Force Equilibrium Research Articles

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.

Generalized element-node complete model and its implementation for the optimal design of a piezo-actuated compliant amplifier

Compliant amplification mechanisms are widely applied to extend the stroke of stacked piezoelectric actuators. Accurate modeling of static and dynamic performances is crucial for the optimal design of complex compliant mechanisms. By generalizing the planar element-node model-based finite element method, this paper proposes a new modeling method capable of describing the spatial complete kinetostatics and dynamics for compliant mechanisms. On the basis of the widely reported complete compliance models for flexure hinges, a versatile stiffness model is established for the hinge with an arbitrary notch shape through the force equilibrium model. The generalized model is then demonstrated by applying for modeling and optimizing a compliant mechanism with dual-stage amplification. The verification through finite element simulations suggests that the maximum modeling error for the kinetostatic and first six resonant frequencies for the mechanisms with and without structural optimizations is less than 20%. Finally, the open-loop and closed-loop performance tests on the prototype with optimized parameters are conducted, demonstrating the effectiveness of the developed modeling and optimization methods.

Numerical studies on tugboat performance during pushing operations

This paper introduces a RANS CFD methodology for the evaluation of tugboat dynamics during pushing operations. Two- and three- dimensional methods that respectively utilize “Dynamic Fluid Body Interactions - (DFBI)” and “Tug Force Equilibrium kinematics-(TFE)” are assessed and compared with the aim to better understand the influence of fluid modelling on ship dynamics. For the DFBI method, an unsteady RANS solver comprising of a dynamic fluid body interaction module and a contact mechanics coupling algorithm are used to predict the forces between a tugboat and an assisted ship. For the TFE method, a steady RANS method is applied and contact actions are calculated as a sum of the hydrodynamic forces on the hull and the propeller. Whereas DFBI accounts for the time variation of the contact forces, the TFE is more rapid and could be used to derive operational decision support criteria. To demonstrate the latter the TFE method is used to derive the pushing forces based on a set of 16 numerical simulations. It is concluded that irrespective of the model used the tugboat speed and orientation may amplify the pushing forces. This effect could be prominent, especially at slow speeds for which the sway force acts in opposite direction to the tug.

Close-contact melting of shear-thinning fluids

This study aims at establishing a model for close-contact melting (CCM) of shear-thinning fluids. We presented a theoretical framework for predicting the variation of liquid melt film thickness and motion of unmelted solid for both Carreau and power-law fluids. We identified the appropriate energy equation considering the convective effect and derived an analytical temperature profile across the liquid film. Using the lubrication approximation, force equilibrium relationships and the corresponding numerical approaches were built. By using laser interferometry and photographic recording methods, we found excellent agreement between numerical solutions and experimental results for Carreau liquids, revealing that the convective effect weakens heat transfer and melting rate. We identified the critical liquid film thickness that determines three situations of CCM in the theoretical model for Carreau fluids. Numerical prediction demonstrated that the CCM of Carreau fluids can be almost equivalent to that of power-law fluids if the initial film thickness is greater than the critical value. Finally, approximate analytical models were developed for both Carreau and power-law models. For the applicability of the approximate analytical solutions, we derived two- and three-dimensional dimensionless phase diagrams of validity range and identified a key dimensionless group $(\varLambda Re)^{4/3}{Re}\left [3\ln (Ste+1)\right ]^{1/3}{Pe}^{-1/3}$ , where $\varLambda$ is dimensionless characteristic time, Re is Reynolds number, Ste is Stefan number and Pe is Peclect number. The reliability of the approximate solutions was verified by comparing with the numerical results. These approximate solutions enable convenient and low-cost computational prediction of the dynamic CCM process of shear-thinning fluids.

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model (DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional (2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin. 40 98108 (2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142 (2019)]. In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability, and translational motion of a 2D fluid system.

Resolution improvement of optoelectronic tweezers using patterned electrodes.

An optoelectronic tweezer (OET) device is presented that exhibits improved trapping resolution for a given optical spot size. The scheme utilizes a pair of patterned physical electrodes to produce an asymmetric electric field gradient. This, in turn, generates an azimuthal force component in addition to the conventional radial gradient force. Stable force equilibrium is achieved along a pair of antipodal points around the optical beam. Unlike conventional OETs where trapping can occur at any point around the beam perimeter, the proposed scheme improves the resolution by limiting trapping to two points. The working principle is analyzed by performing numerical analysis of the electromagnetic fields and corresponding forces. Experimental results are presented that show the trapping and manipulation of micro-particles using the proposed device.

On the spatio-temporal characteristics of the Portevin-Le Chatelier effect in aluminium alloy AA5182: An experimental and numerical study

The Portevin–Le Chatelier (PLC) effect and its spatio-temporal characteristics in the aluminium alloy AA5182 are studied experimentally and numerically in the current work. An extremely high-frequency camera (up to 1000 Hz) is utilized to capture the nucleation and propagation of the PLC bands in uniaxial tension tests with different applied strain rates. The spatio-temporal patterns and the strain accumulation are obtained from digital image correlation (DIC). A transition from continuous to discontinuous band propagation is observed with increasing strain rate. Finite element simulations are carried out using a modified Kubin-Estrin-McCormick (KEMC) model to reproduce the serration morphologies, spatio-temporal patterns and strain accumulation processes. Based on the comparison between experiments and modelling, it is revealed that the strain accumulation and strain ageing processes together decide the subsequent band nucleation. The PLC band inherently brings a strain heterogeneity to the specimen, which results in different levels of work-hardening across the specimen. The strain ageing process, which occurs both inside and outside the PLC band, is found to create another heterogeneity in terms of the solute strengthening. A unique local yield stress minimum leads to a propagating band, while multiple local yield stress minima give a jumping band behaviour. Using that equilibrium forces the work-hardening behind the propagating band to be balanced with the solute strengthening in front of the band, analytical expressions for the band strain and band velocity are derived and verified by the experimental data.

A coupled model of asymmetric GIMP and tetrahedron CPDI based on the penalty contact algorithm for simulating dynamic rock splitting

A coupled material point model (MPM) based on the asymmetric generalized interpolation material point (aGIMP) and the tetrahedron convected particle domain interpolation (CPDI-Tet4) was established to simulate the dynamic splitting of a rock Brazilian disc under small deformation. Furthermore, a boundary-based contact algorithm was developed to accurately describe the contact force between the split bar's aGIMP particles and the rock's CPDI-Tet4 particles. The proposed aGIMP technology enabled particles to move on a non-uniform background grid by changing the original basis functions. A good simulation effect was achieved. It was concluded that the rock particle size plays an important role in the accuracy of the contact algorithm. Two shear failure bands were generated near the contact zones first after the rock specimen reached the force equilibrium state, and then the four arc fracture surfaces grew from the two sides of the shear failure bands and coalesced to a radial fracture surface on the mid-cross section of the specimen. In addition, the tensile strength calculated by the MPM model exhibited the typical rate effect of rock material and was slightly lower than the practical tensile strength of the particle on the radial fracture surface.

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.

Formulation of a generalized truss analogy for the analysis of shear behavior of short jacketed columns

Short columns in a story of a reinforced concrete building tend to fail in shear during an earthquake. They can be strengthened using concrete jacketing. A performance-based evaluation requires the modeling of nonlinear lateral load versus deformation behavior of such a column. While previous studies are available to analyze the behavior of a flexure-critical column, computationally simple method of analysis of the shear behavior of a short column is lacking in the literature.A generalized truss analogy is proposed to predict the shear behavior of short columns beyond diagonal cracking and till failure. Its formulation satisfies equilibrium of forces in the concrete strut and reinforcing bar ties, compatibility of strains in the concrete and ties of the web region of a column, and suitable constitutive relationships of the materials. First, the formulation and computation algorithm as applicable to an original column, are presented in this paper. Next, the method is extended to columns strengthened by concrete jacketing. Its application to a composite jacketed section is implemented using a sandwich model.The validation of the proposed method is presented, comparing the predictions with the lateral load versus deflection behavior curves obtained from the tests of five large-scale shear-critical column specimens (two original and three jacketed), tested as part of this research. The good correlation of the predicted and test results confirmed the application of the proposed method for the nonlinear analysis of shear for short columns.

Solving the general 3-D safety factor by combining Sarma's idea with the assumption of normal stress distribution over the slip surface.

This study proposes a method for determining 3-D limit equilibrium solutions. The method, inspired by Sarma, introduces the horizontal seismic coefficient as a slope failure parameter and implements a modification of the normal stress over the slip surface. Four equilibrium equations are used to solve the problem without compromising the accuracy of the calculations: three force equilibrium equations in the x, y, and z directions and a moment equilibrium equation in the vertical (z) direction. The reliable factor of safety can be determined by calculating the minimum value of the horizontal seismic coefficient. Furthermore, we analyzed several typical examples of symmetric and asymmetric slopes, finding good consistency with the existing literature. This consistency indicates the reliability of the factor of safety we obtained. The proposed method is favored due to its straightforward principle, convenient operation, fast convergence, and ease of programming.

Experimental evidence to understand mechanical causes of retinal detachment following blunt trauma

PurposeThis study aimed to perform an in vitro experiment to simulate retinal detachment caused by blunt impact, and provide experimental evidence to understand mechanical causes of traumatic retinal detachment. MethodsThe experiment was conducted on twenty-two fresh porcine eyes using a bespoke pendulum testing device at two energy levels (0.1J for low energy and 1.0J for high energy). We examined dynamic forces and mechanical responses to the impact, including global deformations, intraocular pressure changes and the energy absorption. Another set of twenty-two eyes underwent pathological examination immediately after being subjected to blunt impact. Twelve additional intact eyes were examined as controls. All pathological sections were scored to indicate whether retinal detachment had occurred. ResultsA dynamic variation in intraocular pressure was detected following impact and exhibited an approximate sinusoidal oscillation-attenuation profile. The peaks of impact force were 12.9 ± 1.9 N at low-energy level and 34.8 ± 9.8 N at high-energy level, showing a significant difference (p < 0.001). The positive and negative peaks of intraocular pressure were 149.4 ± 18.9 kPa and −10.9 ± 7.2 kPa at low-energy level, and 274.5 ± 55.2 kPa and −35.7 ± 23.7 kPa at high-energy level, showing significant differences (p < 0.001 for both levels). Retinal detachments were observed in damaged eyes while few detachments were found in control eyes. The occurrence rate of retinal detachment differed significantly (p < 0.05) between the high- and low-energy impact groups. ConclusionsThis study provided experimental evidence that shockwaves produced by blunt trauma break the force equilibrium and lead to the oscillation and negative pressure, which mainly contribute to traumatic retinal detachment.