Geometric Principles Research Articles

Adaptive Terrain Modeling for Side-Slope Surfaces

Three-dimensional site modeling is an important aspect of Building Information Modeling (BIM), especially in mountainous areas. Accurate site modeling is essential for efficient construction planning and resource allocation. A key issue in site modeling is how to accurately calculate the shape of side-slopes. It involves three sub-problems: geometric representation of side-slopes, determination of fill/cut types, and intersection of side-slopes surface with the terrain surface. To address this, a two-stage method for constructing side-slope models adaptive to terrain is proposed. In the first stage, a marching algorithm along polylines is used to calculate the intersection points of the site boundary polylines with the terrain surface. These intersection points are used to segment the boundary polylines. A rule-based approach is then applied to automatically determine the fill/cut type for each segment. Subsequently, the equations of the side-slopes passing through each segment are derived using geometric principles. In the second stage, a marching algorithm along the plane is used to trace the intersection lines of side-slopes with the terrain. Finally, the side-slopes are rendered with precision by integrating the equations of each segment with the determined intersection lines. The effectiveness of the method is verified through illustrative examples. Algorithm efficiency analysis and 3D modeling illustrations have demonstrated that this method not only boasts accuracy and swift computation but also excels in the level of automation achieved in the modeling process.

Research on Positioning and Tracking Method of Intelligent Mine Car in Underground Mine Based on YOLOv5 Algorithm and Laser Sensor Fusion

Precise positioning has become a key technology in the intelligent development of underground mines. To improve the positioning accuracy of mining vehicles, this paper proposes an intelligent underground mining vehicle positioning and tracking method based on the fusion of the YOLOv5 and laser sensor technology. The system utilizes a camera and the YOLOv5 algorithm for real-time identification and precise tracking of mining vehicles, while the laser sensor is used to accurately measure the straight-line distance between the vehicle and the positioning device. By combining the strengths of both vision and laser sensors, the system can efficiently identify mining vehicles in complex environments and accurately calculate their position using geometric principles based on laser distance measurements. Experimental results show that the YOLOv5 algorithm can efficiently identify and track mining vehicles in real time. When integrated with the laser sensor’s distance measurement, the system achieves high-precision positioning, with horizontal and vertical positioning errors of 1.66 cm and 1.96 cm, respectively, achieving centimeter-level accuracy overall. This system significantly improves the accuracy and real-time performance of mining vehicle positioning, effectively reducing operational errors and safety risks, providing essential technical support for the intelligent development of underground mining transportation systems.

Limiting and optimal Strouhal numbers or tip speed ratios for cruising propulsion by fins, flukes, wings and propellers.

Swimming and flying animals produce thrust with oscillating fins, flukes or wings. The relationship between frequency f, amplitude A and forward velocity U can be described with a Strouhal number St, where St = 2fA/U, where animals are observed to cruise with [Formula: see text]-0.4. Under these conditions, thrust is produced economically and a reverse von Kármán wake is observed. However, propeller-driven craft produce thrust with steadily revolving blades and a helical wake. Here, the simplified aerodynamic geometry of lift-based thrust production is described, applicable to both oscillating and revolving foils. The same geometric principles apply in both cases: if the foil moves too slowly, it cannot produce thrust; if it moves too fast, it produces thrust with excessive power demand. Effective, economic thrust production by animals is not the result of oscillating foils or cyclic vortex shedding; rather, the selection of amplitude and frequency, and wake vortex structure, are corollaries of driving an efficient foil velocity with finite amplitudes. Observed Strouhal numbers for cruising animals appear too low for optimal mechanical efficiency; however, the deviation from optimal efficiency may be small, and there are physical and physiological advantages to relatively low amplitudes and frequencies for swimming and flapping flight.

Photoreconfigurable Metasurface for Independent Full-Space Control of Terahertz Waves.

We present a novel photoreconfigurable metasurface designed for independent and efficient control of electromagnetic waves with identical incident polarization and frequency across the entire spatial domain. The proposed metasurface features a three-layer architecture: a top layer incorporating a gold circular split ring resonator (CSRR) filled with perovskite material and dual C-shaped perovskite resonators; a middle layer of polyimide dielectric; and a bottom layer comprising a perovskite substrate with an oppositely oriented circular split ring resonator filled with gold. By modulating the intensity of a laser beam, we achieve autonomous manipulation of incident circularly polarized terahertz waves in both transmission and reflection modes. Simulation results demonstrate that the metasurface achieves a cross-polarized transmission coefficient of 0.82 without laser illumination and a co-polarization reflection coefficient of 0.8 under laser illumination. Leveraging the geometric phase principle, adjustments to the rotational orientation of the reverse split ring and dual C-shaped perovskite structures enable independent control of transmission and reflection phases. Furthermore, the proposed metasurface induces a +1 order orbital angular momentum in transmission and +2 order in reflection, facilitating beam deflection through metasurface convolution principles. Imaging using metasurface digital imaging technology showcases patterns "NUIST" in reflection and "LOONG" in transmission, illustrating the metasurface design principles via the proposed metasurface. The proposed metasurface's capability for full-space control and reconfigurability presents promising applications in advanced imaging systems, dynamic beam steering, and tunable terahertz devices, highlighting its potential for future technological advancements.

Switchable Pancharatnam-Berry Phases in Heterogeneously Integrated THz Metasurfaces.

The Pancharatnam-Berry (PB) phase has revolutionized the design of metasurfaces, offering a straightforward and robust method for controlling wavefronts of electromagnetic waves. However, traditional metasurfaces have fixed PB phases determined by the orientation of their individual elements. In this study, an innovative structural design and integration scheme is proposed that utilizes vanadium dioxide, a phase-change material, to achieve thermally controlled dynamic PB phase control within the metasurface. By leveraging the material's properties, this can dynamically alter the optical orientation of individual elements of the metasurface and achieve temperature-dependent local phase modulation based on the geometric phase principle. This approach, combined with advanced fabrication processing technology, paves the way for next-generation dynamic devices with customizable functions.

Improved Generalizability in Medical Computer Vision: Hyperbolic Deep Learning in Multi-Modality Neuroimaging.

Deep learning has shown significant value in automating radiological diagnostics but can be limited by a lack of generalizability to external datasets. Leveraging the geometric principles of non-Euclidean space, certain geometric deep learning approaches may offer an alternative means of improving model generalizability. This study investigates the potential advantages of hyperbolic convolutional neural networks (HCNNs) over traditional convolutional neural networks (CNNs) in neuroimaging tasks. We conducted a comparative analysis of HCNNs and CNNs across various medical imaging modalities and diseases, with a focus on a compiled multi-modality neuroimaging dataset. The models were assessed for their performance parity, robustness to adversarial attacks, semantic organization of embedding spaces, and generalizability. Zero-shot evaluations were also performed with ischemic stroke non-contrast CT images. HCNNs matched CNNs' performance in less complex settings and demonstrated superior semantic organization and robustness to adversarial attacks. While HCNNs equaled CNNs in out-of-sample datasets identifying Alzheimer's disease, in zero-shot evaluations, HCNNs outperformed CNNs and radiologists. HCNNs deliver enhanced robustness and organization in neuroimaging data. This likely underlies why, while HCNNs perform similarly to CNNs with respect to in-sample tasks, they confer improved generalizability. Nevertheless, HCNNs encounter efficiency and performance challenges with larger, complex datasets. These limitations underline the need for further optimization of HCNN architectures. HCNNs present promising improvements in generalizability and resilience for medical imaging applications, particularly in neuroimaging. Despite facing challenges with larger datasets, HCNNs enhance performance under adversarial conditions and offer better semantic organization, suggesting valuable potential in generalizable deep learning models in medical imaging and neuroimaging diagnostics.

The Application and Effects of Augmented Reality in Geometry Learning

With the development of new technology, augmented reality (AR) technology is revolutionizing the educational landscape, particularly in geometry. This innovative approach deepens their comprehension of geometric principles and stimulates their motivation to learn. This paper aims to provide a comprehensive introduction to ARs application in the educational field, especially the topic of geometry, and evaluate its effectiveness in improving users in two aspects: motivation and academic results. The study applies the Attention, Relevance, Confidence, and Satisfaction (ARCS) Model to assess the impact of AR in education compared to traditional teaching. It finds that AR boosts student motivation, especially for those with lower academic performance. While AR enhances learning experiences, its effect on improving grades is not immediate. The method that is mainly utilized in this study is reviewing the literature, summarizing, and analyzing critical information from them. And it turns out that short-term grade improvements are not significantly observable, AR technology offers long-term benefits by enhancing engagement and conceptual comprehension through interactive and spatial visualizations.

Fractal Conditional Correlation Dimension Infers Complex Causal Networks.

Determining causal inference has become popular in physical and engineering applications. While the problem has immense challenges, it provides a way to model the complex networks by observing the time series. In this paper, we present the optimal conditional correlation dimensional geometric information flow principle (oGeoC) that can reveal direct and indirect causal relations in a network through geometric interpretations. We introduce two algorithms that utilize the oGeoC principle to discover the direct links and then remove indirect links. The algorithms are evaluated using coupled logistic networks. The results indicate that when the number of observations is sufficient, the proposed algorithms are highly accurate in identifying direct causal links and have a low false positive rate.

Developing engaging STEAM-geometry activities: Fostering mathematical creativity through the engineering design process using Indonesian cuisine context

Enhancing mathematical creativity requires more learning activities that foster creative thinking. However, teachers need more resources and activities to nurture students' creativity in mathematics effectively. Therefore, this study aimed to design STEAM-based geometry activities using the Engineering Design Process (EDP) to explore how such projects can enhance students' mathematical creativity. In this study, creativity focuses on how students use geometric principles to design Wingko Babat as an Indonesian cuisine, making culturally meaningful connections and solving design challenges. The study involved research and development using the analysis, design, development, implementation, and evaluation (ADDIE) model, continuing with a descriptive qualitative approach. The activities designed for the STEAM-Geometry projects allow students to think creatively and elaborate on the engineering design process. Through expert reviews that involved multiple educators, the design activities on the STEAM-Geometry project are reliable and valid. The findings show that the EDP on Geometry project enables students to think creatively. The findings imply that teaching geometry can develop the students' mathematical creativity through the engineering design process in STEAM activities. Furthermore, it indicates that the design activities encompass more than just understanding geometry; they also nurture creativity by applying STEAM principles in the engineering design process. Integrating STEAM principles within culturally meaningful, geometry-based tasks enhances students' critical thinking, creativity, collaboration, and real-world problem-solving skills, preparing them to tackle complex challenges beyond the scope of mathematics.

A Real-Time Chemical Vapor Deposition Optical Monitoring System for Ge1-XSnx Growth Optimization

GeSn has attracted tremendous attention due to its tunable bandgap in recent decades. While the material has been produced through various methods, the Chemical Vapor Deposition (CVD) process has become one of the most essential for fabricating GeSn material since it was first demonstrated. However, the process is generally studied as a black box through input versus output. For example, one could study the change in temperature versus growth rate where changes in film thickness due to temperature change can be plotted only after the growth is finished. Process improvements from the study of these black box studies have yielded understandings in the growth kinematics and the development of growth recipes defining specific growth windows for different films that in many cases are very well understood. The black box treatment of CVD growth studies lacks near real-time feedback for the growth of the film leading to unsuccessful growths that in some cases slow research and in others lead to reduced yields of useful samples for device fabrication.Real-time monitoring of the process both in-situ and ex-situ is essential, as these could enhance understanding of the CVD process and growth dynamics. In this research, we have been developing a sophisticated optical imaging system to monitor the wafer surface morphology with desired magnification and specific areas of a sample during growth. By coupling an optical microscope system and a high-resolution portable imaging system via ports into the CVD reactor, the growth of a sample can be monitored in real time at both the micro and macro scale. As schematically shown in Figure 1, a microscope and an LED light source are mounted to the two 2¾” flanges with an angle of incidence symmetrical along the chamber's vertical center line, and the portable camera is nearly vertically mounted at one of the reactor's optical windows below the horizontal axis. The microscope and the portable camera are designated for distinct functions, a characteristic that is determined by their respective locations and magnification capabilities. By meticulously calculating and applying geometric and optical design principles, such as the imaging area, solid angles, and reflection, we can capture real-time images of the sample surface during its growth.Specifically, using this optical monitoring setup, we could observe the surface morphological change during a GeSn growth on Ge-Vs sample on a Si (100) substrate. This observation led to the early identification of defect formation and post-growth progression of defect formation during the cooling down process. Figure 2 is an example picture taken during the growth for an as-grown GeSn sample showing surface defects indicated by grey spots and edge and surface roughening by the orangish center region noted in the image. This capability would allow for the optimization of growth parameters throughout the entire process that result in larger areas of useful material or provide feedback that allows CVD operators to promptly respond and decide on the subsequent growth early to prevent lost time due to failed growths.Future work is to be accomplished by improvements in the optical system to not only allow for better image quality by using a different camera allowing better focusing, and higher frame rates as well as adjusting light source angle and/or incident camera angle. Acknowledgments The work is supported by the Air Force Office of Scientific Research (AFOSR) (Grant No.: FA9550-19-1-0341, FA9550-20-1-0168). Figure 1

Analysis of the Radial Force of a Piezoelectric Actuator with Interdigitated Spiral Electrodes.

The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the actuating force generated in the radial direction is relatively limited. When used as the actuation element of the manipulator, achieving regulation over a wide range of operating strokes becomes challenging. Therefore, altering the electrode structure is necessary to generate a greater radial force, thus enhancing the positioning and grasping capabilities of the operating arm. This paper investigates a piezoelectric actuator with interdigitated spiral electrodes, featuring a constant pitch between adjacent electrodes. The radial force was tested under mechanical clamping conditions, and the influence of the electrical signal was examined. The characteristics of the electrode structure were described, and the working principles of the piezoelectric actuators were analyzed. Theoretical equations were derived for the macroscopic characterization of the radial clamping force of the actuator, based on the piezoelectric constitutive equation, geometric principles, and Bond matrix transformation relationships. A finite element model was developed, reflecting the features of the electrode structure, and finite element simulations were employed to verify the theoretical equations for radial force. To prepare the samples, encircled interdigitated spiral electrode lines were printed on the PZT-52 piezoelectric ceramic disc using a screen printing method. The clamping force experimental platform was established, and experiments on the clamping radial force were conducted with electrical signals of varying waveforms, frequencies, and voltages. The experimental results show that the piezoelectric ceramic disc actuator with an interdigitated spiral electrode line structure, when excited by a stable sine wave operating at 200 V and 0.2 Hz, generated a peak force of 0.37 N. It was 1.76 times greater than that produced by a previously utilized piezoelectric disc with conventional electrode structures.

A novel method of acetabular component anteversion measurement on plain radiographs

BackgroundAcetabular component anteversion (ACA) markedly impacts the outcome of total hip arthroplasty (THA) and thus is routinely measured on radiographs postoperatively. However, clinical ACA measurement methods are either too complicated or subjective due to three drawbacks: complex calculations, measurement of obscured points, and complex geometric drawings. This study aimed to develop a precise and convenient novel method of measuring ACA on routine radiographs without the three drawbacks and to verify its accuracy and reliability by comparing it against existing methods.MethodsA novel geometric principle to measure ACA was developed. Accordingly, a protractor was designed to measure radiographic anteversion (RA) on anteroposterior (AP) hip radiographs. Three researchers measured RA twice, using the protractor, McLaren’s, and Pradhan’s method on 26 computer-simulated radiographs with pre-set RAs and 20 actual radiographs. Accuracy was assessed by errors on simulated radiographs, and reliability was assessed by results of measurements on simulated and actual radiographs.ResultsThe absolute error of the novel method (1.01° ± 1.06°) was lower than McLaren’s method (1.34° ± 1.16°) (p < 0.05) and not significantly different from Pradhan’s method (1.10° ± 1.02°) (p = 0.392). The protractor’s intra-rater and inter-rater reliability were good-to-excellent or excellent and higher or equivalent to the two other methods.ConclusionsThe novel method avoids the three major drawbacks of conventional methods. Its accuracy is significantly higher than McLaren’s method and comparable to Pradhan’s. The novel method has higher or non-inferior accuracy and reliability than McLaren’s and Pradhan’s methods.

Bond-centric modular design of protein assemblies.

We describe a modular bond-centric approach to protein nanomaterial design inspired by the rich diversity of chemical structures that can be generated from the small number of atomic valencies and bonding interactions. We design protein building blocks with regular coordination geometries and bonding interactions that enable the assembly of a wide variety of closed and opened nanomaterials using simple geometrical principles. Experimental characterization confirms successful formation of more than twenty multi-component polyhedral protein cages, 2D arrays, and 3D protein lattices, with a high (10-50 %) success rate and electron microscopy data closely matching the corresponding design models. Because of the modularity, individual building blocks can assemble with different partners to generate distinct regular assemblies, resulting in an economy of parts and enabling the construction of reconfigurable systems.

Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models

The development of reliable mathematical models and numerical discretization methods is important for the understanding of salt precipitation in porous media, which is relevant for environmental problems like soil salinization. Models on the pore scale are necessary to represent local heterogeneities in precipitation and to include the influence of solution-air-solid interfaces. A pore-network model for saturated flow, which includes the precipitation reaction of salt, is presented. It is implemented in the open-source simulator DuMuX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\ extrm{X}}$$\\end{document}. In this paper, we restrict ourselves to one-phase flow as a first step. Since the throat transmissibilities determine the flow behaviour in the pore network, different concepts for the decreasing throat transmissibility due to precipitation are investigated. We consider four concepts for the amount of precipitation in the throats. Three concepts use information from the adjacent pore bodies, and one employs a pore-throat model obtained by averaging the resolved pore-scale model in a thin-tube. They lead to different permeability developments, which are caused by the different distribution of the precipitate between the pore bodies and throats. We additionally apply two different concepts for the calculation of the transmissibility. One obtains the precipitate distribution from analytical assumptions, the other from a geometric minimization principle using a phase-field evolution equation. The two concepts do not show substantial differences for the permeability development as long as simple pore-throat geometries are used. Finally, advantages and disadvantages of the concepts are discussed in the context of the considered physical problem and a reasonable effort for the implementation and computational costs.

A Comparative Study of Geometric Principles in the Sulba Sutras and the Pythagorean Theorem: Historical Context and Mathematical Applications

This research delves into the geometric principles detailed in the ancient Sulba Sutras and their parallels with the Pythagorean Theorem, traditionally attributed to the Greek mathematician Pythagoras. While the Pythagorean theorem is widely regarded as a cornerstone of Greek geometry, recent studies suggest that its formulation appeared centuries earlier in Indian mathematics, as evidenced in Baudhāyana’s Sulba Sutra (circa 800 BCE). These texts offer extensive insights into the geometric constructions used in Vedic rituals, including the use of Pythagorean triples and transformations between geometric shapes. The Sulba Sutras present a rich mathematical framework, emphasizing practical applications in altar construction, land measurements, and urban planning. This study aims to bridge the research gap by comparing the geometric developments in the Sulba Sutras with Greek formulations, particularly focusing on their mathematical methods, cultural contexts, and historical significance. The findings underscore the advanced state of Indian mathematics and its profound influence on subsequent mathematical traditions, offering a nuanced understanding of the parallel evolution of geometric knowledge across cultures.

Study on stress singularities in cylindrical shells with an arbitrary oriented crack using digital gradient sensing technique

In this paper, the transmitted digital gradient sensing (DGS) technique is applied to analyze stress singularity at the tip of an arbitrary oriented crack in a cylindrical shell. A thoretical model of the opitcal path near the tip of the inclined crack in a cylindrical shell under mixed-mode fracture is proposed based on the geometric optical imaging principle. An optical governing equation of DGS technique is established to relate the mixed-mode stress intensity fractors (SIFs) at the crack tip to the shell geometry parameters and the inclined crack sizes, and the angular deflection contours are theoretically plotted using this govering equation. Uniaxial tensile tests are carried out on polymethyl methacrylate (PMMA) cylindrical shells containing an edge crack with different inclined angles, and the optimal calculation area for the exaction of SIFs is determined from linear elasitic fracture mechanics. The effects of shell radius, shell thick, crack length, and crack angle on the mixed-mode SIFs are studied, respectively. These results show that the DGS technique is effective and accurate to evalute the stress singulary around an arbitrary oriented cracks in cylindrical shells.

Penerapan Kearifan Lokal Samosir dalam Mengeksplorasi Bentuk-Bentuk Geometri

The purpose of this study is to investigate how the Batak people in Samosir use their local knowledge to understand geometric shapes. The literature review research method, which is a data collection strategy focused on the evaluation of relevant and current scientific literature related to the research problem, is used in this publication. The data sources in the study came from Google Scholar, Scopus, and SINTA. Data analysis was carried out qualitatively consisting of data reduction, data presentation, and conclusion drawing. The results of the data analysis show that the way local knowledge is applied to the study of geometric forms shows how Batak culture has used geometric principles in religious ceremonies as well as art and construction. In addition to having a practical and aesthetic purpose, these geometric shapes have a deep philosophical feel that enhances the cultural identity and bond of the community with nature and its ancestors. Through the local wisdom of the Batak people in Samosir, geometric ideas have been successfully identified and applied to various parts of their lives, including traditional house buildings, traditional artifacts, and ulos weaving crafts. Overall, this study shows how the concept of geometry is used organically by Batak local wisdom, which is essential for preserving community peace, fostering cultural identity, and fostering spiritual ties with nature and ancestors.

Analyzing trends and suggested instructional strategies for Geometry education: Insights from Uganda Certificate of Education-Mathematics Examinations, 2016-2022

Geometry education plays a pivotal role in fostering analytical, spatial, and problem-solving skills among students. Nonetheless, there is still a problem with how well geometry training in Ugandan schools accomplishes these objectives and this is evident in the Uganda Certificate of Education (UCE) examinations. To close this gap, a comprehensive examination of data taken from Uganda National Examinations Board (UNEB) reports covering the years 2016 to 2022 was carried out; with an emphasis on candidates’ performance, the study looks at common geometric ideas, pinpoints areas of weakness for candidates, and assesses response quality. This study's content analysis reveals notable variations in the quality of responses to various mathematics areas, with geometry consistently having the largest percentage of poor responses. Interestingly, in most areas, attempt levels positively correlate with response quality; but, in the case of geometry, this correlation reverses, suggesting that learners in this domain confront different problems. These problems include using geometric principles for problem-solving, combining algebraic and geometric concepts, and spatial visualization. The study advocates for using technology, active and problem-based learning; as these approaches provide opportunities for experiential learning, and conceptual knowledge reinforcement to learners. All this will support ongoing attempts to enhance mathematics education, particularly in the field of geometry, within the Ugandan context.

A novel approach to designing compact cyclones for efficient natural gas filtration

This paper presents an innovative method to design cyclone separators based on geometrical principles, and incorporates a coupling iterative algorithm to obtain crucial parameters. The proposed approach allows for simultaneous variation of multiple key parameters, including inlet velocity, inlet height, and pressure drop. Thus, effects of varying one parameter on the others are accounted for. The innovative methodology is utilized to design a novel, high-performance cyclone potentially applicable in natural gas filtration. The introduced cyclone has a uniquely large inlet length to diameter ratio and a small curved cone, making it compact and usable in clusters to handle large flow rates. The cyclone is experimentally tested to evaluate its filtration performance. The results indicate that six micron or larger particles are completely separated, and a cut point diameter of 1 μm is achieved. Finally, the introduced cyclone is numerically investigated to analyze the gas flow behavior and visualize particle trajectories.

Discrete differential geometry-based model for nonlinear analysis of axisymmetric shells

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff–Love hypothesis, and elastic force vector and associated Hessian matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.