Force Equilibrium Research Articles

Stability of the ‘Tensyudai’ of a Japanese castle under a long-term load

‘Tensyudai’ is the term used for the truncated masonry base that supports the main tower (Tensyukaku) of a Japanese castle. In response to concerns regarding the structural integrity and conservation of Tensyudai masonry walls, this study seeks to investigate the mechanism of their collapse and load capacity. A reduced-scale model of Tensyudai, based on Osaka Castle, was constructed and subjected to a vertical load test to evaluate its three-dimensional mechanical properties. This paper postulates a collapse mechanism, and the equilibrium of forces for the Sumiishi and Hiraishi sections of the Tensyudai is analysed, considering the arch effect. Experimental results are compared, using a series of equations to calculate the collapse burden (q c). Additionally, the safety factor is determined, based on the active earth pressures at various masses. The findings indicate that the safety factor of a standard Tensyukaku weight is approximately 25, which rises with increased Tensyukaku weight. Moreover, this study contributes to future research and preservation efforts for historical structures, by shedding light on the structural stability and safety of Tensyudai masonry walls. It can also provide basic data for considering the protection of other masonry wall structures from earthquakes.

Extremal stringy black holes in equilibrium at first order in $\alpha'$

We compute the first-order \alpha'α′ corrections to well-known families of heterotic multi-center black-hole solutions in five and four dimensions. The solutions can be either supersymmetric or non-supersymmetric, depending on the relative sign between two of the black-hole charges. For both cases, we find that the equilibrium of forces persists after including the \alpha'α′ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

Numerical investigation and modeling of sweep effects on inlet flow field of axial compressor cascades

Swept blades are widely utilized in transonic compressors/fans and provide high load, high through-flow, high efficiency, and adequate stall margin. However, there is limited quantitative research on the mechanism of the effect of swept blades on the flow field, resulting in a lack of direct quantitative guidance for the design and analysis of swept blades in fans/compressors. To better understand this mechanism, this study employs a reduced-dimensional force equilibrium method to analyze more than 1500 swept cascades data. Results verify that circumferential fluctuation terms are responsible for inducing radial migration in the inlet airflow field of the swept blade, resulting in variations in the incidence angle and consequently leading to changes in the characteristics of the swept blade. Thus, a combination of simple functions and machine learning is utilized to model the circumferential fluctuation terms and quantify the sweep mechanism. The prediction accuracy of the model is high, with coefficient of determination greater than 0.95 on the test set. When the model is applied in a meridional flow analysis program, the calculation accuracy of the program for the incidence angle is improved by 0.4° and 0.6° at the design and off-design conditions respectively, compensating for the program's original deficiencies. Meanwhile, the model can also provide quantitative guidance for the design of swept blades, thereby reducing the number of design iterations and improving design efficiency.

A Method Based on Fracture Mechanics to Investigate the Deformation of Reinforced Concrete Columns

In the use of non-linear structural performance models, including models that consider the critical over-performance at the failure stage, is very important when performing seismic calculations of reinforced concrete buildings and structures.The use of such models is especially important if the structures have primary damage caused by fire or corrosion, as well as mechanical damage caused by force factors. The purpose of this study is to develop an analytical model of the deformation of eccentrically compressed reinforced concrete columns by considering the failure stage, which includes processes such as peeling of the protective layer, reduction of the stability of the compressed reinforcement and softening of the encased concrete after reaching the design strength. , the existing models that describe the residual behavior of reinforced concrete structures under low cycle loading have been investigated. The models are analyzed considering monotonic curves, which are cyclic deformation boundaries. The model proposed in the research is constructed by analyzing the stages of the stress-strain state of a reinforced concrete column. At each stage, formulas are found for determining moment and curvature by solving equations of equilibrium of internal forces. Calculations based on the obtained model for a particular reinforced concrete column are carried out, monotonous diagrams are obtained, and a conclusion about the significant influence of the level of axial load on the character of deformation is made. On the basis of the obtained model, the construction of hysteresis diagrams under low-cycle loading is expected in the future.

Geometric Conformability of 3D Concrete Printing Mixtures from a Rheological Perspective

The effectiveness of 3D concrete printing (3DCP) relies on understanding the rheological properties of cementitious materials and their time-dependent evolution. These materials exhibit shear-thinning viscosity, an elastic region, and both static and dynamic yield stress, which are challenging to balance in 3DCP. Layer deformation can be caused by factors such as self-weight, the weight of subsequently deposited layers, and the stress induced by the nozzle pressing. Starting at the level of a single filament, the final geometrical conformity of a 3D-printed object is the sum of individual filament conformities. Hence, the control of layer deformation during the printing process is critical. The failure of 3D-printed objects can occur due to two primary mechanisms: material failure, which occurs when the material’s strength is exceeded, resulting in fracture or uncontrolled deformation; and stability failure, where the object cannot retain equilibrium of forces. These mechanisms often interact; extensive deformations resulting from material failure can lead to stability loss, or conversely, stability loss generates local excessive stresses leading to material failure. The governing mechanism depends on various factors, including material and process characteristics, as well as the transient nature of material properties, print strategy, and object design. With this in mind, this research aimed to broaden the understanding of the connection between rheological material properties—primarily yield stress—and the geometric conformability of printed objects. Experimental tests were conducted on pastes using a rheometer, and correlated mortars, allowing for the evaluation of realistic extrusion properties.

Potential field-based formation tracking control for multi-UGV system with detection behavior and collision avoidance

This paper investigates the time-varying formation tracking and collision avoidance problems for multi-unmanned ground vehicle (UGV) system which consists of omnidirectional vehicles on directed topology. To prevent the failure of collision avoidance caused by the lack of information interaction when the directed graph is not unilaterally connected, partial vehicles are elected as observers and their detection behaviors represented by sectors are realized by potential field and yaw control. Firstly, an improved repulsive potential field force is designed, and two composite potential field forces are proposed for single-to-single detection and single-to-multiple detection situations. Inspired by the equilibrium of forces, it is proven that the reconstructed potential field force which is not affected by the complexity of the collision situation can eradicate the local minima or deadlock states. Secondly, in order to generate detection behaviors according to a basic communication graph, an algorithm is put forward. Then, the protocol of position and velocity control, as well as the protocol of yaw control, are presented respectively. The former ensures the realization of formation tracking, while the latter, together with composite potential field forces, makes the detection behavior continuous. Moreover, according to Lyapunov-based theory, it is proven that the given method can achieve time-varying formation tracking and collision avoidance. Finally, simulations demonstrate the theoretical results.

A numerical model for calculating the impact-induced depression

Materials usually have a quasi–brittle behavior under impact loading, even the ductile materials when loading rate is high enough. In this paper, a new numerical model for calculating the transverse impact on a quasi–brittle target is developed and the theoretical deductions with a strict mathematic logicality are illustrated. Herein, the example of a stiff ball impacting a brittle fiber bundle is investigated and the issues of stress wave propagation, inertia force, energy transformation and stress equilibrium are considered. The numerical model that can describe the impacting procedure is derived. With timing, the deformation of brittle fiber bundle, the kinetic energy of stiff ball as well as their displacements are given. Thus, the overall perspective of the impacting procedure is calculated and analyzed. This work offers a physical illustration of impact events by developing a numerical model and displays the insights into the transient procedure, that will contribute to the development of impact mechanics for engineering.

Mechanical Analysis of Road Graben Slopes Based on Saturated-Unsaturated Seepage Theory

As the construction of mountainous highways continues to heat up, the stability analysis of road graben slopes becomes one of the current research hotspots. In this paper, based on the saturated-unsaturated seepage theory, the force analysis of the road graben slope under rainfall conditions and its laws are studied. Firstly, the damage mode of the road graben slope and its three damage stages of creeping deformation, sliding damage and tendency to stability are summarized according to the engineering practice and literature survey, and the right side of the road graben slope from K316+439 to K316+859 of Longlian Expressway is monitored, so as to amend the next theoretical analysis. The three stages of rainfall infiltration were analyzed, the state variables and material variables of soil water were selected according to the continuous medium theory and the soil water suction analysis was carried out. Based on the saturated-unsaturated seepage theory, the fluid-structure interaction mathematical model and soil moisture characteristic curve (SWCC) model under rainfall infiltration conditions were established, and the stress of the cutting slope under saturation conditions was analyzed. The experimental results show that for the soil at the foot of the slope, the infiltration depth of rainfall is limited due to the low permeability coefficient, and the change of seepage field is not obvious; the longer the rainfall is held, the deeper the infiltration depth is, and the rainfall will continuously replenish the groundwater, so the force on the slope of the road graben will increase continuously and finally reach the limit of damage. When the rainfall intensity is 5mm-h-1, the decline of stability coefficient for 48 h is 0.121; the initial stability coefficient of the slope is the largest when the dip angle of the weak interlayer is equal to 25∘, and the stability coefficient decreases rapidly with the rainfall time, and when the rainfall reaches 60 h, the stability coefficient tends to be stable and the equilibrium of the slope force no longer changes.

SpannEnD – a 3D geomechanical model of Germany for the prediction of the recent crustal stress state

Abstract. The recent crustal stress state is a crucial parameter in the search for a high-level nuclear waste repository. It is relevant not only for site selection and short-term stability during operation but also for predicting long-term safety. However, the level of knowledge in this regard is still limited in Germany. It is based on stress orientations and stress regime information from the World Stress Map (WSM) project and pointwise stress magnitude records. We present the results of a 3D geomechanical numerical model that improves the state of knowledge by providing a continuum-mechanics-based prediction of the recent crustal stress field in Germany. The model extends over an area of 1000×1250 km2, covering Germany and nearby regions. It contains 22 geological units, each parameterized with individual properties (density, Young's modulus and Poisson's ratio). We assume linear elasticity, and the finite element method is used to solve the equilibrium of forces. The model is calibrated with horizontal stress magnitude records and validated with additional data, for example, vertical stress magnitudes or data of the WSM project. Our model results are in a good agreement with a mean orientation of the maximum horizontal stress (SHmax) derived from the WSM, as indicated by a mean of the absolute differences of 12∘. Furthermore, the model results lie entirely within the standard deviation of the derived orientation of SHmax. Mean values of the absolute stress differences between calibration data and model results of 4.6 MPa for the minimum horizontal stresses (SHmin) and 6.4 MPa for the SHmax also show a good agreement. The model results can be used, for example, for the calculation of fracture potential, for slip tendency analyses or as boundary conditions for smaller local models. For smaller model volumes, where little or no stress information is available, it provides synthetic stress magnitude data that can be used for calibration. As such, the model provides a valuable starting point for the detailed assessment of stability at yet-to-be-determined siting regions for a high-level nuclear waste repository.

Dynamic thermomechanical analysis on stiffened composite plates with damage

The dynamic thermomechanical analysis on stiffened composite plates with damages are investigated in this article based on the extended layerwise method (XLWM) and three-dimensional finite elements method; a thermomechanical extended-layerwise/Solid-element method (TELW/SE) is established. In TELW/SE, the thermomechanical extended-layerwise method (TELW) and thermomechanical three-dimensional solid elements are used to simulate plate and stiffeners, respectively. The final governing equations are assembled by using the interface conditions to ensure the compatibility of displacements and temperature, together with the internal force equilibrium. Several typical damages in stiffened composite plates can be described accurately in the proposed method, such as delamination, transverse crack and stiffener/plate interface debonding.

Analytical and numerical study on absorption of viscoelastic multilayers with variable cross section and cavity

Polymeric layers or multilayers with air cavities or solid particles have considerable attenuation properties and can be tailored to have acoustic impedance close to water. So, many underwater sound absorbers are made from such multilayer structures. In this work, first, we present a transfer matrix method (TMM) based on force equilibrium to be used for variable cross-section viscoelastic multilayers with cavities. The method can be used for layers with various cavity designs; also, the outer boundary can be conical or any other axisymmetric shape. The formulation is derived for different outer impedance-matched boundary conditions. The study of anechoic coatings with periodic holes is then studied as a special case of the developed TMM. In this regard, the difference between the present formulation and related literature is explained and the TMM results are compared with numerical simulations which are performed using COMSOL. Moreover, the effect of cavity shape and bulk loss factor on the echo reduction properties of the coatings are investigated. It is concluded that for small cavity sizes and with an abrupt change of multilayer cross sections, the echo reduction values are more dependent on bulk loss factor, especially near the resonance frequency.

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.

Implications of reciprocity for the spectra of equilibrium and nonequilibrium Casimir forces

Implications of reciprocity for the spectra of equilibrium and nonequilibrium Casimir forces

IMPROVING SECONDARY SCHOOL STUDENTS’ REPRESENTATIONAL COMPETENCE IN FORCE AND MOTION CONCEPTS

verbally expressed laws, mathematical equations, diagrams, graphs, charts and animations involved in physics which are related to abstract concepts. One aspect of this competence with relevance to physics education is the students’ ability to understand the physics-specific representations in relation to their physical and real-world applications which encompass to static as well as dynamic entities. In this study, attention has been paid to developing, validating and utilizing a lesson-specific assessment tool to identify students’ difficulties in understanding such representations encountered in selected Grade 10 physics-related science lessons presently taught in Sri Lankan government schools, namely, Resultant force, Newton’s laws of motion, Friction and Equilibrium of forces. The tool has been administered as an online test for a sample of 72 selected Grade 11 students who have already completed the lessons in their schools at Grade 10. It consists of 28 multiple-choice questions. It showed a mean score of 52.65% with a standard deviation of 24.94%. The tool gave high reliability (Cronbach's alpha value of 0.795). By analyzing the students’ performance at individual questions of the tool it revealed that the students have certain difficulties in understanding the representations such as the inability to determine the line of action of a force related to a given real-world situation, inability to predict the nature of the motion of an object if the object is acted upon by a constant force continuously, inability to identify difference between the action force and the reaction force mentioned in Newton’s third law of motion which act in two distinct objects, and marking such forces in a free body force diagram. The extent to which the prescribed curriculum materials help the students to overcome these difficulties has been evaluated and some suggested teaching-learning activities have been proposed to improve the students’ representational competence.<p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0036/a.php" alt="Hit counter" /></p>

Improving shape formation under conditions of plane tensile stress

Thin-walled axisymmetric truncated parts made of sheet billets are actively used in rocket and aerospace engineering. Improvement to their shape formation, based on directed material thickness change will ensure the production of parts with minimum thickness variation. This will also enable aviation and space industry enterprises to attain leading positions, as well as reduce labor costs. This work studies the possibility of obtaining thin-walled axisymmetric parts of truncated tapered shape using one of the methods of sheet metal stamping under flat tensile stress conditions (flanging). The mechanism was identified and the analysis of the stress-strain state of the billet during deformation was carried out. This takes into account the minimizing of the difference between the specified and technologically possible thicknesses. A mathematical model was developed to consider the shaping method based on the process of flanging. Theoretical studies were based on the principles of the plastic deformation theory of sheet materials. This was achieved by the following factors: approximate differential equations of force equilibrium; equations of constraint; plasticity conditions; and fundamental constitutive relations under given initial and boundary conditions. The process of flanging was simulated using the LS-DYNA software package with the following initial data of a conical billet made of 12Kh18N10T steel: cone angle 16.4°, thickness Sbillet = 0.3 mm. The aim was to eliminate errors in designing a tool for future implementation of the method on a manufactured die tooling, as well as to confirm the theoretical conclusions on the selection of technological parameters and achieve minimal thickness variation. The steps of computer modeling are presented, indicating the main process parameters such as material model, mechanical characteristics of the workpiece material, type of elements, kinematic loads, conditions of contact interaction of elements with each other, etc.

Prestress design and geometric correction method of cable–truss structures based on equivalent equilibrium force model

Cable–truss structure is a typical form of cable–strut tensile structures, which consists of upper cable system, lower cable system and several vertical struts. As with the general cable–strut tensile structure, only when the reasonable geometric shape matches the feasible prestress distribution can the cable–truss structure obtain structural stiffness and bear the external load. Once the geometric shape is unreasonable, the cable–truss structure is just a mechanism without bearing capacity and cannot be stiffened by introducing prestress. Consequently, a reasonable geometry is the premise for cable–truss structure to become an effective load-bearing system. In this paper, an equivalent equilibrium force model, called EEFM, is proposed according to the geometric-mechanical characteristics of cable–truss structures. A cable–truss structure in this model is split into upper and lower cable systems with equivalent nodal forces. The geometric rationality can be easily evaluated from the equivalent nodal force relationship. According to the geometric topology and equilibrium equation of two cable systems, the self–stress mode of the structure with reasonable geometry can be directly obtained. For structures with unreasonable geometry, the node coordinates of one cable system are corrected based on the other cable system. Several cases are presented to verify the accuracy and validity of the proposed method. This method can be used for shape design, geometric correction and force finding, and has greater advantages for cable–truss structures with asymmetric or complex space configuration.

Nonequilibrium Casimir–Polder Interaction between Nanoparticles and Substrates Coated with Gapped Graphene

The out-of-thermal-equilibrium Casimir–Polder force between nanoparticles and dielectric substrates coated with gapped graphene is considered in the framework of the Dirac model using the formalism of the polarization tensor. This is an example of physical phenomena violating the time-reversal symmetry. After presenting the main points of the used formalism, we calculate two contributions to the Casimir–Polder force acting on a nanoparticle on the source side of a fused silica glass substrate coated with gapped graphene, which is either cooler or hotter than the environment. The total nonequilibrium force magnitudes are computed as a function of separation for different values of the energy gap and compared with those from an uncoated plate and with the equilibrium force in the presence of graphene coating. According to our results, the presence of a substrate increases the magnitude of the nonequlibrium force. The force magnitude becomes larger with higher and smaller with lower temperature of the graphene-coated substrate as compared to the equilibrium force at the environmental temperature. It is shown that, with increasing energy gap, the magnitude of the nonequilibrium force becomes smaller, and the graphene coating makes a lesser impact on the force acting on a nanoparticle from the uncoated substrate. Possible applications of the obtained results are discussed.

Charged strange star coupled to anisotropic dark energy in Tolman–Kuchowicz spacetime

The concept of dark energy can be used as a possible option to prevent the gravitational collapse of compact objects into singularities. It affects the universe on the largest scale, as it is responsible for our universe’s accelerated expansion. As a consequence, it seems possible that dark energy will interact with any compact astrophysical stellar object [Phys. Rev. D 103, 084042 (2021)]. In this work, our prime focus is to develop a simplified model of a charged strange star coupled to anisotropic dark energy in Tolman–Kuchowicz spacetime (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) within the context of general relativity. To develop our model, here we consider a particular strange star object, Her X-1 with observed values of mass =(0.85 pm 0.15)M_{odot } and radius = 8.1_{-0.41}^{+0.41} km. respectively. In this context, we initially started with the equation of state (EoS) to model the dark energy, in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The unknown constants present in the metric have been calculated by using the Darmois–Israel condition. We perform an in-depth analysis of the stability and force equilibrium of our proposed stellar configuration as well as multiple physical attributes of the model such as metric function, pressure, density, mass–radius relation, and dark energy parameters by varying dark energy coupling parameter alpha . Thus after a thorough theoretical analysis, we found that our proposed model is free from any singularity and also satisfies all stability criteria to be a stable and physically realistic stellar model.

Optimized design of the overall shapes of supercavitating vehicles based on a multi-objective adaptive genetic algorithm

The supercavitating vehicle is a new generation of high-speed underwater vehicles enveloped by a large bubble of gas or vapor (i.e., a supercavity) to reduce navigation resistance by an order of magnitude, except for the head and tail. However, due to the limited hydrodynamic forces, it is difficult to ensure stable motion. The overall shape of the vehicle is not only the critical factor to ensure a suitable relative position between the vehicle and its supercavity for stable motion, but also directly affects the ease of generation and development of the supercavity. Therefore, this study focuses on the characteristic parameters of the overall shape of the vehicle and first establishes a multi-objective optimization model based on the dynamic model of the supercavitating vehicle with the incipient supercavitation number and the vehicle volume as the optimization objectives. Then, given the relatively good global, robust and universal characteristics of the adaptive genetic algorithm compared to other algorithms, a multi-objective optimization algorithm is developed and improved using the subsection optimization method for the main optimization variable. The characteristic parameters of the overall shapes are optimized for natural and ventilated supercavitating vehicles using the algorithm based on the multi-objective optimization model so that it is easier to create a supercavity under the conditions of the same flow and force equilibrium and the vehicle has a larger volume. By optimizing the vehicles under different navigation depths and slenderness ratios, the design rules for the characteristic parameters of the overall shape and the control surface parameters are obtained based on the optimization objectives, and the motion state and hydrodynamic characteristics of the optimized vehicles are revealed.

COMPARISON OF SCALED HYBRID SIMULATIONS AND SHAKING TABLE TESTS ON A 2-SPAN REINFORCED CONCRETE BRIDGE

Hybrid simulation is a testing paradigm combining experimental and computational simulations through a hybrid model which comprises scaled physical and numerical representation of various parts of a structural system. The physical and numerical elements interact within a single model by satisfying the displacement compatibility and the force equilibrium at the common nodes. Hybrid simulation offers numerous advantages, including cost savings and a deeper understanding of complex structures. In this paper, an investigation has been carried out to study the effect of scaling on the accuracy of hybrid simulations of a 2-span reinforced concrete highway bridge. The experimental program included hybrid simulations on 1/10, 1/8 and 1/6 scaled models of a two-span reinforced concrete bridge loaded to failure under seven (7) consecutive seismic events. The seismic motions replicating the 1994 Northridge earthquake in California, were applied with progressively increasing amplitudes. The results of shaking table tests on a 1/4 scaled model of the bridge were used to study the accuracy and reliability of different scales of the hybrid simulations.