superimposition. Subsequently, movements of maxillary teeth in the horizontal plane (cross-section) after staged treatment and width of upper and lower dentition were measured by three-dimensional model superimposition in the real world and Invisalign Progress Assessment separately. Consequently, the data collected from these two methods were compared. In Invisalign Progress Assessment, movements of maxillary teeth in the horizontal plane after staged treatment was 2.31 (1.59,3.22) [median (upper quartile, lower quartile)] millimeter (mm), while in three-dimensional model superimposition, the result was 1.79 (1.21,3.03) mm. The difference between the two groups is significant (P < 0.05). Intercanine width upper, intermolar width upper, intercanine width lower, and intermolar width lower were 36.55 ± 2.76 mm, 56.98 ± 2.62 mm, 28.16 ± 1.85 mm, 53.21 ± 2.72 mm separately in Invisalign Progress Assessment and were 36.48 ± 2.78 mm, 56.89 ± 2.58 mm, 28.05 ± 1.85 mm, 53.16 ± 2.64 mm separately in three-dimensional model analysis, which was no significant difference among these groups (P > 0.05). The data from Invisalign Progress Assessment was not in parallel with what was achieved from model superimposition with palate as a reference completely. The accuracy of model superimposition in Invisalign Progress Assessment needs further investigation, whereas the accuracy of model analysis in Invisalign Progress Assessment was accurate. Thereby, results from Invisalign Progress Assessment should be interpreted with caution by the orthodontist in the clinic.

A novel three-dimensional analytical tornado model constructed based on force balance analysis

The analytical model for tornado vortices is crucial in both the wind field characterization and the tornado-resistant design of civil structures. The objective of this study is to derive a novel three-dimensional analytical tornado model from the vortex governing equations simplified based on the force balance analysis in tornado-like vortices (TLVs). First, TLVs with different swirl ratios are generated in a numerical simulator utilizing the large-eddy simulation. Then, the forces in the axisymmetric vortex governing equations are calculated for time-averaged TLVs. The governing equations in the single-cell TLV are simplified by ignoring some significantly small terms. Finally, a novel three-dimensional analytical tornado model, which contains the radial, tangential, and vertical velocity as well as the pressure, has been proposed and validated. The result shows that the force balance in the single-cell TLV is simpler than that in TLVs with larger swirl ratios. In the single-cell TLV, the viscous forces in the radial and vertical directions can be neglected, while the tangential viscous force remains to play an important role in the force balance. The proposed model mitigates the limitations of existing models in describing single-cell tornado vortices, such as only two-dimensional velocity being given, the neglection of the vertical shear effects near the ground, and the infinite velocity at high altitudes. It shows good agreement with the numerical and experimental TLVs as well as the real tornado.

A Critical Discourse Analysis of a Female Vice-Presidential Candidate’s Acceptance Speech

This instrumental qualitative case study examined the acceptance speech of Professor Naana Jane Opoku-Agyemang, the first female vice presidential candidate of a major political party in Ghana. The study aimed to identify the discourse elements and cohesive devices used in the speech and to evaluate how she conveyed her political ideology and gender identity. Specifically, the research question was: which discourse elements and cohesive devices were employed, and how were political ideology and gender identity manifested in the speech? The data consisted of an eight-page speech delivered on July 28, 2020, in Accra, containing 3,972 words. Fairclough's (2015) Three-Dimensional textual analysis model was used for data analysis, which includes description, presentation and interpretation, and explanation of social reasons. Results showed that Professor Opoku-Agyemang used discourse elements and cohesive devices such as 'however,' 'also,' and 'second' to highlight her academic and political expertise and present herself as a qualified vice presidential candidate. She aimed to inspire women and encourage them to aspire to any position, including becoming the president of Ghana. The study's findings contribute to existing literature and can inform future research on female political representation, exposing the approaches of a marginalized group and their use of speeches to gain recognition within Ghana’s political space and beyond.

다양한 작동 조건에서의 마이크로 터보젯 엔진 성능 예측을 위한 통합 해석 모델 구현 연구

In this study, an integrated CFD analysis implementation were conducted for the commercial micro turbojet engine, JetCat P300-RX, which has a maximum thrust of 300 N. A three-dimensional integrated analysis model includes major components of the micro gas turbine engine. A steady-state RANS (Reynolds Averaged Navier-Stokes) analysis was performed using ANSYS CFX V20.2. For the turbulence model and combustion model, the k-ω SST (Shear Stress Transport) model and the EDM (Eddy Dissipation Model) model were applied, respectively. The analysis were performed for various engine speed (RPM) conditions from 30,000 RPM to 106,000 RPM and various altitude conditions from sea level to 3.0 km. And the analysis results were verified by comparing with the actual engine test results. The comparison results showed that most of the performance parameters, such as thrust, exhaust gas temperature (EGT), air flow rate, and compression ratio in all analysis conditions (RPM and altitude) are in good agreement with the ground test results of commercial engines.

Using crop fall patterns to provide an insight into thunderstorm downbursts

This paper examines whether crop fall patterns due to thunderstorm downburst-like events can provide an insight into the flow structure of a downburst. To explore this phenomenon, a novel three-dimensional analytical model for the velocity flow field is derived and coupled with a generalised plant model which is capable of modelling crop failure. Through this approach we have established the concept of the lodging front – a dimensionless variable used to quantify the spatial extent of crop failure. Crop failure is shown to result in a diverging pattern and the angles at which the crop falls has been shown to collapse onto a single curve when suitably normalised. Comparison with full-scale data suggests that the model is capable of predicting realistic crop fall patterns and could potentially be used in the future to assess the strength of downbursts.

Study on the Effect of Initial Delamination on Tensile Behavior of Offshore Wind Turbine Blade Spar Cap

Delamination damage to spar caps seriously endangers the operation safety of offshore wind turbines. The effect of initial delamination of various depths and areas on the ultimate tensile load of laminates is studied based on experiments and numerical simulation, and an effective method for predicting the residual tensile strength of laminates with high thickness is proposed. Three groups of initial delamination specimens with different characteristics were fabricated, and static displacement tensile tests were carried out. An accurate three-dimensional numerical analysis model was established, and the results were in good agreement with the experimental values, with the overall error of the failure load being less than 6%. Furthermore, a numerical model for a 20-ply high-thickness spar cap laminate was established to predict the effect of delamination on tensile strength. The results showed that, for the same depth of initial delamination, the difference in delamination area had little influence on the tensile strength. The dangerous locations of delamination were at the shallow surface and at the ratio of 0.3–0.4 in the thickness direction, and the maximum decrease in tensile strength was 14.86%; meanwhile, it was found that delamination on the middle surface had no significant effect on tensile strength.

A three-dimensional numerical pressure transient analysis model for fractured horizontal wells in shale gas reservoirs

Shale gas development has greatly contributed to the world's energy supply. Pressure transient analysis (PTA) has extremely helped the development of shale gas. In this paper, a three-dimensional numerical model for transient pressure analysis of multi-stage fractured horizontal wells (MFHWs) in shale gas reservoirs was proposed, which was based on the embedded discrete fracture model (EDFM). The adsorption effect of shale gas, stress sensitivity of shale reservoir, and high-velocity non-Darcy flow in fractures were considered in this model, and the model was solved by Matlab Reservoir Simulation Tool (MRST). The discrete process of governing equations is described in detail, the typical MFHW pressure transient response curve of a shale gas reservoir was obtained, different flow regimes were divided, and three-dimensional pressure distribution profile of different flow stages were drawn to clearly understand the flow states of shale gas in the reservoir. The effects of different flow mechanisms and fracture properties on the log–log curves of the MFHW pressure transient response were analyzed in detail. The numerical PTA model proposed in this paper not only considers a variety of complex flow mechanisms of shale gas, but also accurately describes the characteristics of complex fracture network of shale reservoirs in three-dimensional conditions through EDFM. In addition, the problems of the incomplete description of shale gas flow stages by conventional analytical methods and semi-analytical methods were avoided through the numerical solution. The pressure response behavior of fluid in shale gas reservoir can be better explained by using this model, which helps to reduce the uncertainty of shale reservoir development.

Investigating the Biomechanics of the Human Mandible Through Three-Dimensional Modeling and Finite Element Analysis

Investigating the Biomechanics of the Human Mandible Through Three-Dimensional Modeling and Finite Element Analysis

WFS1 autosomal dominant variants linked with hearing loss: update on structural analysis and cochlear implant outcome

BackgroundWolfram syndrome type 1 gene (WFS1), which encodes a transmembrane structural protein (wolframin), is essential for several biological processes, including proper inner ear function. Unlike the recessively inherited Wolfram syndrome, WFS1 heterozygous variants cause DFNA6/14/38 and wolfram-like syndrome, characterized by autosomal dominant nonsyndromic hearing loss, optic atrophy, and diabetes mellitus. Here, we identified two WFS1 heterozygous variants in three DFNA6/14/38 families using exome sequencing. We reveal the pathogenicity of the WFS1 variants based on three-dimensional (3D) modeling and structural analysis. Furthermore, we present cochlear implantation (CI) outcomes in WFS1-associated DFNA6/14/38 and suggest a genotype-phenotype correlation based on our results and a systematic review.MethodsWe performed molecular genetic test and evaluated clinical phenotypes of three WFS1-associated DFNA6/14/38 families. A putative WFS1–NCS1 interaction model was generated, and the impacts of WFS1 variants on stability were predicted by comparing intramolecular interactions. A total of 62 WFS1 variants associated with DFNA6/14/38 were included in a systematic review.ResultsOne variant is a known mutational hotspot variant in the endoplasmic reticulum (ER)-luminal domain WFS1(NM_006005.3) (c.2051 C > T:p.Ala684Val), and the other is a novel frameshift variant in transmembrane domain 6 (c.1544_1545insA:p.Phe515LeufsTer28). The two variants were pathogenic, based on the ACMG/AMP guidelines. Three-dimensional modeling and structural analysis show that non-polar, hydrophobic substitution of Ala684 (p.Ala684Val) destabilizes the alpha helix and contributes to the loss of WFS1-NCS1 interaction. Also, the p.Phe515LeufsTer28 variant truncates transmembrane domain 7–9 and the ER-luminal domain, possibly impairing membrane localization and C-terminal signal transduction. The systematic review demonstrates favorable outcomes of CI. Remarkably, p.Ala684Val in WFS1 is associated with early-onset severe-to-profound deafness, revealing a strong candidate variant for CI.ConclusionsWe expanded the genotypic spectrum of WFS1 heterozygous variants underlying DFNA6/14/38 and revealed the pathogenicity of mutant WFS1, providing a theoretical basis for WFS1-NCS1 interactions. We presented a range of phenotypic traits for WFS1 heterozygous variants and demonstrated favorable functional CI outcomes, proposing p.Ala684Val a strong potential marker for CI candidates.

Stochastic analysis of excavation-induced wall deflection and box culvert settlement considering spatial variability of soil stiffness

In this study, a three-dimensional (3D) finite element modelling (FEM) analysis is carried out to investigate the effects of soil spatial variability on the response of retaining walls and an adjacent box culvert due to a braced excavation. The spatial variability of soil stiffness is modelled using a variogram and calibrated by high-quality experimental data. Multiple random field samples (RFSs) of soil stiffness are generated using geostatistical analysis and mapped onto a finite element mesh for stochastic analysis of excavation-induced structural responses by Monte Carlo simulation. It is found that the spatial variability of soil stiffness can be described by an exponential variogram, and the associated vertical correlation length is varied from 1.3 m to 1.6 m. It also reveals that the spatial variability of soil stiffness has a significant effect on the variations of retaining wall deflections and box culvert settlements. The ignorance of spatial variability in 3D FEM can result in an underestimation of lateral wall deflections and culvert settlements. Thus, the stochastic structural responses obtained from the 3D analysis could serve as an effective aid for probabilistic design and analysis of excavations.

Lateral Circulation in an Elongated Curved Tidal Channel

Abstract The dynamic theory of curvature-induced lateral circulation has been developed for open channel flows but not for oscillatory tides. A linear three-dimensional analytical model was developed to investigate the lateral circulation in an elongated tidal channel with mildly curved bends of which the radius of curvature is larger than the width. The curvature-induced lateral circulation has two components with the same amplitude, namely, a periodic component having an overtide frequency and a steady component. The combination of the two components allows the strength of the lateral circulation to vary periodically and the rotation direction to be unchanged during a tidal period. Friction modifies the strength and structure of the lateral circulation. The phase between the lateral flow and streamwise tidal flow decreases with increasing friction, indicating that the two flows are not necessarily in phase unless friction is strong. The lateral circulations driven by the Coriolis and curvature centrifugal forces augment each other during one phase and compete in the opposite phase, and the relative importance of the two circulations is determined by the Rossby number and friction. The adaptation time is the same for spinup and spindown of the curvature-induced lateral circulation and is determined by water depth and vertical eddy viscosity. The estimation of the adaptation time depends on the leading modes because the transition solution of the curvature-induced lateral circulation comprises a series of cosine modes. These results provide a theoretical basis for interpreting curvature-induced lateral circulation in tidal channels and coastal headlands. Significance Statement The dynamic theory of curvature-induced lateral circulation in a tidal flow remains unexplored. The purpose of this study is to understand the essentials of curvature-induced lateral circulation in an elongated tidal channel using a three-dimensional analytical model. The results showed that the curvature-induced lateral circulation has two components with the same amplitude: a periodic component having an overtide frequency and a steady component. This is significantly different from the curvature-induced lateral circulation associated with open channel flows, which is steady and in phase with the streamwise flow. Future work may show the role of curvature-induced lateral circulation in streamwise dynamics and mass transport.

Digital evaluation of the effect of nanosilica-lithium spray coating on the internal and marginal fit of high translucent zirconia crowns

ObjectivesTo evaluate the effect of a nanosilica–lithium spray coating on the internal and marginal fit of high translucent zirconia crowns using a digital evaluation method. MethodsA three-dimensional analysis model of a zirconia abutment was digitally scanned using a dental scanner, and 30 monolithic high translucent zirconia crowns were designed and fabricated. They were divided into groups (n = 10) according to the surface treatment method: (1) no treatment: as-sintered zirconia; (2) airborne-particle abrasion with 50 μm Al2O3 particles; and (3) nanosilica–lithium spray coating. Three-dimensional data for the abutment, crown, and crown seated on the abutment were obtained using a dental scanner. The three-dimensional seated fit between the crown and abutment was reconstructed using registration technology, and a three-dimensional (3D) deviation analysis was used to evaluate the effect of different modification methods on the internal and marginal fit of the crowns using root mean square (RMS) values. ResultsThe 3D deviation analysis of all groups conformed to a normal distribution (P > 0.05), and the variance was homogeneous (P > 0.05). The different surface treatments had no significant effect on the RMS values in the occlusal, axial, and marginal regions of the high translucent zirconia crowns (P > 0.05). ConclusionsNanosilica-lithium spray coating for the modification of as-sintered zirconia is clinically feasible and does not affect the internal or marginal fit of high translucent zirconia crowns. Clinical significanceNanosilica–lithium spray coating does not affect the adaptation of zirconia crowns and is a clinically feasible surface treatment method for zirconia. It is unnecessary to add the setting values of the internal and marginal fit when fabricating nanosilica–lithium-sprayed zirconia crowns.

Performance Analysis of rotating pole shoe superconducting machine with dual coils

With the improvement of high temperature superconducting (HTS) materials, HTS machines have shown better competitive advantages in wind power generation and other fields. However, the conventional structure of superconducting machines has led to low reliability of the machines due to the complex structures such as brush and rotating dewar. Based on the analysis of the properties of second-generation high-temperature superconducting strips — YBCO strips, a kind of rotating pole shoe superconducting machine (RPHTSM) with dual HTS coils is proposed in this paper, which avoids the use of brush and rotating dewar used in the conventional HTS machine. The three-dimensional model for magnetic field analysis of the RPHTSM is established and the structure of the RPHTSM is optimized according to the calculation. A two-dimensional simplified model was developed and based on which the output performance of the machine was calculated. By comparing with the conventional HTS machine, it is concluded that the dual-coil RPHTSM has great advantage in reducing the consumption of superconducting strips and the inertia of the rotor.

Influence and Optimization of Geometric Parameters for Small-Radius Curved Tunnel Based on Response Surface Method

Compared with straight tunnels, small-radius curved tunnels are more common and have more complex influencing factors in urban underground traffic. Therefore, the seismic evaluation of small-radius curved tunnels is of great significance for the safe operation of underground structures. This paper used numerical analysis and the response surface method to analyze the influence of buried depth, curve angle and curve radius on the seismic response of a small-radius curved tunnel. For this purpose, seventeen three-dimensional (3D) numerical analysis models of the small-radius curved tunnel considering different geometric parameters are established. In addition, the optimal geometric parameters of displacement response and acceleration response of the small-radius curved tunnel are studied by using the method of multi-objective optimization design. The results show that buried depth has a pronounced influence upon the displacement response of the small-radius curved tunnel, whilst the buried depth and curve radius are the key parameters affecting the acceleration response of the small-radius curved tunnel. The optimal parameter configuration of the small-radius curved tunnel is the maximum buried depth, the maximum curve angle and the maximum curve radius within the value domain.

A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media

Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity and continuity equation equivalent to the continuum model are formulated based on the principle of flow balance. Subsequently, the unified form for flow velocity and continuity equation is established based on the local coordinate system, and a finite line-element method is developed, in which three-dimensional steady free surface flow is reduced to one-dimensional form, and the numerical difficulty is greatly decreased. The proposed line-element model is validated by the good agreements of free surface locations with other methods through steady flow in a rectangular dam and a right trapezoidal dam, respectively. It is found that the proposed line-element model is not heavily dependent on the mesh size and penalty parameter. Steady free surface flow on the left bank abutment slope of the Kajiwa Dam in Southwestern China is further evaluated, and a parabolic variational inequality algorithm based on the continuum model is also employed for comparison. The consistent results indicate that the proposed line-element model can capture the steady free surface flow behavior as well as the continuum-based method. Moreover, the proposed line-element model can rapidly achieve accurate solutions whether for simple examples or for complicated engineering applications.