Moment Balance Research Articles

Educational interactive graphics tool for teaching the Cross process

The program demonstrates to students in the Structural Analysis discipline of the Civil Engineering course how the Cross Process (Moment Distribution Method) works for continuous beams, visually showing the physical interpretation of the method associated with the calculations in the same way as they are done in calculation memory. In addition to the calculations, the program shows the structural model with the loads (uniformly distributed forces across each span), its deformation, and its bending moment diagram. The program, with open source code, was implemented in the Java language, based on the Object Oriented Programming paradigm – OOP.The program for calculating continuous beams using the Cross Process has four canvases. It is on these canvases that the structural models, their diagrams, and their results will be drawn. The user can interact using the mouse to model the continuous beam, create new internal supports, remove internal supports, modify the dimensions of the spans, or modify the load values. The student can track the results by following the incremental analysis of the method step by step. Furthermore, the student can interfere in the iterative solution process by forcing the bending moment balance of any internal node in any order. All these procedures help the student to understand the analysis process. Well-documented source code is also an essential component for learning the method.

A predictive walking energy model based on gait phase with suspended backpack

Walking with heavy loads is a common task in military affairs and daily life. Considering that the shoulder and leg muscles fatigue will be caused during walking, which will affect the walking endurance and physical health. However, the suspended backpack is found to improve the energy efficiency of walking with a load. In this study, A lightweight suspended backpack is designed and proposing a model for estimating the metabolic cost of a suspended backpack based on gait phase. In this study, four inertial measurement units (IMUs) are fixed on the thigh and shank, six flexible pressure sensors are mounted on the soles of the feet and shoulders, respectively. The gait is defined as four successive phases. For each phase, the muscle tension is solved based on the muscle moment balance theory. Based on the phase segmentation method, the ECCF index is calculated by adding the gait phase constraint and backpack data calculation into the energy prediction model, and the relatively accurate data is obtained. In addition, In order to study the effects of the suspended backpack with different parameters on the cost metabolism, gait phase and biomechanics, the subjects need to carry the same load of 16.5 kg to walk 400 m at the different speeds, respectively. A group of seven healthy subjects in the same walking condition need to conduct two experiments: suspended backpack work (SB) and ordinary backpack (OB). The experimental results show that the suspended backpack can reduce plantar pressure and shoulder pressure in the SB condition. And at the speed of 5.0 km/h, ground reaction force (GRF) and shoulder reaction force (SRF) were reduced by 11.59 % and 13.22 % in the SB condition compared to the OB condition, respectively.

An innovative moment balanced inference engine for predicting recycled concrete aggregate strength and minimizing mixture CO2 emissions

Recycled concrete aggregate (RCA) has an important role to play in reducing CO2 emissions and encouraging sustainable practices in the construction industry. This study introduces Optical Microscope Algorithm - Moment Balance Machine (OMA-MBM) as an innovative AI-based inference engine to improve the accuracy of RCA strength prediction. MBM improves the principles of Support Vector Machine (SVM) by considering moments to identify the optimal moment hyperplane. Backpropagation Neural Network (BPNN) is employed for weight assignment, and OMA is utilized for parameter optimization. The performance of the developed OMA-MBM was benchmarked against several machine learning models, including SVM, BPNN, PSO-SVM, and GWO-SVM, achieving the lowest error metrics with RMSE values of 9.711, 0.708, and 0.709 for compressive, flexural, and tensile strengths, respectively. It also scored the highest overall performance, represented by Reference Index of 1.000. Moreover, the model was successfully used to identify optimal RCA mixture designs in terms of achieving designated material strength requirements with the lowest CO2 emissions. The robustness of model predictions was further validated across diverse applications, i.e., Boston housing prices, vehicle fuel consumption, and building energy efficiency. These findings confirm the robustness and generalizability of OMA-MBM as an accurate predictive tool for development of sustainable construction.

A partially debonded rigid elliptical inclusion with a liquid slit inclusion occupying the debonded portion

We derive a closed-form solution to the plane strain problem of a partially debonded rigid elliptical inclusion in which the debonded portion is filled with a liquid slit inclusion when the infinite isotropic elastic matrix is subjected to uniform remote in-plane stresses. The original boundary value problem is reduced to a Riemann–Hilbert problem with discontinuous coefficients, and its analytical solution is derived. By imposing the incompressibility condition of the liquid slit inclusion and balance of moment on a circular disk of infinite radius, we obtain a set of two coupled linear algebraic equations for the two unknowns characterizing the internal uniform hydrostatic tension within the liquid slit inclusion and the rigid body rotation of the rigid elliptical inclusion. As a result, these two unknowns can be uniquely determined revealing the elastic field in the matrix.

Assessment of Kinematic and Dynamic Characteristics of Shoulder Mechanism

Introduction: The thorax, clavicula, scapula and humerus comprise the finite element musculoskeletal model of the shoulder mechanism, which has been used to analyse its kinematic and dynamic behaviour. The study aims to reflect upon the analysis of the kinematic and dynamic behaviour of the shoulder mechanism. Materials and Methods: A comprehensive literature search was conducted to identify the relevant literature. Databases such as PubMed, Scopus and Google Scholar were used to search for literature published between 2000 and 2023. Results: The scapulothoracic gliding plane’s motion restrictions, which convert the shoulder girdle into a closed-chain mechanism, are represented in the model along with 16 muscles, 3 joints and 3 extracapsular ligaments. The locations of the humerus and shoulder girdle that were recorded in ten subjects during loaded and unloaded humeral abduction and anteflexion are the input variables. Conclusion: The length dependence of electromyography (EMG) amplitude and the unknown force-length relationship makes it difficult to compare muscle force predictions and EMG measurements. The conclusion is that complicated musculoskeletal models cannot be validated using EMG amplitude. The force and moment balance of the three joints are used to examine the function of the muscles. This model allows for an investigation of the function of morphological components and offers useful insight into the mechanics of the shoulder mechanism.

Calculation of Lateral Stability of Tank Trucks and its Relationship with Filling Rate

To investigate a theoretical algorithm model of the lateral stability of tank trucks and its relationship with the liquid filling rate, the shifting of the liquid centroid during non-full loading is considered. The deformation of the suspension and tires under load is assumed to exhibit a linear relationship. Using the principle of moment balance, a calculation model for the maximum stable roll angle and rollover critical acceleration of tank trucks based on the “liquid–tank–vehicle” tri-coupling is established, and the relationship between the maximum stable roll angle and rollover critical acceleration of tank trucks is analyzed and compared. Based on the result and a specific tank truck model, the effects of the liquid filling rate on the maximum stable roll angle, rollover critical acceleration, and tank tilt angle of tank trucks are investigated using numerical analysis methods. A comparison with the lateral stability of ordinary trucks loaded with solid goods is performed to further examine the effect of the liquid filling rate on the lateral stability of tank trucks. The results show that the maximum stable roll angle and rollover critical acceleration are consistent indicators for evaluating the lateral stability of tank trucks; the lateral stability of tank trucks decreases owing to the shift in the liquid centroid inside the tank; as the liquid filling rate increases, the lateral stability of the tank trucks deteriorates slightly.

A new Hermite finite element for nonlinear Kirchhoff rods: The plane case

AbstractThis article presents the formulation of a finite element method for nonlinear Kirchhoff rods, based on a interpolation of the rod's geometry in terms of Hermite shape functions. The critical use of the same interpolation scheme for both the geometry and the kinematics of the rod is shown to lead to the correct invariant properties of the final numerical formulation, thus leading to the correct resolution of the fundamental equilibrium relations along it (balance of forces and moments). The so‐called “self‐straining” is completely avoided. Several numerical examples are presented illustrating the adequacy of the proposed formulation for the analysis of thin rods undergoing large finite deformations.

Online Identification of Aerodynamic Parameters of Experimental Rockets Based on Unscented Kalman Filtering

Online identification of aerodynamic parameters of experimental rockets was completed based on unscented Kalman filtering (UKF). Numerical simulation, hardware-in-the-loop (HIL) simulation, and flight tests were conducted. The identification error of aerodynamic force in numerical simulation and HIL simulation is within 2%. For flight test data, trajectory reconstruction was performed using the identified aerodynamic forces, and the results showed that the identification results were more accurate than the interpolation table calculation results. The flight test identification results show that the identification method can complete parameter online identification under the conditions of limited performance of onboard computers, real sensor errors, and servo response. The approximate linear correlation between α and δe and the reason for their formation from the moment balance were analyzed. It was pointed out that when the recognition sampling period is long, this phenomenon will affect the identification of parameters, and a solution is proposed.

Mathematical Modeling for the Optimal Cost Design of Circular Isolated Footings with Eccentric Column

This article shows a model for the design of circular isolated footings and the column placed anywhere in the footing under minimum cost criteria. Some designs for obtaining the diameter, effective depth, and steel areas of the footing under biaxial bending assume the maximum and uniform pressure at the bottom of the footing supported on elastic soils. All these works consider the column placed at the center of the footing. Three numerical problems are given (each problem presents four variants) to determine the lowest cost to design the circular footings under biaxial bending. Problem 1: Column without eccentricity. Problem 2: Column with eccentricity in the direction of the X axis of one quarter of the diameter of the footing. Problem 3: Column placed at the end furthest from the center of the footing on the X axis. The results are verified by the balance of moments, one-way shear or shear and two-way shear or punching. The new model shows a saving of 17.92% in the contact area with soil and of 31.15% in cost compared to the model proposed by other authors. In this way, the proposed minimum cost design model for circular footings will be of great help for the design when the column is placed on the center or edge of the footing.

A kinematic method for generating earthquake sequences

Computational earthquake sequence models provide generative estimates of the time, location, and size of synthetic seismic events that can be compared with observed earthquake histories and assessed as rupture forecasts. Here we describe a three-dimensional probabilistic earthquake sequence model that produces slip event time series constrained across geometrically complex non-planar fault systems. This model is kinematic in nature, integrating the time evolution of geometric moment accumulation and release with empirical earthquake scaling laws. The temporal probability of event occurrence is determined from the time history of geometric moment integrated with short-term Omori-style rate decay following each earthquake achieving long-term time-averaged moment balance. Similarly, the net geometric moment monotonically controls the probability of event localization, and seismic events release geometric moment with spatially heterogeneous slip on three-dimensional non-planar fault surfaces. We use this model to generate a synthetic earthquake sequence on the Nankai subduction zone over a 1,250-year-long interval, including 700+ MW=5.5−8.5 coseismic events, with decadal-to-centennial scale quiescent intervals quasi-periodic great earthquake clusters followed by aftershock sequences.

Analysis of the Drive Torque for the Spiral Pipe Section of an Earth Pressure Balanced Shield Tunnel Screw Conveyor

The driving torque of the shield machine is intricately linked to the soil silo muck load and the mechanical properties of both the muck and the spiral structure. Considering the shield screw conveyor’s mechanical structure and operational conditions, based on the momentum moment balance conditions, the separate calculation method was used to derive the spiral driving torque in the helical casing, the friction torque in the bearing and the friction torque of the sealing ring through mechanical analysis, and finally a torque calculation expression for the spiral pipe section was established. The research results provide technical guidance for the design and manufacture of shield screw conveyors and safe tunneling during construction.

Research on the Anti-Swing Control Methods of Dual-Arm Wheeled Inspection Robots for High-Voltage Transmission Lines

This paper presents an anti-swing control method to prevent situations where inspection robots detach and fall off transmission lines during obstacle crossing due to excessive swing angles caused by the rotation of the robot around the transmission line. Firstly, an obstacle-crossing model for the inspection robot was constructed and the causes of robot swinging phenomena were analyzed, in addition to their impact on obstacle crossing stability. By combining this with the obstacle-crossing model, a moment balance equation was established for the inspection robot. This equation can be used to solve mapping relationships between body offset and the tilt angle of transmission line gripping arms. We propose an anti-swing control strategy by adjusting the angle of the transmission line gripping arm’s pitching joint to make the body offset approach zero, and by utilizing the advantages of fuzzy logic in the fuzzy PID algorithm compared with the traditional PID algorithm, it can adaptively avoid the occurrence of robot swinging phenomena. The experimental results of obstacle-crossing experiments under no wind and wind turbulence conditions indicated that the proposed anti-swing control method in this study can effectively keep the body offset to within 3 mm. Compared with the methods of not using anti-swing control and using traditional PID anti-swing control, in the absence of wind effects, the peak values of body offset were reduced by 96.53% and 18.85%, respectively. Under the influence of wind turbulence, the peak values of body offset were reduced by 97.02% and 27.12%, respectively. The effectiveness of the anti-swing control method proposed in this paper has thus been verified.

Model tests and numerical simulation of overtopping-induced breach process of the asphalt concrete core dam

Although asphalt concrete core dams have been widely constructed, the mechanism of overtopping-induced dam breaches during catastrophic floods remains unclear, especially concerning the structural failure process of the core wall. This study utilizes a flume model test system to examine the overtopping-induced breach process of an asphalt concrete core dam based on the Sheyuegou Dam breach case in Xinjiang, China. The model tests showed the continuous erosion of dam shell material and structural failures of the core wall during dam breaching, highlighting the significant impact of the erosion-resistant asphalt concrete core wall on the dam breach process. The overtopping breach process of an asphalt concrete core wall dam can be divided into three stages: the asphalt concrete core wall is gradually exposed by backward erosion of the dam shell material until the first structural failure occurs; one or multiple structural failures of the core wall happen due to breach enlargement by continuous erosion of dam shell material until peak breach flow is reached; multiple structural failures of the core wall take place as the breach in the dam shell deepens and widens until breach morphology stabilizes. A numerical model is developed to simulate the overtopping-induced breach process of the asphalt concrete core dam based on the breach model tests. This model utilizes a soil erosion formula to estimate the dam shell material's erosion rate and calculate the exposed length of the asphalt concrete core wall. In addition, the moment balance method is employed to determine the overturning moment and length at each structural failure and the overturning instances of the exposed core wall due to hydrodynamic force and soil pressure. A notable feature of the numerical model is its ability to depict the coupled effects of soil erosion and structural failures of the asphalt concrete core wall during dam breaching. This numerical model is applied to a back analysis of the Sheyuegou dam breach process. The comparison between measured and calculated results indicated that the breach hydrograph and breach evolution process accurately represent the actual breach process of the Sheyuegou dam, with the relative errors of essential dam breaching parameters remaining within ±25 %. Sensitivity analysis showed that the thickness variation of the asphalt concrete core wall significantly influences the dam breach process, with the order of impact on critical breaching parameters being time to peak, final breach size, and peak breach flow. The results provide valuable insights into the simulation of the overtopping failure process of asphalt concrete core dams.

Present-day crustal movement and seismic moment balance on major active faults around the easternmost segment of the Kunlun fault, Tibetan Plateau, China

After the 2021 Ms 7.4 Madoi, China earthquake located south of the eastern Kunlun fault, the coseismic Coulomb stress changes show that the earthquake potential is enhanced towards the easternmost segment of the Kunlun fault. Before the 2008 Mw 7.9 Wenchuan, China earthquake, the easternmost segment of the Kunlun fault is considered to being a region with the highest frequency occurrence of moderate-to-strong earthquakes in mainland China, where there are still at least three seismic gaps at present, indicating an urgent earthquake hazard. The tectonic deformation pattern is closely related to the development and occurrence of earthquakes. In this study, we collect all the available GPS data to obtain a crustal movement velocity field with high precision and high resolution by removing nontectonic effects within the study area. The GPS velocity profile and two-dimensional strain rates are then derived from the updated GPS velocities to analysis the characteristics of crustal deformation. Our results demonstrate that the Longriba fault zone slips predominantly right-laterally with the rate of 5.2 ± 0.5 mm/yr and the crustal shortening rate is ∼0.5 mm/yr across the Longriba and Longmenshan faults. Along with notable crustal extension and contraction, the principal strain rate field is distributed in a wide area on the northwest part of the Longmenshan fault, and decreases southwestward along the Longmenshan fault zone. In addition, we provide the time series of 8 campaign GPS stations which have never been published before. Moreover, the moment deficit estimate is a well-established way of assessing the earthquake hazard at a specific fault. Accompanying with the inverted slip rates and locking depth, we estimate the rates of moment accumulation on major faults and compare them with the seismic moment released on each fault derived from the Chinese historical earthquake catalog which extends for more than 2000 years in many regions. We find that the moment deficit is mainly concentrated on the Longriba fault with a value of 4.18 × 1017 Nm/yr. The Longriba fault have accumulated enough seismic energy to generate one Mw > 7.7 earthquake on it, or two Mw > 7.5 earthquakes on its two branches in the future. This study is an essential indicator for understanding the present-day tectonic deformation pattern in the Tibetan Plateau and is also helpful for seismic hazard assessment.

Combined control algorithm based on synchronous reinforcement learning for a self-balancing bicycle robot

In this paper, balance control of a bicycle robot is studied without either a trail or a mechanical regulator when the robot moves in an approximately rectilinear motion. Based on the principle of moment balance, an input nonaffine nonlinear dynamics model of the bicycle robot is established. A driving velocity condition is proposed to maintain the robot balance. The nonaffine nonlinear system is transformed into an affine nonlinear system by defining the equivalent control. Subsequently, a feedback linearization controller is designed for the equivalent control. We design a combined control algorithm of synchronous policy iteration based on the actor–critic architecture. The actor neural network (NN) is designed based on the feedback linearization control law. Weight tuning laws for the critic and actor NNs are proposed. The system closed-loop stability and convergence of the NN weights are guaranteed based on the Lyapunov analysis. The optimality of the equivalent control policy is guaranteed. To satisfy the driving velocity condition, the values of the steering angle and driving velocity are determined based on the optimal equivalent control. The effectiveness of the proposed algorithm is verified through simulations and real experiments.

Theoretical prediction and test validation for frictional action of stacked steel disk springs with low initial cone angle

To examine the frictional action of stacked disk springs with low initial cone angle, axial compression tests were conducted by varying sizes and stacked forms of springs. Each stacked form exhibited stable and predictable behavior and the increase of parallel springs improves frictional dissipation. Lubricating greases can reduce but not eliminate the frictional action. The finite element analysis (FEA) employing friction coefficients from 0.2 to 0.3 can match test results on the whole. Verifications show that some existing predictions, except for the prediction from the standard, can well reflect the frictional action between the end plates and disk springs. Besides, convenient formulas to correctly reflect the frictional action between parallel springs are still needed due to existing theoretical models with either low precision or implicit and complicate calculation of relative sliding deformations between parallel springs. Therefore, based on a method employing either the moment balance or the energy balance, theoretical models and convenient formulas to predict the frictional action for the stacked springs in parallel were proposed. Furthermore, a formula to comprehensively consider the frictional action for springs stacked in both parallel and series was given. The effectiveness of the proposed formulas was verified by comparing with both the FEA and the test results. In addition, possible contacts between springs and the control bar would induce additional frictional actions, which can be compensated in some degree by appropriately adjusting the friction coefficients. Equivalent coefficients that can be employed in the formula of the standard to improve precision were provided.

A theoretical calculation method based on nonlinear analysis of offshore rigid monopile on sandy slopes under combined loading

This study proposes a nonlinear analytical method to predict the response of combined loaded offshore rigid monopiles near sandy slopes. Considering the slope effect, the method discusses the ultimate soil resistance before and behind the pile separately. The method assumes that the subgrade reaction modulus varies nonlinearly with relative density but linearly with depth. The equilibrium equation for the pile-soil system is obtained from the balance of forces and moments. By analyzing four mechanical models of rigid monopiles under combined loading and selecting three of them as the basis, a failure mode determination method is provided. The accuracy of this method is verified by comparing with indoor model test, 3D FEA model test and centrifugal test.

Thrust enhancement and degradation mechanisms due to self-induced vibrations in bio-inspired flying robots

Bio-inspired flying robots (BIFRs) which fly by flapping their wings experience continuously oscillating aerodynamic forces. These oscillations in the driving force cause vibrations in the motion of the body around the mean trajectory. In other words, a hovering BIFR does not remain fixed in space; instead, it undergoes oscillatory motion in almost all directions around the stationary point. These oscillations affect the aerodynamic performance of the flier. Assessing the effect of these oscillations, particularly on thrust generation in two-winged and four-winged BIFRs, is the main objective of this work. To achieve such a goal, two experimental setups were considered to measure the average thrust for the two BIFRs. The average thrust is measured over the flapping cycle of the BIFRs. In the first experimental setup, the BIFR is installed at the end of a pendulum rod, in place of the pendulum mass. While flapping, the model creates a thrust force that raises the model along the circular trajectory of the pendulum mass to a certain angular position, which is an equilibrium point and is also stable. Measuring the weight of the BIFR and the equilibrium angle it obtains, it is straightforward to estimate the average thrust, by moment balance about the pendulum hinge. This pendulum setup allows the BIFR model to freely oscillate back and forth along the circular trajectory about the equilibrium position. As such, the estimated average thrust includes the effects of these self-induced vibrations. In contrast, we use another setup with a load cell to measure thrust where the model is completely fixed. The thrust measurement revealed that the load cell or the fixed test leads to a higher thrust than the pendulum or the oscillatory test for the two-winged model, showing the opposite behavior for the four-winged model. That is, self-induced vibrations have different effects on the two BIFR models. We felt that this observation is worth further investigation. It is important to mention that aerodynamic mechanisms for thrust generation in the two and four-winged models are different. A two-winged BIFR generates thrust through traditional flapping mechanisms whereas a four-winged model enjoys a clapping effect, which results from wing-wing interaction. In the present work, we use a motion capture system, aerodynamic modeling, and flow visualization to study the underlying physics of the observed different behaviors of the two flapping models. The study revealed that the interaction of the vortices with the flapping wing robots may play a role in the observed aerodynamic behavior of the two BIFRs.

A Coupled‐Dipolar Plasmonic Antenna for Enhanced and Directional Emission from a Single NV Center at the Generalized Kerker Condition

AbstractPlasmonic antennas are widely used to achieve substantial emission rate enhancement. These antennas suffer from significant absorption losses that preclude the observation of Kerker conditions in such systems. The perfect balancing of the Mie‐scattering moments in an antenna at the generalized Kerker condition provides radiation directionality to its far‐field scattering pattern and zero absorption losses, a situation not achievable for a plasmonic system. Here, using both theoretical and computational approaches, the superposition of Mie‐scattering moments induced by coupling two individual silver (Ag) cylinders in a coupled‐dipolar plasmonic antenna is discussed. This results in the balancing of multipolar moments to a large extent with unidirectional scattering and hence the generalized Kerker condition in a plasmonic system. By placing a nanodiamond‐based single NV‐ center in the plasmonic gap‐cavity formed between the two Ag cylinders, >300 times Purcell enhancement is achieved with improved emission directionality leading to 80% collection efficiency. The proposed coupled‐dipolar plasmonic antenna is well suited for generating bright single photon emissions with a GHz emission rate, which is helpful for quantum photonic applications.

A Generic Model for Benchmark Aerodynamic Analysis of Fifth-Generation High-Performance Aircraft

This paper introduces a generic model for the study of aerodynamic behaviour relevant to fifth-generation high-performance aircraft. The model design is presented, outlining simplifications made to retain the key features of modern high-performance vehicles while ensuring a manufacturable geometry. Subsonic wind tunnel tests were performed with force and moment balance measurements used to develop a database of experimental validation data for the platform at a freestream velocity of 20 m/s. Numerical simulations are also presented and validated by the experiments and further employed to ensure the vortex behaviour is consistent with contemporary high-performance platforms. A sensitivity study of the computational predictions from the turbulence modelling approach is also presented. This geometry is the first in a suite of representative aircraft geometries (the Sydney Standard Aerodynamic Models), in which all geometries, computational models, and experimental data are made openly available to the research community (accessible via this link: https://zenodo.org/communities/ssam_gen5/) to serve as validation test cases and promote best practices in aerodynamic modelling.