Moment Equilibrium Research Articles

Fundamental issues of the strength of reinforced concrete slabs during punching

Introduction. The calculation model of the strength of slabs during punching, adopted in domestic regulatory documents, contains a number of contradictions to the physical side of the process. So it is known from experience that even before the moment of destruction, many cracks develop in concrete. Therefore, its tensile strength, which is the basis of the current model, is exhausted long before the destruction of the structure. The current model does not take into account the longitudinal reinforcement of the slabs, which is one of the main factors in ensuring strength during penetration. There are similar disadvantages in foreign models. The accuracy of normative calculation methods, both domestic and foreign, is low. Aim. Creation of a method for calculating of the slabs for punching, which correctly takes into account all known features of the structure and has high accuracy. Materials and methods. The method of calculating of the strength of slabs for penetration is considered, which is based on the condition of equilibrium of moments of external and internal forces, in contrast to the normative method, which considers the equilibrium of projections of all forces on the vertical axis. Results. A calculation method has been developed that does not contradict the known experimental data on the operation of slabs during punching. It was possible to correctly take into account the work of the longitudinal reinforcement of the slab. The high accuracy of the proposed calculation method is shown. Conclusions. The conducted research allows us to take a fresh look at the essence of the punching process. The mechanism of destruction, which has fundamental differences, is considered. The proposed calculation method allows us to obtain results comparable in accuracy with the best numerical models.

Research on intelligent optimal allocation control strategy for stability and braking of heavy tyre blowout vehicle

The traditional control strategy mainly compensates and corrects the driving state of heavy vehicles with a tyre blowout, and rarely considers the need for emergency braking. It is also difficult to effectively coordinate the problems of lateral yaw, slip and tailspin, and longitudinal braking performance degradation. For this, an intelligent optimization allocation control strategy combining stability control and braking control is innovatively designed in this article. The joint simulation model for heavy tyre blowout vehicles is built based on the Dugoff tyre blowout model and the TruckSim vehicle model. A linear quadratic form regulator stable control based on the particle swarm optimization algorithm optimization is used to dynamic equilibrium of the additional yaw moment generated by the vehicle tyre blowout. A logic threshold braking control based on adaptive adjustment is adopted to achieve an ideal braking effect for the vehicle. In order to simultaneously consider the stability and braking performance of vehicles with blowout tyre, a braking force distribution strategy and a fuzzy optimization allocation algorithm are proposed to achieve coordination of lateral and longitudinal control strategies. The results indicate that intelligent optimized allocation control can effectively correct the deviation trajectory of a heavy tyre blowout vehicle, enabling it to achieve rapid braking while maintaining stability.

Anthropomorphic modular gripper finger actuated by antagonistic wire and shape-memory alloy (SMA) springs

Abstract. The traditional underactuated grippers can only passively adapt to the contour of the object, and the passive contact process may lead to the object slipping, affecting the stability of the grasping process. In this paper, an anthropomorphic modular gripper finger actuated by antagonistic wire and shape-memory alloy (SMA) springs, which can actively control the grasping morphology according to the characteristics of the objects to be grasped, is proposed. The wire drive simulates the flexor muscle, and the SMA and reset springs simulate the extensor muscles of the finger, which antagonistically control the grasping morphology of the finger. It is more in line with the grasping characteristics of the human hand. According to the moment equilibrium principle of the finger joints, the deformation model of the gripper is established, the influence of the wire tension and the equivalent stiffness of the finger joints on the grasping morphology is analyzed, and the theoretical joint angle results are verified by the Adams simulation; finally, the experimental system of the gripper is constructed, and the verification of the deformation morphology of the single finger and the gripper's enveloping–grasping experiments is completed. The results show that according to the contour size of the object, by actively controlling the wire force of the gripper and the equivalent stiffness of the interphalangeal joints, the enveloping–grasping action of different objects can be completed and the stable grasping of objects of different shapes and sizes can be realized.

Analysis of Aerostatic Performance of a Flexure Pivot Tilting Pad Air Journal Bearing

Abstract Aerostatic performance of a flexure pivot tilting pad air journal bearing is examined with several numerical simulation under various working conditions. The air pressure distribution in the bearing clearance is obtained by solving the Reynolds equation with the finite difference method (FDM). The code consists of 3 main parts: mass flow rate equilibrium, moment equilibrium, and shaft equilibrium. They are used to study the gas pressure at the downstream of the nozzles, the motion of pads, and the position of the shaft in the bearing, respectively. Code accuracy is verified by comparing the results with those in other articles. This work lays the foundation for future research.

The Character of Couples and Couple Stresses in Continuum Mechanics

In this paper, the concepts of moments and couples in mechanics are examined from a fundamental perspective. Representing a couple by its moment vector is very useful in rigid body mechanics, where the states of internal stresses and deformation are not studied. This is because only the moment of couples appears in the governing equation of moment equilibrium. On the other hand, when considering the state of internal stresses and deformation in continuum mechanics, not only the moment of couples but also the line of action of their constituent parallel opposite forces must be specified. In defining a well-posed problem for a continuum, including the governing equations of moment equilibrium or motion, boundary conditions, and constitutive relations, only the moment of couples (e.g., body couples, couple tractions, couple stresses) appear without specifying the line of action of the constituent parallel forces. Nevertheless, the physical state of stress and deformation in the continuum must be unique and determinate. Therefore, this physical requirement imposes some restrictions on the form of body couples, couple tractions, and couple stresses. Here, the uniqueness of interactions in the continuum is used to establish that the continuum does not support a distribution of body couples or a distribution of surface twisting couple tractions with normal moments. Furthermore, the mechanism of action of the couple traction as a double layer of shear force tractions is established, along with the skew-symmetric character of the couple stress moment tensor.

ASSESSMENT OF TRANSIENT VIBRATION EFFECTS OF A ROCKING STRUCTURE ON TWO-PARAMETER UPLIFTING FOUNDATION MODEL

This study is on assessment of transient vibration of a rocking structure on two-parameter uplifting foundation model. This foundation model, Filonenko-Borodich (F-B) considers effect of continuity and interactions of the structure with the surrounding foundation surface. The foundation model aids uplift because of its elastic and flexible nature. During ground movement, some forces are generated which cause foundation to vibrate, rock and sometimes uplift due to increasing upward forces and then leading to reduction in the spring stiffness and increase in soil flexibility. This sometimes causes upward trend in the structural response which might affect structural integrity and stability. The use of damping and its effects on the structure response considering uplift are evaluated for a structure on two-parameter foundation. Equations describing the motion were developed by summing forces acting on the structure and foundation, considering equilibrium of moments for the conditions of before uplift and during uplift of the system in accordance using Newton’s second law of motion, D’Alembert’s principles. The resulting equations were solved by applying them in Duhamel Integral form and Simpson’s method used for the numerical solution for the structure responses. The result showed an upward trend in the structural responses during uplifting hence uplift of building foundation is not always beneficial.

Deformation, shape transformations, and stability of elastic rod loops within spherical confinement

Mechanical insight into the packing of slender objects within confinement is essential for understanding how polymers, filaments, or wires organize and rearrange in limited space. Here we combine theoretical modeling, numerical optimization, and experimental studies to reveal spherical packing behavior of thin elastic rod loops of homogeneous or inhomogeneous stiffness. Across varying loop lengths, a rich array of configurations including circle, saddle, figure-eight, and more intricate patterns are identified. A theoretical framework rooted in the local equilibrium of force and moment is proposed for the rod loop deformation, facilitating the determination of internal and contact forces experienced by the rods during deformation. For the confined homogeneous rod loops, their stable and metastable configurations are well described using proposed Euler rotation curves, which offer a concise and effective approach for configuration prediction. Moreover, formulated analysis on the stability and critical force for homogeneous rod loops on great circles of the spherical confinement are performed. For inhomogeneous rod loops with two segments of differing stiffness, the stiffer segment exhibits less deviation from the great circle, while the softer segment undergoes more pronounced deformation. These findings not only enhance our understanding of buckling and post-buckling phenomena but also offer insights into filament patterning within confining environments.

A virtual wind tunnel for deforming airborne wind energy kites

This paper presents a quasi-steady simulation framework for soft-wing kites with suspended control unit employed for airborne wind energy. The kites are subject to actuation-induced and aero-elastic deformation and are described by a coupled aero-structural model in a virtual wind tunnel setup. Key contributions of the present work are a kinetic dynamic relaxation algorithm and a procedure to define a physically consistent initial state. For symmetric actuation, the kite is pitch-statically stable and the simulations converge to a static equilibrium state. Most soft-wing kites are not roll-statically stable and do not find a static equilibrium without a symmetry assumption, as this introduces non-zero roll- and yaw moments. Another important contribution is the introduction of a steady circular flight state that enables convergence without a symmetry assumption. By neglecting gravity, the kite can fly in a perfectly circular turning motion around the wind vector with a constant radius and constant rotational velocity without requiring active control input. In an idealized wind-aligned tether case, the difference in aerodynamic- and centrifugal force application centers makes it impossible to achieve both a force- and moment equilibrium. This was resolved by including an elevation angle that introduces a radial tether force component, which introduces a centrifugal and aerodynamic force difference. Therefore, an operating point with roll equilibrium can be found where the kite finds a static equilibrium, enabling the first quasi-steady simulations of turning flights. Simulated quantifications of soft-wing kite turning behavior, i.e., turning laws, contribute to better kite- and control design.

Developing Dynamic System Responses Model Based on Nanotechnology by Incorporating the Finite Element Analysis

The dynamic model of complex structure has set incredible progression with the use of finite element analysis (FEA), especially in the field of vibration control and nanotechnology. Main focus of this research is to conduct a frequency analysis in ANSYS and a state space model of the beam under the platform of MATLAB. This allowed a system to develop an active dynamic model for vibration control. To enhance test and analysis of the cantilever beam of Aluminium 6061T6, a new method has been proposed to predict the dynamic response of a cantilever beam under sinusoidal base excitation. This was achieved by creating an analytical model for the cantilever beam using moment and force equilibrium equations. The authenticity of the proposed method was made by comparing the results with experimental data. Additionally, to control vibration, a Proportional-Integral-Derivative (PID) controller was developed using the system model. The FEA in the ANSYS platform provided a cantilever beam model. Also, its mathematical modelling has been done. The proposed method utilizes a novel disturbance rejection control scheme that eliminates an unknown disturbance. Experimental results indicate that the control system results in gradually decreased beam vibration amplitude. The state space approach discussed in the work could be a valuable tool for studying the behaviours of nanomaterials.

The geometry of the equilibrium of forces and moments in shells

AbstractWe demonstrate that the internal forces and moments in a shell structure can be described by 4 vectors in 3 dimensional space which could be used to express the equilibrium of a shell graphically. The internal forces and moments described by 2 of the 4 vectors actively carry imposed loads and imposed couples, while the other 2 describe ‘redundant’ internal forces and moments that are purely in equilibrium with themselves. Nevertheless redundant stresses and moments are important in controlling internal stresses and satisfying boundary conditions. We show that forces and moments ‘flow’ across a shell in exactly the same way that fluid flows, with a combination of irrotational flow and incompressible flow. The aim is that these ideas can help in the initial design of those shell structures which have to rely on bending moments in addition to membrane action in supporting loads, and also in the interpretation of results from an analysis using the finite element method. We demonstrate the use of the technique for the design of an umbrella structure like those built by Amancio Williams.

Joint Stress Analysis of the Navicular Bone of the Horse and Its Implications for Navicular Disease.

The horse's navicular bone is located inside the hoof between the deep flexor tendon (DDFT) and the middle and end phalanges. The aim of this study was to calculate the stress distribution across the articular surface of the navicular bone and to investigate how morphological variations of the navicular bone affect the joint forces and stress distribution. Joint forces normalised to the DDFT force were calculated from force and moment equilibria from morphological parameters determined on mediolateral radiographs. The stress distribution on the articular surface was determined from the moment equilibrium of the stress vectors around the centre of pressure. The ratio of the proximal to the distal moment arms of the DDFT, as well as the proximo-distal position and extent of the navicular bone, individually or in combination, have a decisive influence on the position and magnitude of the joint force and the stress distribution. If the moment arms are equal and the bone is more proximal, the joint force vector originates from the centre of the joint surface and the joint load is evenly distributed. However, in a more distal position with a longer distal moment arm, the joint force is close to the distal edge, where the joint stress reaches its peak. Degenerative navicular disease, which causes lameness and pathological changes in the distal portion of the bone in sport horses, is likely to be more severe in horses with wedge-shaped navicular bones than in horses with square bones.

Design and Analysis of Modular Gripper Finger Actuated by Antagonistic Wire and Shape Memory Alloy Springs

The traditional underactuated grippers can only passively adapt to the shape contour of the object to complete the envelope or grasping action. In this paper, a wire and shape memory alloy (SMA) spring‐based differential drive gripper finger are proposed, which can actively control the grasping morphology according to the objects to be grasped, and are more in line with the grasping characteristics of the human hand. The wire simulates the flexor muscle, and the SMA and reset springs simulate the extensor muscle of the finger, which together control the finger morphology. According to the principle of moment equilibrium, the static mechanical model of the gripper is established, and the influence of the wire driving force and the equivalent stiffness of the finger joints on the grasping morphology are analysed, and the theoretical grasping force is verified by ADAMS simulation. A comparative analysis of the grasping force between the non‐active and active morphology control is presented. Finally, the experimental system of the gripper is constructed, and the verification of the deformation morphology of the single finger and the gripper’s grasping experiments is completed. The results show that according to the contour size of the object, by actively controlling the wire force of the gripper and the equivalent stiffness of the joints, the enveloping or grasping action for different objects can be completed. In addition, the grasping force of the finger can be improved by actively controlling the grasping morphology.

Modeling the joint rotational stiffness of a radial-type flight intersection joint: An analytical approach, numerical simulation, and experimental validation

Joint rotational stiffness (JRS) of a flight intersection joint (FIJ) and its accurate quantification play an essential role in studying the dynamic modal characteristics of a flight vehicle. This JRS of a FIJ is mostly determined through elaborate experiments due to the non-availability of a reliable predictive model. Therefore, in this paper, an analytical model is proposed to evaluate JRS of a radial type FIJ when subjected to external bending moment. In this model, at first, the tensile and compressive part of the FIJ section is identified by determining the neutral axis position. The respective part's contributing stiffness is then estimated by employing a spring-mass model. Later, the JRS expression is derived from the moment equilibrium condition and expressed as a function of the stiffness of the tensile and compressive part and neutral axis position. Subsequently, finite element analysis (FEA) is conducted with different numbers of screws, followed by detailed experimental investigations. The proposed analytical model is validated with the results from FEA and experiments for different screw configurations of FIJ. Further, the proposed model is extended to account for the effect of joint clearances on the JRS and the corresponding moment-rotation characteristics of the FIJ.

Coned disk spring with friction or restraint at its edges: Explicit solution and experimental study

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials.

Modeling and Testing for Slotted Disk Springs Considering Linearly Gradient Thickness and Friction

The slotted disk spring has been widely used given its nonlinear characteristics. However, the number of studies on them is limited, and the influences of nonuniform thickness have not been investigated theoretically and experimentally. Additionally, the hysteresis caused by friction has been neglected in most studies. By introducing the symmetric friction condition and the dimensionless thickness variation parameter, the present study establishes a mathematical model for slotted disk springs with linearly graded thickness. By treating the slotted segment as a number of cantilever beams with both a linearly gradient thickness and width, a new analytical formula is developed to characterize the load–deflection of slotted disk springs based on the moment equilibrium equation. The proposed model allows the direct quantification of the influences of the thickness variation parameter and the symmetric friction condition on the load–deflection characteristics. To validate the proposed model, slotted disk springs with different parameter configurations are designed and tested. Comparisons between measured and theoretical results illustrate that the proposed model can effectively describe the load–deflection characteristics of slotted disk springs with both uniform thickness and linearly gradient thickness. Due to the hypothetic linear variable width of slotted segments, the proposed model has a better performance in predicting slotted disk springs with rectangular slots.

Symplectic stiffness method for the buckling analysis of hierarchical and chiral cellular honeycomb structures

Structure-function-material integration design based on the buckling instability of flexible cellular structures has attracted much attention. According to the reversible and repeatable characteristics of buckling deformation, phonon bandgap switches, the autonomous drive of soft robots, programmable logic controllers, and reusable spacecraft landing buffer devices can be designed. Based on the Hamiltonian variational principle and symplectic eigen expansion, a theoretical analysis model of the symplectic stiffness method is established, and analytical expressions for the stiffness of several typical buckling modes of elastically supported beams are obtained. The analytical closed-form expressions for the macroscopic buckling strength of honeycombs are obtained according to the bending moment equilibrium equation. The buckling modes of regular hexagonal, hierarchical hexagonal, and tri-chiral honeycombs are obtained by numerical simulation and experimental verification, and some novel higher-order modes are observed. Uniaxial compression experiments reveal that these higher-order buckling modes can be triggered by adjusting the geometric parameters of the unit cells. The high agreement between experimental, numerical, and existing literature results for the failure surfaces of cellular structures verifies the effectiveness of the proposed symplectic stiffness method. In a word, the buckling modes can be designed to meet different functional requirements by changing the initial configuration of flexible cellular structures. This provides a new idea and theoretical guidance for the development of metamaterials and structures with tailored properties.

Nonlinear vibration of pinned FGP-GPLRC arches under a transverse harmonic excitation: A theoretical study

The non-linear in-plane primary resonance of functionally graded porous (FGP) sinusoidal arches made of graphene platelet reinforced composites (GPLRC) subjected a transverse harmonic excitation is investigated in this paper. To eliminate the coupling of inner forces and facilitate the derivation, the neutral plane-based equations of motion are established considering the force and bending moment equilibrium conditions. By utilizing an incremental harmonic balance (IHB) technique, the frequency response features, dynamic time history, and limit cycle under primary resonance and 1/2 super-harmonic resonance are determined. FE analysis is conducted to verify the accuracy of the presented results. To further examine the computational efficiency of IHB procedure, a fourth order Runge–Kutta method is used to determine the structural responses as a counterpart. Comprehensive parametric studies are then carried out, particular focus is paid to the cases of material compositions, geometric properties, and dynamic parameters on the frequency response characteristics. It is found that the increasing porosity coefficient significantly exacerbates the left-inclined softening behaviors of the frequency response curves. On the contrary, the left-inclined effect continues to weaken as the GPL weight fraction gradually grows.

Slope stability analysis based on improved radial movement optimization considering seepage effect

Among various effecting factors, groundwater is commonly known as one of the major triggers for slope failures. Thus, it is great significant of considering the contribution from groundwater seepage in slope stability analysis. In this study, the effect from groundwater seepage are considered as the interaction force (infiltration force) between water and soil materials for static and moment equilibrium analysis. Based on Rigorous Janbu method, the implicit equations are determined for estimating the minimum factor of safety and locating the non-circular critical failure surface. A new metaheuristic algorithm, Improved Radial Movement Optimization (IRMO), was adopted to figure out such complex, nonlinear and constrained optimization problem due to its high precision and stability. The effectiveness of the proposed methodology is validated by four different cases including homogeneous and inhomogeneous slopes from the literature. Comparative studies in different optimization algorithms have been carried out to validate the stability and efficiency of proposed IRMO algorithm accordingly. The results indicate that proposed approaches could acquire a more acceptable and stable result with more efficient way in slope stability analysis considering seepage effect over several existing methods.

Determination of Passive Earth Pressure on a Cantilever Retaining Wall in a Narrow Foundation Pit Based on Logarithmic Spiral Sliding Surface

The distribution of passive earth pressure on a cantilever flexible retaining wall in a narrow foundation pit is significantly affected by the adjacent retaining wall and the width of the foundation pit. The deformation mode of the cantilever retaining wall rotating around the displacement zero point makes the soil layer below the displacement zero point retain a nonlimit passive state. The functional relationship between soil mechanical parameters and horizontal displacement in the nonlimit state region, considering the influence of displacement, is established. A new combined failure mode of the soil mass in the passive zone of the narrow foundation pit is proposed, which is the logarithmic spiral fracture surface in the nonlimit state region and the broken line fracture surface in the limit-state region. On this basis, a passive earth pressure calculation model of a narrow foundation pit is proposed and solved by differential layer method. The solution of the passive earth pressure coefficient strictly meets the static equilibrium conditions in vertical and horizontal directions as well as the moment equilibrium conditions. A numerical example is used to analyze the influence of the width of the foundation pit. The smaller the narrow foundation pit width, the greater the passive earth pressure in the lower soil layer and it even greatly exceeds the Coulomb earth pressure distribution. The earth pressure distribution acting on the lower part of the wall near the zero point of displacement decreases sharply and bends. The passive earth pressure distribution is calculated by the theoretical method and compared with the laboratory model test results as well as the engineering test results. It is found that the proper selection of the initial soil mechanical parameters affects significantly the magnitude and distribution of lateral pressure in the nonlimit state region. When the internal friction angle of soil φ0 is small, the lateral pressure in the lower nonlimit state area is relatively small. When both φ0 and δ0 are small, the pressure distribution is closer to the test results and the existing theoretical calculation results.

Assessment of residual stresses in welded T-joints using contour method

Welded T-joints are commonly used in manufacturing of stiffened panels or crossbeams. However, welding of web-to-flange joint induces residual stresses and distortions resulting in significant challenges during both manufacturing and service. These issues can ultimately impact the structural performance, including fatigue and stability, and lifetime of the weldment. The purpose of current paper is determining the distribution and magnitude of manufacturing-induced longitudinal residual stresses in welded T-joints. Influence of hot rolling, thermal cutting, prestressing, welding, etc. are all included using the so-called contour method. Deformed surfaces are measured using coordinate measuring machine after wire electrical discharge machining of specimens. An inverse linear elastic finite element analysis is carried out for assessing residual stresses after data smoothing. Two-dimensional longitudinal residual stress patterns are evaluated in representative cross-sections clearly indicating high stress peaks near the welds, even exceeding yield strength of the base material. In addition, longitudinal membrane residual stresses are determined based on through-thickness stresses. In addition, a simplified residual stress model, satisfying the requirement for equilibrium of internal forces and bending moments, is developed for welded T-joints with double-sided fillet welds based on contour method results.