Force Distribution Research Articles

Finite element analysis of occlusal stress in cervical dentin: effects of thickness and cross-section

Background & objectiveThe cervical region of dentin plays a crucial role in the distribution of masticatory forces, with vertical root fractures often initiating and spreading from this area. This study investigates the distribution of occlusal stresses in the cervical region of root dentin, considering varying thicknesses and cross-sections, using Finite Element Analysis.Materials & methodsSections from central and premolar teeth were imported into CAD to create 3D models. The tooth structure and surrounding tissues were modeled using mechanical properties such as Young’s modulus and Poisson’s ratio. Four cross-sectional shapes—circular, oval, sand clock, and kidney—were designed. A force of 50 Newtons, representing the occlusal force of the opposing tooth, was applied to the palatal surface of the models at a 60° angle for anterior teeth and a 45° angle for premolars. The stress distribution in the cervical dentin was then analyzed.ResultsVon Mises stress values indicated that stress points were highest in the kidney, sand clock, oval, and circular cross-sections, respectively. Increased thickness of the residual dentinal wall resulted in reduced maximum and minimum stress and a smaller area of stress regions. In all cross-sections, the minimum and maximum stress points were predominantly on the palatal and buccal sides of the cervical dentin, respectively.ConclusionThe study demonstrated that stress distribution in teeth varies with different root cross-sections, with higher stress observed in the sand clock and kidney cross-sections. Thinner dentin in the cervical region leads to greater stress concentration, especially in the buccal area of the tooth.

Study on vehicle impact force on bridge piers: Impact force simplification and distribution characteristics analysis

Study on vehicle impact force on bridge piers: Impact force simplification and distribution characteristics analysis

Numerical Investigation of Mechanical Response of Sand‐Rubber Mixture by Material Point Method

ABSTRACTSand‐rubber mixture (SRM), a composite material made of recycled rubber and sand, is gaining increasing attention in construction engineering due to its lightweight nature, cost‐effectiveness, ease of processing, and other advantages. However, the mechanical behavior of SRM remains a complex issue as the addition of rubber not only increases the types of contacts between grains, but also changes the contact topology with rubber undergoing significant deformation. This study presents a numerical investigation of the intricate mechanical behavior of SRM based on the material point method (MPM) tailored for modeling the assembly of deformable grains. The employed approach introduces multiple meshes for handling the kinetic and deformation of individual grains and a discrete element method (DEM)‐type contact algorithm to directly address the intricate interaction in SRM, being capable of accurately modeling the complex behavior of SRM. Furthermore, rubber membranes in the biaxial shear test are simulated with material points with sufficient deformation capacity to accurately simulate the actual loading boundary. We first validated the accuracy and effectiveness of the proposed method through a series of benchmarks. Subsequently, one‐dimensional compression and biaxial shear simulations were conducted on the SRM to investigate the influence of rubber content (RC) and confining pressures. Both macroscopic deformation and the microstructural characteristics are examined. The results indicate that increasing RC leads to a more uniform contact force distribution, and a more stable force chain network, while higher confining pressure enhances the particle connectivity within the SRM.

Impact of mandibular 4-implant overdenture base construction techniques on assessment of occlusion with digital occlusion analysis system (clinical crossover study)

BackgroundOcclusion plays a crucial role in the long-term success and prognosis of implant-supported overdentures. The method used to fabricate the overdenture base, whether conventional or CAD/CAM milled, could influence occlusal contact balance. However, definitive evidence on this matter remains lacking. Thus, this study aimed to compare two fabrication techniques, CAD/CAM milled and conventional, for four-implant-supported complete mandibular overdenture bases, with a specific focus on their impact on occlusal balance.MethodsEdentulous patients participated in this study received four-implant supported mandibular overdentures constructed using two different types of overdenture bases: CAD/CAM milled and conventional bases. A total of 21 patients, representing 42 overdentures, were enrolled in the study. Occlusal adjustments were made for each overdenture after picking up of attachments. The patients were classified randomly and equally into two groups: Group I: patients delivered maxillary complete dentures opposed to four implant-supported mandibular overdentures constructed with CAD/CAM milling followed by conventionally constructed dentures. Group II: patients delivered maxillary complete dentures opposed to four implant-supported mandibular overdentures constructed with conventional method followed by CAD/CAM milled dentures. According to the type of denture bases, dentures were classified into two equal groups: Group A: CAD/CAM constructed overdenture bases. Group B: conventionally constructed overdenture bases. For each overdenture group, occlusal analysis measurements were recorded at overdenture delivery (T0) and after three months of denture wearing (T3). Data was analyzed using the Statistical Package of Social Science (SPSS) program. Repeated measures ANOVA were used to test significant differences in occlusal force distribution between observation intervals, groups and locations followed by Bonferroni post hoc test for multiple comparisons. Independent samples t-test was used to compare occlusal force between groups. P is significant if < 0.05 at confidence interval 95%.ResultsComparing different occlusal contact locations in each group at (T0) showed a significant difference between anterior and posterior locations whereas comparing different occlusal contact locations in each group at (T3) showed a significant difference between molar and premolar locations for group B while insignificant between molar and premolar locations for group A. The comparison between different intervals within group A revealed insignificant differences while significant occlusal changes at premolar and molar regions were presented within group B.ConclusionsThe four implant-supported CAD/CAM milled overdenture bases offer greater advantages over conventional ones in terms of occlusal contact stability.Clinical Trial Registry Number(NCT06080815))08/10/2023).

Development of wrench-based system for occlusal force analysis: a biomechanical approach to evaluate dental occlusion

BackgroundThe forces of the jaw muscles are transmitted to the dentition and the temporomandibular joints (TMJs). Imbalances in the force distribution can lead to occlusal trauma, excessive tooth wear, or TMJ osteoarthritis, making the assessment of bite force (BF) distribution clinically significant. Existing thin-film BF measurement devices capture the magnitudes of a system of BFs distributed at multiple occlusal contacts (OCs), but fail to capture their directional components, limiting their clinical utility. This study aimed to develop a method for representing BF systems as a wrench, a simplified force-couple model, using digital dentistry tools and to evaluate its reliability in terms of interexaminer reproducibility.MethodsA semi-automated system was developed to integrate thin-film BF measurement data with digital models of maxillary and mandibular dental arches. BF systems were represented as wrenches with six parameters: force magnitude, axis location (x, y), axis orientation (frontal, sagittal), and pitch (moment-to-force ratio).Ten young adult participants (5 women, 5 men; mean age: 20.1 ± 2.9 years) were recruited. BF measurements were performed on all participants using the developed system. Two independent examiners manually assigned BFs to the identified OCs separately, and the reliability of these assignments was evaluated based on inter-examiner agreement. Intraclass correlation coefficients (ICCs) for wrench parameters were calculated to assess the consistency of biomechanical outcomes using appropriate statistical tests, with significance set at p < 0.05.ResultsThe proposed system allowed substantial automation, and the manual steps were limited to segmenting the interocclusal record model for each mandibular tooth and assigning BFs to the identified OCs. The interexaminer agreement was evaluated for the BFs assigned to the identified OCs, which yielded an 87% match rate. Furthermore, the impact on wrench parameters was assessed using ICCs, which ranged from 0.93 to 0.99, indicating high reliability.ConclusionsThe developed system efficiently integrates BF measurements and three-dimensional OC analysis, providing a practical method for clinical evaluation of the BF systems. In addition, the system provided consistent outcomes in biomechanical analyses across different examiners.

Light‐Driven Rotational Control of Ferrofluid Liquid Marbles in Magneto‐Optical Traps for Optical and Acoustic Modulation

AbstractOptically induced rotation relies on dynamic optical forces acting on microscopic particles via spatiotemporal light modulation, angular momentum transfer, or recoil forces. However, rotating macroscopic particles using light fields with intensity, polarization, or phase variations is challenging, especially underwater, due to the low torque of electromagnetic fields. This study demonstrates stable optical trapping and switchable light‐induced rotation of millimeter‐scale liquid marbles (LMs) in a uniform, time‐invariant DC magnetic field. These LMs, composed of self‐assembled ferrofluid droplets encapsulated by superhydrophobic particles with high photothermal conversion efficiency, float on a fluid surface and are stably trapped via controlled surface tension forces. Light‐induced photothermal interactions within the magneto‐optical field generate significant angular momentum, driving rotation through the Kelvin body force—resulting from a thermo‐magnetic gradient—and surface tension forces. This enables optically induced rotation of magnetically trapped coupled LMs, with angular velocity tunable via magnetic and optical field strength, fluid viscosity, and surface tension. Torques exceeding 170 nN·µm are achieved with a 200 mW CW laser, modulating underwater optical transmission at 1–4 Hz. This approach advances reversible optical torque generation and optical communication in fluidic systems. Additionally, ultrasonic waves modulate rotation by altering the nonequilibrium force distribution within ferrofluid LMs.

Comparison of occlusal force distribution and digital occlusal analysis methods of single posterior implant restorations: an in vivo study

BackgroundOcclusion plays a crucial role in maintaining masticatory function and temporomandibular joint (TMJ). Single implant supported restorations are widely used for posterior tooth replacement, but they require careful occlusal adjustment due to the absence of periodontal ligament. Digital occlusal analysis methods, such as digital impressions and Occlusense, provide quantitative assessments of occlusal contacts and force distribution. However, their accuracy and clinical relevance remain uncertain.MethodsIn this prospective clinical study, occlusal force distribution was evaluated before and after placement of single implant supported restoration using the Medit i700 intraoral scanner and OccluSense system. Measurements were performed before and after prosthesis under standardised conditions. Occlusal contact areas and force distributions were analysed using CloudCompare and ImageJ software. Statistical analysis was performed using Kruskal–Wallis test and Kendall's Tau-B correlation analysis.ResultsA total of 20 patients were included in the study. Post-restoration measurements revealed significant changes in occlusal force distribution in different segments of the dental arch (p < 0.001). Strong correlations were observed between Medit and OccluSense measurements (p < 0.001).ConclusionSingle-unit implant restorations significantly alter the occlusal force distribution, affecting not only the restored tooth but also the adjacent and opposing teeth. Both Medit i700 and OccluSense provided valuable information, with OccluSense providing a more detailed representation of occlusal force density. These findings suggest that digital occlusal analysis methods can help optimise occlusal adjustments for implant restorations.Trial registrationThe current study was registered in ClinicalTrials.gov (ID: NCT06862973) First posted: 07/03/2025. Retrospectively registered.

Determination of winding destroy limit area for a power series of amorphous core transformers

The amorphous steel core transformer features a unique structure with a rectangular winding, resulting in an uneven distribution of electromagnetic force compared to the circular winding of silicon core transformers. Consequently, evaluating the electromagnetic added value and identifying the destructive areas of the winding is crucial. In this paper, the combination of Matlab and the finite element technique is developed to calculate the magnetic field, short-circuit current, and electromagnetic force for a 3-phase amorphous transformers (22/0.4 kV) during short-circuit faults. The findings establish a relationship between the electromagnetic force value during a short circuit and the winding radius, as well as identify the areas where the winding damage is confined based on the transformer power sequence. These research results assist designers, manufacturers, and transformer operators in determining the appropriate harmful conditions of short-circuit electromagnetic force for the windings.

Evolution of force network, contact network, and tensile force chains in rock-like bonded granular materials under unconfined and confined compression: A DEM study

This study numerically investigates contact forces and the contact network in unconfined and confined compression tests on rock-like bonded granular materials using the particle-based discrete element method (DEM). Statistical analysis of contact force magnitudes and polar distributions under varying confining pressures reveals a significant influence of confining pressure on force evolution. Additionally, contact force distribution is closely related to internal structures and external loads. The relationship between contact force and geometrical features of the contact network is analyzed, along with the three-stage evolution of the relationship between force anisotropy and stress ratio, driven by contact network changes. Tensile force chain lengths follow an exponential distribution. Without confinement, tensile force chains remain stable until crack formation, whereas under confinement, they increase in number and length before decreasing due to the occurrence of cracks. Higher confinement results in shorter, fewer tensile force chains. Finally, the number, orientation and force magnitude of new tensile contacts are analyzed to further elucidate tensile contact evolution in bonded granular materials.

Vertebral artery dissection with cerebellar stroke after use of a percussive massage device: illustrative case.

Vertebral artery dissection is a rare condition often due to blunt cerebrovascular injury (BCVI). Electric massage devices have rarely been documented as an etiology of BCVI; however, their use has become widespread. The authors present an illustrative case and literature review of right vertebral artery BCVI and cerebellar infarct following the use of an antique electric massage device. A 65-year-old male presented with acute onset vertigo and nausea after using an antique electric massage device on his neck to relieve muscle tension. BCVI in the right vertebral artery was identified via CT angiography (CTA). MRI of the brain confirmed associated cerebellar infarction. Follow-up catheter cerebral angiography confirmed a right V3 segment intraluminal thrombus and V4 segment dissection. After inpatient observation, the patient was discharged on oral anticoagulation. At the 1-month follow-up, he reported no new symptoms, and CTA revealed resolution of the V3 thrombus and healing V4 dissection. The authors report the first case of MRI-proven stroke in association with vertebral artery BCVI after the use of an antique electric massage device. This case highlights the need for kinetic studies to assess the force distribution of percussive instruments in an effort to prevent injuries. https://thejns.org/doi/10.3171/CASE24812.

Kinetostatic Modeling and Performance Analysis of Redundant-Actuated 4-PSS&amp;S Compliant Parallel 3-DOF Micro-Rotation Mechanism

This paper presents a novel redundant-actuated 4-PSS&amp;S compliant parallel micro-rotation mechanism (P represents the actuated prismatic joint and S denotes the spherical pair) with three rotational degrees of freedom. First, compliance models of the flexure spherical hinge, each branch and the whole mechanism are established using the compliance matrix method. Then, the mechanism is simplified as an equivalent spring system to establish two kinetostatic models, with their correctness validated through finite element simulations. Finally, a comparative analysis is conducted on the performance of the 3-PSS&amp;S mechanism, non-redundant-actuated 4-PSS&amp;S mechanism and redundant-actuated 4-PSS&amp;S mechanism. The results show the following: ① For the 4-PSS&amp;S mechanism, redundant actuation with optimized actuating force distribution effectively reduces the peak actuating force by up to 50% (average 40.95%), achieving an average 10.79% reduction compared to the 3-PSS&amp;S mechanism. ② The 4-PSS&amp;S mechanism’s output stiffness increases by 26.68% in the θx and θy directions and by 33.31% in the θz direction compared to the 3-PSS&amp;S mechanism. ③ Optimal force distribution significantly reduces the parasitic axis drift of the redundant-actuated 4-PSS&amp;S mechanism at the constrained flexure spherical hinge S3, indicating higher motion accuracy. ④ The workspace volume of the redundant-actuated 4-PSS&amp;S mechanism expands by 94.32% compared to the 3-PSS&amp;S mechanism and by 372.89% compared to the non-redundant-actuated 4-PSS&amp;S mechanism.

Dynamic response characteristics of shallow-buried biased small clearance tunnel subjected to various ground shaking

The axial force and bending moment of tunnel lining are crucial for lining stability. To investigate the response patterns of axial force and bending moment in shallow-buried biased small clearance tunnels under various conditions – including different adjacent slope angles, loading wave types, peak loads, and loading directions – extensive numerical simulations were conducted. The numerical results were subsequently verified through large-scale vibration table physical model experiments. The findings reveal that the variation patterns of lining axial force and bending moment under bidirectional coupled seismic waves demonstrate similarity to those under vertical seismic waves. Vertical seismic motion exerts a more pronounced influence on lining axial force response. Seismic wave peak intensity significantly affects lining axial force and bending moment, with both parameters showing gradual increases corresponding to peak load escalation. The arch shoulder of the slope-side right tunnel lining exhibits particularly strong axial force and bending moment responses. While Darui wave, Wenchuan wave, and Kobe wave produce essentially consistent axial force and bending moment response patterns in tunnel linings, their magnitudes differ substantially. Seismic wave type primarily influences response magnitude rather than characteristic patterns of axial force distribution. Increasing slope angles adjacent to tunnels correlate with heightened axial force and bending moment responses in linings. A logarithmic functional relationship exists between slope angle and response values at the lining arch shoulder. These findings provide valuable references for seismic design of shallow-buried biased small clearance tunnels.

Characterization of Force Distribution and Force Chain Topology in Asphalt Mixtures Using the Discrete Element Method.

The force chain network within asphalt mixtures serves as the primary load-bearing structure to resist external forces. The objective of this study is to quantitatively characterize the contact force distribution and force chain topology structure. The discrete element method (DEM) was employed to construct simulation models for two stone matrix asphalt (SMA) and two open-graded friction course (OGFC) mixtures. Load distribution characteristics, including average contact force, load bearing contribution and contact force angle, and force chain topological network parameters, clustering coefficient, edge betweenness and average path length, were analyzed to elucidate the load transfer mechanisms. The findings of the present study demonstrate that the average contact force between aggregate-aggregate contact types in specific particle sizes significantly exceeds the average contact force of the same particle size aggregates. For SMA16 and OGFC16 asphalt mixtures, the load-bearing contribution of aggregates initially increases and then decreases with decreasing particle size, peaking at 13.2 mm. SMA13 and OGFC13 mixtures demonstrate a consistent decline in load bearing contribution with decreasing aggregate size. The analysis of the force chain network topology of the asphalt mixture reveals that SMA mixtures exhibited higher average clustering coefficients in force chain topological features in comparison to OGFC mixtures. It indicates that SMA gradations have superior skeletal load-bearing structures. While the maximum nominal aggregate size minimally influences the average path length with a relative change rate of 3%, the gradation type exerts a more substantial impact, exhibiting a relative change rate of 7% to 9%. These findings confirm that SMA mixtures have more stable load-bearing structures than OGFC mixtures. The proposed topological parameters effectively capture structural distinctions in force chain networks, offering insights for optimizing gradation design and enhancing mechanical performance.

Force Loss and Distribution of Load in Hands with Carpal Tunnel Syndrome

Abstract Background Carpal tunnel syndrome is the most common entrapment syndrome of a peripheral nerve and is causing pain, sensory deficits and atrophy of the thenar. Aims The functional deficit due to paralysis of the median nerve is not yet fully understood. For a better knowledge of the impact due to carpal tunnel syndrome, the force and contact area of the fingers, thumb and palm in addition with the load distribution of patients with carpal tunnel syndrome were subjected to a differentiated analysis. Methods For this clinical study, 30 patients with carpal tunnel syndrome were analysed by Manugraphy. The manugrahy sytem consists of 3 cylinders covered with pressure sensor matrices. The cylinders had circumferences of 100, 150, and 200 mm, corresponding to 32, 48, and 64 mm diameters, respectively. The grip strength and the contact area of the affected hand were compared to the healthy opposite hand with regard to the median difference for three different cylinder sizes. In addition, the areal forces of seven anatomical areas of the hand (thumb, four fingers, thenar and hypothenar) were analysed. Results The grip force of the affected hand was significantly reduced with 11-16% compared to the opposite hand for the 100 and 200 mm cylinder, and 4% for the 150 mm cylinder. The contact area between hand and cylinder was reduced by 5% (100 mm), 3% (150 mm) and 2% (200 mm) due to muscle atrophy. Analysis of the areal forces showed the most significant deficit in the middle and ring finger. Conclusion Although the thumb and thenar are considered most severely affected by carpal tunnel syndrome, the force deficit was most severe in the middle and ring finger. This is probably caused by sensitive impairment and the fact, that the stabilisation of the thumb is affected by the carpal tunnel syndrome and therefore results in a reduced force transmission.

Mechanical Damage Prediction for Artillery Steel Considering High-Temperature Friction and High-Speed Impact

High-temperature friction and high-speed impact are the primary sources of mechanical damage to artillery steel, severely restricting the interior ballistic properties and service life of barrel weapons. A hydrodynamic friction model is first proposed to express the high-temperature friction behavior between the rotating band and the barrel. Additionally, this article deduces a contact force model to describe the high-speed impact behavior between the center band and the barrel. The general expression of mechanical damage can be obtained by the hydrodynamic friction and contact force models. Meanwhile, this article calculates the frictional coefficient and contact force distribution during the artillery launching combined ABAQUS with polynomial chaos expansion. The experimental verification of the hydrodynamic friction and contact force models is organized, and the detailed assessments show that the frictional coefficient and contact force responses have good agreement with experimental data. Finally, this article gives the mechanical damage evolution based on the general mechanical damage model. The mechanical damage of the barrel chamber is mainly located at the muzzle and 1/6 barrel length position from the beginning of rifling.

Ultrasensitive and Reliable Diamond MEMS Magnetic Force Sensor with 3D Imaging at Room Temperature

AbstractDeveloping magnetic force sensors with a simple structure, high sensitivity, and exceptional reliability at room temperature remains challenging due to frequency fluctuations and noise suppression issues. In this work, an ultra‐sensitive and highly reliable magnetic force sensor is presented by integrating a single‐crystal diamond (SCD) MEMS resonator with a permanent magnetic particle. The magnetic particle serves as the sensing element, enabling precise detection of magnetic field gradients under a field bath. The SCD‐based MEMS sensor exhibits outstanding performance, achieving an ultra‐low detectable force of 1.8 × 10−16 N/Hz1/2, a high magnetic sensitivity of 0.303%/(mT/mm), and a response time of 98.8 ms in the first mode at room temperature. Notably, the resonant frequency fluctuation is remarkably low, reaching 7.89 × 10−4 Hz at room temperature, ensuring stable and reliable operation. Furthermore, a 3D magnetic force imaging sensor based on the SCD platform, capable of visualizing the 3D distribution of magnetic forces is demonstrated. This work lays a solid foundation for the advancement of SCD MEMS‐based magnetic imaging sensors, offering unparalleled sensitivity, reliability, and tunable spatial resolution for next‐generation magnetic imaging applications.

Mechanical Modeling of the Premolar: Numerical Analysis of Stress Distribution Under Masticatory Forces

The advancement of digital technologies has revolutionized the medical field, offering new opportunities for the biomechanical analysis and simulation of anatomical structures. This study explored the modeling of mandibular and dental components using advanced methods such as finite element analysis (FEA) and three-dimensional modeling. Special attention was given to the distribution of masticatory forces and their impact on premolars, highlighting the biomechanical differences between restorative materials such as amalgam and composites. The results indicate that each material presents specific advantages depending on the loading conditions, emphasizing the need for personalized dental treatments. This study confirms the effectiveness of numerical methods in optimizing the design of dental structures and supports the applicability of these techniques in orthodontics, maxillofacial surgery, and dental prosthetics.

Oscillations of the Oil Pipeline Axis with Consideration of the Inertia Component When Pumping Diesel Fuel

This study examines a single-span beam crossing without longitudinal deformation compensators during diesel fuel pumping. In addition to static forces, namely, the weight of the pipeline and the transported product, the analysis considers vertical components of inertial forces acting on the oil product and the pipeline itself. These forces are directed perpendicularly to the abscissa axis connecting the endpoints of the crossing. The inertial effects cause significant vertical oscillations of the pipeline, which have not been sufficiently addressed in previous research. This work aims to study these oscillations to determine the displacements of points along the pipeline axis, the magnitudes of the inertial forces, and the resulting bending moments at the crossing. A classical Fourier series method is applied to solve the formulated boundary value problem. The results show that oscillations occur in the vertical plane, are symmetrical relative to the center of the span, and are undamped. The maximum vertical displacement reaches approximately 57 mm at the midpoint of the crossing, and the oscillation period is around 0.415 s. Inertial force distribution and bending moments are also symmetric about the center. A detailed analysis with small time steps confirmed that the oscillations are strictly periodic, exhibiting equal displacements in the upward and downward directions. The results highlight that fatigue loads arise during the operation of such crossings, which is important for assessing the strength and stability of oil pipeline structures under real operating conditions.

Efficiency of using an increased area grillage as part of a columnar pile foundation

In this paper, we propose to apply the idea of an integrated foundation used for slab grillage to a columnar pile foundation. In mass design, having determined the required number of piles based only on their bearing capacity, they try to place them in a pile as compactly as possible to reduce the cost of the grillage, whose work is not taken into account. If the piles are placed at a considerable distance from each other or compactly placed under the column, but the grillage size is sufficiently large, this can compensate for the small number of piles by including the grillage in the work The mathematical modelling of the pile foundation operation was performed using the SOFiSTiK software package. A study of the implementation of the pile foundation with a soil foundation was carried out, depending on the grillage size, length, number, placement of piles in the grillage and soil conditions. Homogeneous sandy and clayey foundation soil is considered. It is shown that in the case of using complex pile foundations with sparse pile placement and increased grillage area, the efficiency of the foundation as a whole and its individual elements increases. In order to save materials, it is possible to reduce the number of piles in a group while increasing the grillage size without losing the bearing capacity of the foundation. It is known that a pile is a much more expensive structure than a grillage, so reducing the number of piles while increasing the overall size of the grillage can lead to a more economical solution. The mathematical modelling of the pile foundation operation using the SOFiSTiK software package confirmed the main conclusions on the distribution of forces between the elements of the pile foundation, obtained earlier by physical modelling on small-scale models and using the Plaxis 3D Foundation software package.

Automated form‐finding method of spoke cable net structures using physics‐constrained neural network

AbstractThe spoke cable‐net structure is a typical flexible tensile structure that relies solely on cables as load‐bearing components. Its unique topological characteristics, composed of ring cables and radial cables, determine that the main challenge in its form‐finding lies in controlling the spatial configuration of the inner ring. Existing computational methods primarily rely on numerical iteration based on empirical trial and error, which makes it difficult to effectively address the multi‐variable coupling problem between the prestress distribution and the geometric configuration of the ring cables. Accordingly, this paper aims to establish a deep learning‐based autonomous form‐finding framework driven by geometric constraints and physical equations to achieve the simultaneous intelligent solution of prestress distribution and spatial configuration. The effectiveness and versatility of the proposed method are validated through case studies with various regular and irregular geometric forms. To enhance the precision of form‐finding for structures with intricate geometries, a dual‐optimizer strategy integrating the adaptive moment estimation and limited‐memory Broyden Fletcher Goldfarb Shanno algorithms is implemented. For a spoke cable‐net structure spanning 100 m, the intelligent form‐finding accuracy can be maintained within 1 cm, ensuring a satisfactory form‐finding outcome. The proposed deep neural network (DNN) method automatically correlates cable force distribution with geometric configuration, offering a novel computational approach and solution pathway for the automated shape determination and configuration design of flexible cable structures.