Force Moment Research Articles

Suffusion of irregular concave gap-graded sand with resolved CFD-DEM

The complex morphologies of particles are a crucial factor influencing suffusion in gap-graded granular soils. However, the micro-mechanism of soil suffusion composed of irregular concave particles remains unclear. To this end, a systematic numerical simulation that considers particle concavity and aspect ratio is performed with the resolved discrete element method (DEM) and computational fluid dynamics (CFD) approach. The macro responses of suffusion of particles with varying morphologies, e.g., cumulative eroded particle mass and sample profile, are revealed and interpreted from a microscopic view, e.g., particle rotation, coordination number, and moment. It is found that the rotation of irregularly shaped particles during suffusion requires overcoming the moment applied by the surrounding particles. Particles with bigger contact force or irregularity require a higher moment to be overcome, thus significantly increasing their suffusion resistance. Irregularly shaped particles can adjust their orientation to reduce the moment and drag force applied to them. At the same aspect ratio, particles with larger concavity are more likely to interlock with each other, with increasing the coordination number of the soil packing and shrinking the pore channel for particle migration. A shape parameter considering both concavity and aspect ratio is finally proposed to characterise the influence on suffusion.

Derivation of a generalized Langevin equation from a generic time-dependent Hamiltonian

Abstract The traditional Mori-Zwanzig formalism yields equations of motion, so-called generalized Langevin equations (GLEs), for phase-space observables of interest from the microscopic dynamics of a many-body system governed by a time-independent Hamiltonian using projection techniques. By using time-ordered propagators and time-independent projection operators, we derive the GLE for a scalar observable from a generic time-dependent Hamiltonian. The only restriction in our derivation is that the time-dependent part of the Hamiltonian and the observable of interest depend on spatial phase-space variables only. If the observable obeys Gaussian statistics and the time-dependent part of the Hamiltonian can be expressed as an odd power of the observable, the friction memory kernel in the GLE becomes proportional to the second moment of the complementary force, as is the case for a time-independent Hamiltonian in the Mori-Zwanzig formalism.

Short cross-laminated timber plates subjected to out-of-plane loads

The use of cross-laminated timber (CLT) panels has increased significantly, driven by the demand for more sustainable structural solutions. When used in short spans, the load capacity of CLT panels can be significantly enhanced; however, their behaviour and failure mechanisms differ from those of large spans. This study evaluates the mechanical behaviour of short-span CLT panels made from Pinus taeda L. under out-of-plane loads, through experimental analyses on full-scale panels. Fourteen industrially manufactured panels were tested in four-point bending tests, using adhesive weights of 250 and 220 g/m². The values of maximum bending moment, shear force, and their respective resistances were analysed based on the observed failure modes. The transverse modulus of elasticity was determined using strain gauges. It was found that short panels, with a span-to-depth ratio of 9 ≤ l/h ≤ 12, exhibited bending moment and shear force failures, with no significant differences between adhesive weights. Discrepancies in shear resistance and stiffness values compared to existing standards suggest the need for reduced-specimen testing for greater accuracy.

Digital Models and 3D Biomechanics Analysis in Orthodontics. Part 1: Vector Calculations

Biomechanics is essential for optimizing orthodontic appliances and controlling dental movement. Charles J. Burstone pioneered a three-dimensional (3D) approach in orthodontics, advocating for a shift beyond appliance-focused methods. Initially, biomechanics studies were constrained to two-dimensional (2D) analysis due to the complexities of 3D evaluation. Despite progress in computational tools and digital modeling, orthodontic biomechanics has largely maintained a 2D orientation. This paper advances orthodontic biomechanics into 3D, re-evaluating concepts previously limited to 2D frameworks. A dedicated software, DDP-Ortho (Ortolab, Poland), is introduced to enable orthodontists to analyze and resolve biomechanical challenges in 3D, facilitating appliance designs with precise 3D force systems. The representation and calculation of force vectors and moments in 3D are detailed, emphasizing the inherent complexity absent computational support. Key processes such as vector subtraction and addition, fundamental for assessing and refining orthodontic force systems, are explained. Additionally, the vector split (couple replacement) method, previously described in 2D, is extended to 3D, addressing the unique constraints and challenges of this approach. These tools promise to refine the accuracy and effectiveness of orthodontic treatments, setting the stage to examine the interactions between 3D force systems and dental movement, which will be addressed in a subsequent paper, to broaden the potential of contemporary orthodontic therapy.

A refined nonlinear theoretical model for mechanical analysis of tunnels subjected to strike-slip faulting with multiple fault planes

During strike-slip fault dislocation, multiple fault planes are commonly observed. The resulting permanent ground deformation can lead to profound structural damage to tunnels. However, existing analytical models do not consider multiple fault planes. Instead, they concentrate the entire fault displacement onto a single fault plane for analysis, thereby giving rise to notable errors in the calculated results. To address this issue, a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations. The analytical model considers the number of fault planes, nonlinear soil‒tunnel interactions, geometric nonlinearity, and fault zone width, leading to a significant improvement in its range of applicability and calculation accuracy. The results of the analytical model are in agreement, both qualitatively and quantitatively, with the model test and numerical results. Then, based on the proposed theoretical model, a sensitivity analysis of parameters was conducted, focusing on the variables such as the number of fault planes, fault plane distance (d), fault displacement ratio (η), burial depth (C), crossing angle (β), tunnel diameter (D), fault zone width (Wf), and strike-slip fault displacement (Δfs). The results show that the peak shear force (Vmax), bending moment (Mmax), and axial force (Nmax) decrease with increasing d. The Vmax of the tunnel is found at the fault plane with the largest fault displacement. C, D, and Δfs contribute to the increases in Vmax, Mmax, and Nmax. Additionally, increasing the number of fault planes reduces Vmax and Mmax, whereas the variation in Nmax remains minimal.

Variation In Response to Limb Loading Instruction on Knee Mechanics During Squatting in Early Recovery Following Anterior Cruciate Ligament Reconstruction.

On average, individuals in early recovery following anterior cruciate ligament reconstruction (ACLr) improve limb loading symmetry (LLS) with instruction to equalize weight distribution between limbs during squats. However, the extent to which these instructions improve knee extensor loading symmetry (KLS) or reduce intra-limb compensations is not known. Determine how limb loading instructions influence knee and intra-limb loading in individuals 3-4 months post-ACLr and to explore variations in responses across individuals. Controlled Laboratory study. Research Laboratory. Individuals 109.4 days (18.2 days) post-ACLr (n=20) and healthy matched controls (CTRL; n=19). Participants performed double limb squats in natural (N; no instruction) and instructed (IN; instruction to evenly distribute weight between limbs) conditions. Between limb and knee loading symmetry were calculated as the ratio of vertical ground reaction force and knee extensor moment impulse, between surgical(Sx):matched and non-surgical(NSx):matched limbs (ACLr:control), respectively. Intra- limb hip/knee (H/K) extensor loading distribution was calculated in Sx:matched limbs. LLS (N: 0.86; IN: 0.93, P < 0.001; ES:0.83) and KLS (N: 0.54; IN: 0.62, P=0.007; ES:0.67) improved with instruction in the ACLr group with no change in CTRL. H/K ratio did not change for either group. K-means clustering, considering natural and change (natural- instructed) in LLS, KLS, and H/K ratio, described response to instruction across three clusters: 1) ACLr: n=3; CTRL: n=9, were symmetrical in both conditions, 2) ACLr: n=14, showed some improvement in symmetry, 3) ACLr: n=3, only improved LLS. Average data suggests that weightbearing instruction improved LLS to within 7%, but a 38% knee loading deficit remained, and intra-limb compensation did not improve. Data- driven clusters indicate that three ACLr subjects were similar to controls, fourteen improved LLS, KLS and H/K distribution, and three only improved LLS with worsening KLS and H/K.

Flexural behavior of reinforced concrete arch ribs

For many years, arch bridges have been celebrated for their striking appearance and structural effectiveness. However, the response of arch bridges to dynamic loadings, particularly during earthquakes, remains poorly understood, and reliable seismic design guidelines are lacking. Previous research has suggested that reinforced concrete (RC) arch ribs may experience flexural yielding at their springings due to the interaction of axial force and bending moment under earthquake loading. To assess the ductile behavior and ensure the adequate performance of RC arch ribs, a comprehensive investigation combining experimental and analytical approaches was conducted in this study, taking into account the influence of high axial load and the hollow section configuration present in RC arch ribs. The test results revealed that all RC arch ribs exhibited a typical flexural failure mode. As the axial load increased, the lateral load bearing capacity also increased, but the displacement ductility decreased significantly. Comparing different section configurations, the RC arch rib specimen with a double-cell boxed section demonstrated higher lateral load bearing capacity but lower displacement ductility compared to the single-cell boxed section, while the energy dissipation capacity was approximately similar for both section configurations.

Is biomechanical loading reduced in individuals with unilateral transtibial amputation during fast-paced walking when using different ankle/foot prostheses? A pragmatic randomized controlled trial.

Sound side loading is a risk factor for osteoarthritis development, which has been noted to reduce when using advanced prostheses during normal-paced walking in individuals with unilateral transtibial amputation (UTTA). However, descriptions of loading during fast-paced walking remain relatively unreported. Therefore, the aim of this study was to describe the biomechanical loading of individuals with UTTA while using different ankle/foot prostheses during fast-paced walking. A blinded, randomized control trial was conducted in a group of K3-K4 ambulators, who used 3 different prosthetic feet (1. a solid ankle cushioned heel foot prosthesis [SACH], 2. a standard energy storage and return foot prosthesis [ESAR], and 3. a novel ESAR foot prosthesis [N-ESAR]) in a 2-week randomized crossover design. The spatiotemporal and kinetic data of the participants' fast walking pace were collected. Data were analyzed using a mixed model and one-way analysis of variances (p < 0.05) and Cohen d. Twenty individuals with UTTA (age: 40 ± 16 years; height: 1.76 ± 0.09 m; and BMI: 24.72 ± 3.63 kg/m2) participated in this study. There were minimal changes in the spatiotemporal data between the different prosthetic feet. When the participants used the N-ESAR feet, they had a lower peak vertical ground reaction force (p = 0.02) and external knee adduction moment (p = 0.02) on the sound side, as well as a higher distal shank power on the prosthetic side (p < 0.01). Overall fast-paced walking resulted in higher sound side loading forces compared with normal-paced walking. However, use of the N-ESAR prosthesis reduced the biomechanical loading on the sound side in individuals with UTTA while walking at a fast pace compared with the ESAR and SACH prostheses. The percentage change in the biomechanical loading from normal- to fast-paced walking of the N-ESAR foot was also larger compared with the other prostheses, perhaps because of the individuals' ability to achieve a faster walking pace when using the N-ESAR prosthesis. Longitudinal intervention studies should be performed to further investigate the possible benefits of using advanced prostheses.

Experimental study and numerical analysis of a novel serrated-and-plate truss structure

High-speed rail station has extensive span and height, making daylighting a challenge. This paper proposes the serrated-and-plate truss structure (SPTS) to improve station daylighting. SPTS combines a serrated truss structure (STS) for daylighting and a plate truss structure (PTS) for lateral stability and deformation resistance. A downscaled SPTS with support-loading system is designed and built to test mechanical properties. It has 264 stress and 19 displacement measuring points, tested under four vertical and two horizontal load cases. Maximal stress and displacement are 150.7 MPa and 5.07 mm, with peak chord axial force and column base bending moment of 13.5 kN and 663.7 kN mm. Simulated and measured results match well, confirming the numerical method's accuracy. Thermal effects of SPTS are studied via conventical and extreme thermal analyses, with stress and displacement well below limits. Seismic spectrum and time-history analyses indicate SPTS stress and deformation at 63.9 % and 68.3 % of limits. Comparative analysis across 64 load cases reveal that STS is significantly less stable and resistant to deformation than SPTS, validating PTS's boundary constraint effects. Experimental and numerical studies confirm SPTS's engineering applicability and provide valuable references for similar truss structure research.

Constructing a model of the axis form in a S-shaped riser of a cultivator paw

When cultivating the soil, a force of resistance to the movement of cultivator paw acts on it. It has a variable value and causes a moment of force applied to the riser of the paw. Under the action of the moment, the elastic axis of the riser changes its shape. This affects the position of the paw in the soil. The form of an S-shaped riser whose elastic axis consists of two circle arcs has been considered in this study. During cultivator operation, one part of the riser bends, increasing the curvature of the elastic axis, and the other, on the contrary, unbends, that is, its curvature decreases. The modeling of the shape of the elastic axis of the paw riser is based on the theory of resistance of materials, according to which the curvature of the elastic axis of the cantilevered band is directly proportional to the applied moment and inversely proportional to its stiffness. If the shape of the cross-section of the riser along its entire length is unchanged and the properties of the metal are also the same, then the stiffness is constant. In the case of small deflections of the band, the linear theory of bending is used, but the deflections in the riser are significant, so the nonlinear theory has been used for this case. At the same time, it is taken into account that the elastic axis of the riser already has an initial curvature, the sign of which changes after passing through the point of connection of the component arcs. To model the shape of the elastic axis of the S-shaped paw riser, the deformation of the arcs of the circles that form this paw was calculated separately. Numerical integration methods were used to find the shape of the deformed elastic axes of both parts of the riser. They were connected into a whole and a deformed elastic axis of the S-shaped riser was obtained. Two variants of the riser with different lengths of their elastic axis, but the same height and the same angle of entry into the soil, were considered. The combination of the component arcs of the riser shows that, under the action of the same force, the deviation from the specified movement depth for one riser is 2 cm, and for the other – 4 cm.

Investigation of the large-diameter monopiles response under flow-controlled loading

The mechanical behavior of monopile support systems for offshore wind turbines under current-induced loads was investigated through numerical simulations. Using the Large Eddy turbulence model, the fluid-structure coupling was analyzed in both unidirectional and bidirectional directions. In the unidirectional coupling, the pressure and velocity profiles of the fluid around the pile were determined. While in the bidirectional coupling, the force distribution, pile displacement, and moment distribution were obtained, along with the current-induced load transmitted from the pile to the soil. The coupling analysis revealed that the fluid flow around the pile exhibited cyclic loading behavior due to the interaction between the fluid and the pile, effectively resulting in an oscillating pile within a steady flow. Additionally, the pile’s stress distribution remained within the tensile yield limit of the steel, indicating a stable state in the fluid-pile model within the given flow conditions. Furthermore, the soil reaction forces obtained from the fluid-pile-soil coupling model validated the accuracy of the current-induced load calculations. This study introduces a novel approach that considers the fluid-pile-soil coupling, offering valuable insights for pile foundation design. The findings of this research have significant engineering implications and practical value, providing a robust foundation for future offshore wind turbine installations.

Bending of Curved Composite Beam with Interlayer Slip

Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam is subjected to uniform bending. The paper presents solutions for stresses, radial displacement, and slip. The end cross sections of the layered curved beam are loaded by zero moment force couples, as a result of which each cross section of the beam is loaded by zero moment force couple resultant.

Design Method of a Novel Interface Connection Device for Multiscale Test Model Considering Multiparametric Similarity of Internal Forces

ABSTRACTThe multiscale model of building structures, as a balanced solution between accuracy and cost, has been widely used in the analysis of structural seismic performance. A reasonable interface connection method can accurately ensure load transfer and motion coordination between models of different scales. In this paper, a novel interface connection device and the corresponding design method for a multiscale test model of building structures were proposed, in which the upper structure with smaller sized components was replaced by a simplified story‐scale model, and the lower structure was adopted as a component‐scale model. The overall and local equations of motion for this multiscale model were established. For the interface connection between different scale models, a design method considering multiparametric similarity of shear force, axial force, and bending moment was proposed. In this method, the internal nodes at the interface of the component scale model were decomposed, and the coupling relationship of internal force between two adjacent nodes was established. The axial force of each node was decoupled into the interstory shear force and bending moment provided together. Additionally, the overturning moment is provided by adding the overlapping domain. According to the equilibrium relationships of the nodes at the interface, the corresponding transfer matrix was provided, and the design method of the interface connection device was proposed. The accuracy and feasibility of the method were validated by static and shaking table tests on a frame structure.

Combined genetic algorithm and response surface methodology‐based bi‐optimization of a vertical‐axis wind turbine numerically simulated using CFD

AbstractIn this study, computational fluid dynamic (CFD) simulation of a vertical axis wind turbine (VAWT) geometry based on the Unsteady Reynolds–Averaged Navier–Stokes equations was investigated. In addition, the relationship between the geometric parameters of the VAWT and the two response variables, that is, moment and lift force, was determined using response surface methodology (RSM). Then, the Non‐Dominated Sorting Genetic Algorithm (NSGA‐II) was used to solve the multi‐objective optimization problem. The results obtained from the RSM showed that the lift force of the turbine is more sensitive to the change in the blade chord length, and the output moment of the turbine is more sensitive to the change in the rotor radius. Using the NSGA‐II multi‐objective optimization algorithm and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, it was determined that among the optimal values of the independent variable, the most optimal response occurs in blade chord length = 0.18 m, rotor radius = 0.4 m, blade pitch angle = −3.27° and number of blades = 4. In these optimal values of the independent variables, the values of the dependent variables, which included the turbine's moment and the blades’ lift force, were obtained as 9.58 N m and 57.89 N, respectively.

Seismic response control of shear frame structure using a novel tuned-mass type composite column

Concrete filled steel tube (CFST) column is widely applied in shear frame structure in seismic-prone area owing to its superior earthquake resistant performance. However, CFST column might still suffer damage under a severe earthquake. This paper proposes a novel tuned-mass type column-in-column (CIC) system to improve the seismic behavior of the CFST column and hence protect the structure. The CIC system is formed by splitting the CFST column into a primary column and a secondary column, while the overall cross section area and hence the load-bearing capacity is not changed. By optimally selecting the springs and dashpots to interconnect the two columns, the CIC can act as a non-conventional tuned mass damper (TMD) to reduce seismic vibrations of structures. To demonstrate the proposed CIC concept, a single-story and a five-story frame structure with and without control are designed. Nonlinear time history analyses are performed to study the seismic responses of these structures considering different seismic design levels, earthquake ground motions and CIC control schemes. Numerical results show that the CIC system can effectively reduce the seismic induced story acceleration, displacement and drift ratio of frame structures with the reduction ratios approximately between 21 % and 30 %, and the ratios on reducing the base shear force and bending moment are between 27 % and 31 %, and between 34 % and 49 %, respectively. The proposed CIC control concept is a new solution for mitigations of seismic responses of CFST frame structures.

Numerical analysis of FRP retrofitting in RC beam-column exterior joints at high temperatures and predictive modeling using artificial neural networks

PurposeThe purpose of this study is to perform a numerical analysis of fiber-reinforced polymer (FRP) retrofitting in reinforced concrete (RC) joints at high temperatures and predict models using artificial neural networks (ANN). The aim was to gain insights into their structural behavior across a range of loading conditions from room temperature to 800°C. Additionally, the research assessed the efficiency of carbon fiber-reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) and aramid fiber reinforced polymer (AFRP) strengthening in enhancing the structural performance of the critical sections.Design/methodology/approachThe linear numerical simulations were conducted to evaluate the performance of RC beam-column joints using finite element modelling (FEM) analysis. The ANN model demonstrated exceptional effectiveness in predicting the stiffness of frames with openings, establishing itself as the premier machine learning algorithm for frame stiffness estimation. In the conventional model, 300°C was proven to be an effective temperature approach. Subsequently, maintaining a constant temperature of 300°C, an in-depth analysis of nearly 30 models of three retrofitting techniques was conducted under thermomechanical loading.FindingsThe CFRP retrofits yielded 15% less deflection and 30% more stress than the remaining FRPs, and the ANN models predicted the deflection, main stresses, bending moment and shear force. The ANN model results were compared with those of other frequently used models. The R thresholds (R = 0.954, 0.981, 0.986, 0.968, 0.978 and 0.936) for training, testing and validation indicated that the ANN model achieved data variability. The findings indicate that the ANN model is more accurate because of the strong connection between the numerical model and the prediction.Originality/valueTo identify the pinpoint of critical segments within the rehabilitation section and determine the most effective wrapping method among the three laminates.

Inelastic deformation accrued over multiple seismic cycles: Insights from an elastic-plastic slider-and-springboard model

We study a toy model designed to build physical insight into the problem of slow accumulation of non-recoverable strain in fault blocks over multiple earthquake cycles. The model consists of a thin, horizontal elastic-plastic plate (springboard) in frictional contact with a vertical, rigid wall moving downward at a steady speed. Our model produces stick-slip cycles consisting of interseismic plate downwarping and coseismic plate upwarping as long as the moment of the frictional force at the contact does not exceed the maximum (purely plastic) bending moment the plate can sustain. We show that the duration of individual earthquake cycles and the spatial pattern of interseismic deflection are controlled by two stress ratios involving the peak yield stress of the plate, the frictional strength of the fault and the coseismic stress drop. We show that non-recoverable plate deflection accumulates over successive earthquake cycles if the plate’s yield strength decreases through time, causing a progressive decrease of the aforementioned stress ratios. We derive scaling relations between the rate of accumulation of inelastic deformation, the relative tectonic plate velocity, and the rate of lithospheric weakening. Our results are consistent with observations of long-term permanent deformation of natural fault regions.

Study of Unsymmetrical Magnetic Pulling Force and Magnetic Moment in 1000 MW Hydrogenerator Based on Finite Element Analysis

The large dimensions of the 1000 MW hydroelectric generator sets require high mounting accuracy. Small deviations can lead to asymmetry, which in turn triggers unbalanced magnetic pulls and moments. Therefore, symmetry is a central challenge in the installation and operation of giant hydroelectric generators. In this paper, the effects of radial eccentricity, axial offset, and rotor shaft deflection on the unbalanced magnetic pull and moment are investigated by transient finite element analysis of the asymmetric magnetic field. The results of the time-domain and frequency-domain analyses show that asymmetric operation generates unbalanced magnetic forces and moments. These forces and moments increase linearly with increasing offset or deflection rate. When the eccentricity meets the installation criteria, the unbalanced magnetic pull forces are small and within acceptable limits. This study helps to understand the relationship between asymmetry and unbalanced magnetic pulling forces in large hydroelectric generators, and provides a theoretical basis for standardizing installation deviation control.

Study on plastic yield surfaces of pyramidal lattice materials with circular and rectangular cross-sections

The yield surfaces and the evolution of yield surfaces of a bending-dominated pyramidal lattice material under complex stress states considering the coupling effect of axial force and bending moment of a strut are studied theoretically. The two-dimensional primary yield surfaces, secondary yield surfaces, and complete yield surfaces of pyramidal lattice materials of two kinds of cross-section struts are obtained, and the analytical expressions of yield surfaces are established. The effects of the inclination angle and diameter-to-length ratio of the struts on the yield surfaces of pyramidal lattice materials with circular cross-sections are discussed. The results provide a basis for analyzing homogenized plastic properties of complex lattice material structures.

Advances in longitudinal equivalent bending stiffness analysis-novel nonlinear characteristics in the assembly process of prefabricated subway stations

The longitudinal bending stiffness of quasi-rectangular prefabricated subway stations plays a great important role in studying their mechanical behavior and conducting safety assessments. To address the issue of immature stress assumptions for existing prefabricated subway stations, three stress assumptions and five bending modes are proposed while considering the coupling effect between axial force and bending moment. The study investigates novel nonlinear characteristics in the longitudinal equivalent bending stiffness and the influencing factors during the assembly of an existing subway station. An effective method for identifying the longitudinal bending modes suitable for the prefabricated subway station is established, the proposed solution has a good agreement with measured longitudinal bending stiffness efficiency. The study demonstrates that the longitudinal bending mode of the prefabricated subway station shifts from "upward convex" to "downward concave" due to the stepwise assembly method. The longitudinal bending stiffness efficiency displays a significant hysteresis curve, eventually stabilizing at approximately 1 %. Upon completion of the monitoring ring assembly, the concrete bears both longitudinal tensile and compressive stress. When assembling 10 rings from the monitoring ring, the longitudinal reinforcing bars bear tensile stress. The longitudinal bending stiffness of the prefabricated subway station exhibits significant time-variable characteristics throughout the assembly process. The research findings can provide effective references for the analysis of longitudinal mechanics and bending performance during the assembly process.