Geometric Boundary Research Articles

Susceptibility of hydraulic structures to internal erosion: modeling of suffusion process

Internal erosion is a primary cause of hydraulic structure failure, manifesting as two key phenomena: piping erosion and suffusion. These processes differ in their geometrical and hydraulic boundary conditions, resulting in varying levels of failure risk. Piping erosion is the more hazardous and rapid process, often leading to immediate failure if not promptly addressed. In contrast, suffusion gradually alters the permeability of the medium, potentially culminating in failure after a prolonged period of development. In this study, we propose a model for suffusion based on Darcy’s law, Papamichos' erosion law, and Einstein's viscosity evolution relation. The model describes the temporal evolution of the average porosity in the porous medium, the concentration of eroded particles in the fluid, and the mass of particles eroded, while highlighting the impact of hydraulic and mechanical parameters, such as the erosion coefficient and maximum porosity, on this evolution. The numerical solution is obtained using the finite difference method, with the sample discretized into elementary layers. For discretization, an explicit off-centered scheme was adopted. The simulation results reveal that suffusion is strongly influenced by soil hydraulic and mechanical parameters, particularly the erosion coefficient (λ) and final porosity (Ømax).

An automated system for 2D building detection from UAV-based geospatial datasets

The focus of this manuscript is on integrating optical images and laser point clouds carried on low-cost UAVs to create an automated system capable of generating urban city models. After pre-processing both datasets, we co-registered both datasets using the DLT transformation model. We estimated structure heights from the LiDAR dataset through a progressive morphological filter followed by removing bare ground. Unsupervised and supervised image classification techniques were applied to a six-band image created from the optical and LiDAR datasets. After finding building footprints, we traced their edges, outlined their borderlines, and identified their geometric boundaries through several image processing and rule-based feature identification algorithms. Comparison between manually digitized and automatically extracted buildings showed a detection rate of about 92.3 % with an average of 7.4 % falsely identified areas with the six-band image in contrast to classifying only the RGB image that detected about 63.2 % of the building pixels with 25.3 % pixels incorrectly identified. Moreover, our building detection rate with the 6-band image was superior to that attained by performing traditional image segmentation for only the LiDAR DEM. Shifts in the horizontal coordinates between corner points identified by a human operator and those detected by the proposed system were in the range of 10–15 cm. This is an improvement over traditional satellite and manned-aerial large mapping systems that have lower accuracies due to sensor limitations and platform altitude. These findings demonstrate the benefits of fusing multiple UAV remote sensing datasets over utilizing a single dataset for urban area mapping and 3D city modeling.

Metal-Organic Framework Sub-Nanochannels within the Confined Micropipettes: Precise Construction Makes It a Universal Aptamer-Based Sensing Platform.

It is crucial to precisely construct metal-organic framework (MOF) sub-nanochannels at the tip of micro/nanopipettes for fundamental research and sensing applications. The quality of the MOF modification plays a significant role in influencing subsequent research, particularly in sensing applications. In this work, we present a precise method of constructing MOF sub-nanochannels at the tip of glass micropipettes, which serve as a universal aptamer-based sensing platform for the selective detection of proteins. In situ scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS) mapping, and fluorescence microscopy results demonstrate that the synthesized MOF (UiO-66) nanocrystals fully block the orifice of glass micropipettes (UiO-66-GMs) without forming any nanometer-scale cracks and remain confined within the geometric boundaries of the orifice. The terminal phosphate-modified aptamer readily binds to the surface of UiO-66-GMs through metal (Zr)-phosphate coordination, ultimately forming the aptamer sensor (Apt-UiO-66-GMs). The selective quantification of proteins is achieved via a decrease in current resulting from protein binding to the aptamer. Our results indicate that the precisely constructed Apt-UiO-66-GMs sensor enables highly selective and sensitive detection of SARS-CoV-2 nucleocapsid protein and holds potential for real sample detection. Furthermore, given the sharp tip of the micropipets and the external sensing interface we have constructed, our aptamer-based sensing platform also opens avenues for single-cell analysis and in vivo sensing.

Modified Easley formula for elastic critical global shear buckling stress of corrugated steel webs considering real boundary conditions

The real juncture between corrugated steel webs (CSWs) and flanges follows a multi-segmented line, distinct from that of flat steel webs. Classic methods may yield significant deviations in predicting the elastic global shear buckling capacity of CSWs of various scales due to their failure to consider real boundary constraints. Therefore, a universally applicable formula for calculating the elastic critical global shear buckling stress of CSWs, which accounts for real boundary conditions, is proposed. This formula is pertinent to both large-scale engineering CSWs and small-scale testing CSWs. This study commenced with a comprehensive reassessment of the elastic global shear buckling calculation method. Subsequently, the influence of geometric parameter ratios on the elastic critical global buckling stress was examined. The primary parameter was identified and employed to improve the global buckling coefficient. The proposed calculation method was validated using different corrugation configurations, including 1000-type, 1200-type, 1600-type, 1800-type, and 2000-type CSWs, as well as other CSWs used in experimental settings. These results were compared with those obtained from other reference methods. Findings indicate that the accuracy of the classic theoretical method is affected by variations in both boundary conditions and geometric dimensions due to the constraint effect of real boundary conditions. Under the real boundary conditions, the elastic critical global shear buckling stress of CSWs with simply supported boundary conditions is close to that of CSWs with consolidated boundary conditions. The ratio of web height to corrugation depth primarily affects the elastic global shear buckling capacity, which decreases as the ratio increases. The Easley formula can be modified based on the web height to corrugation depth ratio. Comparisons of numerous numerical and theoretical results reveal that the proposed calculation method exhibits commendable computational precision. In comparison to alternative formulas, the proposed method demonstrates enhanced consistency for calculating CSWs with varying geometric dimensions and boundary conditions, thereby demonstrating its favorable applicability. These conclusions provide valuable reference for the shear design of CSWs.

Three-dimensional buckling analysis of stiffened plates with complex geometries using energy element method

A novel numerical method, energy element method (EEM), is proposed for the three-dimensional (3D) buckling analysis of stiffened plates with complex geometries. The problem is formulated in a cuboidal domain, and any complex geometric stiffened plate is modeled by assigning cutouts within the cuboidal domain. The stiffened plate is considered as an energy body and is discretized using Gauss points with variable stiffness properties to simulate its energy distribution. Incorporating the extended interval integration, Gauss quadrature, variable stiffness properties, and Chebyshev polynomials, the strain energy of stiffened plates with complex geometries can be numerically simulated by putting the stiffness and thickness of Gauss points in the cutouts to zero in the cuboidal domain. Using the principle of minimum potential energy and Ritz solution procedure, the deformation and buckling behaviors of stiffened plates with complex geometries can be captured. As a result of the new formulations in EEM, new standard energy functionals and solving procedures have been developed. In addition, Gauss points are generated within the energy elements accounting for the geometric boundaries of the stiffened plate, which are characterized by level set functions. EEM is employed to investigate complex-shaped stiffened plates with straight or curvilinear stiffeners, and the results are compared to those obtained using FEM or mesh-free method. The precision, generalization, and stability of EEM are demonstrated.

Exploring FEA Techniques for Bending Rectangular Glass Plates into Parabolic Shapes

Abstract: A structural Finite Element Analysis (FEA) was conducted, incorporating both linear and nonlinear analysis. The investigation considered geometric nonlinearity, material nonlinearity, and boundary nonlinearity, also known as contact analysis. All boundary conditions, loadings, and material properties used in the analysis were based on real-world conditions. Experimental validations were performed to confirm the accuracy of the FEA results, providing strong confidence in the investigation's findings.

Knowledge-based model generation for aircraft cabin noise prediction from pre-design data

The climate targets set out in the “European Green Deal” call for the consideration and implementation of climate-friendly propulsion concepts and sustainable fuels in future aircraft configurations. This puts the use of very efficient propeller engines into the focus of aircraft design. However, these pose major challenges, especially to cabin acoustics, due to high, tonal sound pressure levels on the fuselage. The design of noise control measures requires the competence to predict the resulting interior noise as early as possible in the design process of the vehicle. This requires a high level of geometric and structural detail regarding the fuselage structure and cabin components. With increasing frequency range, the necessary structural details also increase, which have to be resolved in the simulation models due to the associated decreasing structural wavelength. Especially in the context of aircraft pre-design, there is usually not enough information available for a detailed vibro-acoustic modeling of the fuselage and cabin components, which allows a meaningful prediction of the vibrations and thus the cabin noise. Therefore, the knowledge-based tool Fuselage Geometry Assembler (FUGA) is developed for the targeted enrichment of preliminary design data with knowledge for detailed numerical analyses. This paper describes the knowledge-based geometry and model generation in FUGA, which can consider the necessary (increasing) level of detail for the vibro-acoustic prediction already in the preliminary design. For this purpose, aircraft data sets in the preliminary design data format Common Parametric Aircraft Configuration Schema (CPACS) form the modeling basis. Originating from the aircraft preliminary design, these initially describe the outer shell of the vehicle and are extended by detailed structural information that defines the geometric boundary conditions for component placement in cabin design. For the cabin components, the open-source geometry kernel Open Cascade Technology (OCCT) is used to provide geometries at the level of detail required for subsequent analyses. The geometry models are then discretized in open source (e.g. Gmsh) or commercial meshers and further used for numerical analysis. Finally, the prediction of cabin noise is demonstrated as a Proof of Concept using the example of a short-haul propeller-driven aircraft and the feasibility of the proposed method is indicated by investigating the sensitivity of resulting simulation models to the fuselage skin thickness.

Development of a novel circular saw blade substrate with high stiffness for mitigating vibration noise and improving sawing performance

The circular saw blade substrates featuring a large diameter-thickness ratio and multiple saw teeth are increasingly required to accomplish the first or second machining tasks with high efficiency in sawing operations. However, the weak bending stiffness of this substrate can easily cause intense vibrations and harsh noises, while its special structure characteristics pose further challenges to vibration mitigation. This research develops a novel circular saw blade substrate with high bending stiffness to improve dynamic stability. Taking the geometric features and boundary conditions of the substrate into account, a transverse vibration differential equation for high-speed sawing operation is established to investigate the relationship between the mode shapes of the substrate and the stability performance of the sawing system. Theoretical analysis shows that the laminated structure can enhance the bending stiffness. Using this finding, the novel substrate is designed equipped with an m-shaped damping cavity and a laminated core structure, and its dynamic performance is quantified by the complex modulus law and thin-plate vibration theory. Then, the optimized design of the relevant materials and geometrical dimensions of the novel substrate is executed by the pseudo-density method. Finally, the novel substrate is fabricated and then certified by sawtooth point dynamics tests and sawing experiments. The experimental results show that the sawing quality of the novel substrate is improved by more than 50.2 %, and the sawing vibration and weighted sound pressure level are reduced by about 35 % and 12 dB(A), respectively, compared with the conventional one.

Quantum computing intelligence algorithm for structural topology optimization

Structural topology optimization methods that are driven by the geometric features of components, such as the Moving Morphable Component (MMC), are widely explored due to their convenient interaction with design software. However, these methods exhibit significant sensitivity to the initial positioning of components, limiting their suitability for applications involving complex geometric boundaries. This study addresses these challenges by introducing a novel dual-layer optimization framework that employs a quantum computing-based intelligent optimization algorithm, Quantum-behaved Particle Swarm Optimization (QPSO). The potential drawbacks of the MMC method in engineering applications, particularly its sensitivity to initial conditions, are critically examined, leading to the proposal of a global-gradient hybrid framework for geometry feature-driven topology optimization. This proposed method demonstrates superior capability in optimizing material arrangements compared to the original MMC framework and enhances engineering applicability, making it more suitable for real-world applications. Through three representative examples, the limitations of the original MMC method are illustrated, and the advantages of the proposed dual-layer framework are highlighted. The results indicate that this method not only overcomes sensitivity issues but also stably identifies superior configurations, particularly for structures with complex geometric boundaries, providing models that facilitate interaction with CAD systems. This method offers a robust and precise approach for optimizing designs in various engineering fields.

Enhanced damage segmentation in RC components using pyramid Haar wavelet downsampling and attention U-net

Damage identification in post-earthquake reinforced concrete (RC) structures based on semantic segmentation has been recognized as a promising approach for rapid and non-contact damage localization and quantification. In damage segmentation tasks, damage regions are often set against complex backgrounds, featuring irregular geometric boundaries and intricate textures, posing significant challenges to model segmentation performance. Additionally, the absence of public datasets exacerbates these challenges, hindering advancements in this field. In this paper, a pyramid Haar wavelet downsampling attention UNet (PHA-UNet) semantic segmentation network is proposed, and a database containing 1400 images of damaged RC components (PEDRC-Dataset) with pixel-level annotations is established. In the proposed PHA-UNet, attention mechanisms, multiscale feature fusion, Haar wavelet downsampling, and transfer learning are introduced to address above challenges. Finally, the proposed PHA-UNet is compared with four existing image segmentation architectures on both the Cityspace and the PEDRC-Dataset.

Robust optimization of geometrical properties of flow diverter stents for treating cerebral aneurysm: A proof-of-concept study

This study presents a novel approach to optimize the design of flow diverter (FD) stents for cerebral aneurysm (CA) treatment. By addressing sources of uncertainty in cardiovascular simulations, including geometrical and physical properties and boundary conditions, we aim to assess the applicability of robust optimization techniques to the FD design, establishing a foundation for acquiring robust FDs that are capable of operating consistently under various real-world scenarios. Blood flow in a simplified 2-dimensional CA and FD model was simulated through computational fluid dynamics (CFD). A design space exploration method, incorporating Latin hypercube sampling and Kriging surrogate models, was employed to obtain the optimal solution. The objective was to maximize the reduction in velocity and vorticity within the CA sac. This study used non-intrusive polynomial chaos expansion (PCE) to quantify and propagate the input uncertainties through the computational model and compute the statistical moments of velocity and vorticity reductions. To assess the effect of uncertain sources on objective functions, a sensitivity analysis method based on Sobol indices was applied. Robust optimization involved simultaneously optimizing the mean and standard deviation of velocity reduction. Additionally, we accounted for patients’ specific conditions and repeated the robust optimization. The results indicate that blood Hematocrit and inlet velocity are the most impactful uncertain sources in FD optimization. Moreover, the obtained Pareto front shows that in robust designs, FD struts are concentrated in the distal region of the CA neck, while optimal designs have more struts in the proximal region. This study proposes an FD that compromises robustness and optimality with a velocity reduction of 72.31 % and a standard deviation of 0.00343.

Energy Element Method for Three-Dimensional Vibration Analysis of Stiffened Plates with Complex Geometries

A novel numerical method, the energy element method, is proposed for the three-dimensional vibration analysis of stiffened plates with complex geometries. The problem is modeled in a cuboidal domain, and a cuboidal energy element is developed for the simulation of the structural components. To simulate the energy distribution of the structure, stiffened plates are treated as discrete energy systems, where variable stiffness is used to characterize their energy distribution in a cuboidal domain and a global admissible function is used to approximate their vibrational behavior. With extended interval integral, Gauss quadrature, variable stiffness, and Legendre polynomials used for numerical integration in the cuboidal domain, the cuboidal energy element can offer sufficient precision with sufficient Gauss points for simulating the strain energy of stiffened plates with complex geometries. The Gauss–Legendre quadrature will provide accurate integration results if the integral domain is cuboidal. Otherwise, small cuboidal energy elements are generated with denser Gauss points to capture the geometric boundaries. As the numerical model is constructed on a standard geometric domain, all energy functionals and computational procedures are standard. Three-dimensional vibration problems are investigated for variously shaped stiffened plates with straight or curvilinear stiffeners. The present results are compared with analytical, numerical, and experimental results published in the literature.

Manually directional splitting of in-situ intact igneous rocks into large sheets

This paper presents a directional large-area rock fracturing method. The method had distinctive features compared with other common fracturing methods. The area of the fracturing surface could reach 10–500 m2. The fractured rock was sheet-like in shape, with a thickness of 6–8 cm. The main fracturing tools and procedures used were described in the paper. This paper analysed the reason for controllable and directional (also mode-I) rupturing in rock from the view of fracture mechanics. Counter-intuitively, the fracturing surface of the rock sheet had an angle (approximately 25°) to the loading direction (i.e., the orientation of the maximum principal compressive stress). The rupture behavior was controlled by the relationship between the load and the geometric boundary of the rock. It is found that the fracturing surface can suddenly and rapidly propagate after a certain strike by calculating the energies of the rock sheet. The striking energy could be converted into elastic strain energy, which accumulates in a very-slightly bent rock sheet step by step until exceeds the bearing limit of rock sheet. Most of the stored elastic strain energy was subsequently released in the form of splitting energy, leading to rock fracturing. This study provides insights into the occurrence of tectonic earthquakes.

Dynamic Simulation and Collision Detection for Flexible Mechanical Systems with Contact Using the Floating Frame of Reference Formulation

Abstract Contact simulation is essential in modelling mechanical systems. The contact models require accurate geometric information, which is determined through collision detection methods. When the mechanical system includes flexible bodies such as structural components, the dynamic formulation and collision detection can be more challenging, as the geometric boundaries of such components keep changing during the simulation. The floating frame of reference (FFR) formulation is suitable for flexible systems with small deformation. In this work, a stable and efficient dynamic simulation method is introduced for flexible systems with contact based on the FFR formulation. In addition, a curve-based collision detection method is proposed, which is more consistent with the dynamic formulation and more efficient than common existing collision detection methods. Case studies of flexible beams and multibody systems are employed to demonstrate the performance of the proposed dynamic simulation and collision detection methods.

Topology Optimization with Explicit Components Considering Stress Constraints

Topology optimization focuses on the conceptual design of structures, characterized by a large optimization space and a significant impact on structural performance, and has been widely applied in industrial fields such as aviation and aerospace. However, most topology optimization methods prioritize structural stiffness and often overlook stress levels, which are critical factors in engineering design. In recent years, explicit topology optimization methods have been extensively developed due to their ability to produce clear boundaries and their compatibility with CAD/CAE systems. Nevertheless, research on incorporating stress constraints within the explicit topology optimization framework remains scarce. This paper is dedicated to investigating stress constraints within the explicit topology optimization framework. Due to the clear boundaries and absence of intermediate density elements in the explicit topology optimization framework, this approach avoids the challenge of stress calculation for intermediate density elements encountered in the traditional density method. This provides a natural advantage in solving topology optimization problems considering stress constraints, resulting in more accurate stress calculations. Compared with existing approaches, this paper proposes a novel component topology description function that enhances the deformability of components, improving the representation of geometric boundaries. The lower-bound Kreisselmeier–Steinhauser aggregation function is employed to manage the stress constraint, reducing the solution scale and computational burden. The effectiveness of the proposed method is demonstrated through two classic examples of topology optimization.

An efficient method to generate near-ideal hollow beams of different shapes for box potential of quantum gases.

Ultracold quantum gases are usually prepared in conservative traps for quantum simulation experiments. The atomic density inhomogeneity, together with the consequent position-dependent energy and time scales of cold atoms in traditional harmonic traps, makes it difficult to manipulate and detect the sample at a higher level. These problems are partially solved by optical box traps made of blue-detuned hollow beams. However, generating a high-quality hollow beam with high light efficiency for the box trap is challenging. Here, we present a scheme that combines the fixed optics, including axicons and prisms, to pre-shape a Gaussian beam into a hollow beam with a digital micromirror device (DMD) to improve the quality of the hollow beam further, providing a nearly ideal optical potential of various shapes for preparing highly homogeneous cold atoms. The highest power-law exponent of potential walls can reach a value over 100, and the light efficiency from a Gaussian to a hollow beam is also improved compared to direct optical shaping by a mask or a DMD. Combined with a one-dimensional optical lattice, a nearly ideal two-dimensional uniform quantum gas with different geometrical boundaries can be prepared for exploring quantum many-body physics to an unprecedented level.

On the Geometric Boundary of Some Convex Sets

On the Geometric Boundary of Some Convex Sets

Optimized Design of Low Emission Zones in SUMO

Focusing on the critical challenge of air pollution in urban areas, primarily caused by vehicular emissions, this study proposes an innovative process for Low Emission Zones (LEZ) design within the Simulation of Urban Mobility (SUMO) framework. Our primary focus is on enhancing urban mobility through the strategic design of LEZs, while simultaneously maintaining or even improving emission levels. The novel aspect of the approach lies in the use of LEZs with minimal geometric boundaries, strategically designed to balance the reduction of CO2 emissions and the necessity of fluid urban transportation. LEZs are calculated using genetic algorithms that optimize a cost function balancing emissions and travel time while applying topological and specific constraints. Several experiments are simulated with SUMO to compare the efficiency of urban mobility under various LEZ configurations and different traffic demands. The results show the improvement of the approach in comparison with traditional LEZ design methodologies. The proposal not only preserves or even reduces the emission levels, but also actively improves urban mobility and traffic flow. This empirical evidence strongly supports the feasibility and effectiveness of the proposed solution in different urban scenarios. The design of the heuristic enables the possibility to create dynamic LEZs that may be changed depending on demand, weather, or any other varying conditions that affect traffic and emissions, preserving the mobility concerns of the users.

Three-dimensional elastoplastic post-buckling analysis of functionally graded plates using a novel meshfree Tchebychev-radial point interpolation approach

This paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs).

STATIC BENDING RESPONSE OF COMPOSITE PLATES RESTING ON VARIABLE ELASTIC FOUNDATIONS

This article introduces a finite element approach for examining the static bending behavior of composite plates. The method considers the variable mechanical characteristics of plates and utilizes an elastic foundation with varying stiffness values. The plate's calculation expressions and equilibrium equations are derived using the new style shear deformation theory. The article uses a mesh composed of four-node rectangular components to solve the equilibrium equation. Each node in the mesh has six degrees of freedom. The solution's dependability and convergence are confirmed by comparing it with previously published findings. Based on this premise, the study presents numerical findings that examine how various geometric factors, materials, boundary conditions, and elastic foundations affect the static bending behavior of composite panels. This research is a great resource for engineers, providing excellent guidance for the design, production, and utilization of these structures in real-world applications.