Force Balance Condition Research Articles

Analytical Method of the Shear Lag Effect in Thin-Walled Box Girders Based on the Shear Flow Distribution Law

This paper presents an analytical method based on the shear flow distribution law to study the shear lag effect of thin-walled single- and double-cell box girders. The first step in this method is to determine the box girder’s shear flow distribution. Subsequently, a series of novel improved longitudinal displacement functions mathematically expressed as cubic parabolas are established. The parabolic origin of these functions is located at the zero point of the shear flow corresponding to each plate; the unknown parameters used to describe the function form can be determined according to the shear flow distribution, the continuity conditions, and the axial force balance condition. Then, the variational energy method is adopted to derive the governing differential equations. The shear lag effect in thin-walled single- and double-cell box girders under several boundary conditions and load cases is studied and analytical expressions for the shear lag coefficient are derived. Finally, results obtained using the proposed method are validated via comparison with numerical results. The results show that the proposed method can provide reasonable predictions for the shear lag effect of single- and double-cell box girders, and that this method is more straightforward and practical. In addition, the shear lag coefficients at different webs are not entirely equal, which is related to the distance from the web to the zero point of the shear flow.

Comparative analysis of mechanical properties for wood frame and reinforced concrete frame based on deformation energy decomposition method

As a typical orthotropic material, the mechanical properties of wood in the parallel and perpendicular-to-grain directions are very different. Based on mathematical orthogonality, mechanical force balance condition, and energy comparability, the deformation energy decomposition method of planar wood element is proposed, and then the quantitative and visual analysis of the basic deformation performance of wood structure is realized. The basic deformation performance of wood structure and isotropic structure is analyzed using the deformation energy decomposition method, and the seismic performance of wood frame structure and concrete frame structure is compared. The results show that the lateral resistance and beam ductility of wood frame are greater than those of concrete frame under seismic load. However, the reduction of deformation energy proportion of wood frame beam leads to greater deformation energy of the frame column, so it is suggested to take targeted strengthening measures to the bottom of the wood frame column and the joint area.

Modeling of Dynamic Cutting Force considering Flank Wear and Analysis of Tool Wear Mechanism in Milling 508III Steel

508III steel is widely used to manufacture the key components of water chamber head of nuclear island evaporator because of its excellent performance. Due to the large milling parameters and their high strength, hardness, and adhesion, cemented carbide tools are subjected to large cyclic mechanical load. Serious tool wear and low service life have become more prominent problems in the cutting process. Therefore, the research on the dynamic cutting force and wear mechanism of cemented carbide tools for milling 508III steel is attracting more and more attention. In this study, based on the theory of cutting mechanics and the force balance condition of circular tool cutting unit, the cutting force model under ideal condition was established. On this basis, the tool dynamic cutting force model considering flank wear was constructed. The tool wear experiment of milling 508III steel was carried out under different cutting parameters, and the change curve of tool wear life and the actual dynamic cutting force at different cutting time were obtained. And the accuracy of the established dynamic cutting force model was verified. Scanning electron microscopy and energy dispersive X-ray spectroscopy were used to analyze the wear morphology and mechanism of cemented carbide tools. The research findings can are of great significance for revealing the tool failure mechanism of milling water chamber head, reasonably selecting machining parameters, and improving the machining quality and efficiency of nuclear power parts.

Thermocapillary migration of a deformed droplet in the combined vertical temperature gradient and thermal radiation

Thermocapillary migration of a deformed droplet in the combined vertical temperature gradient and thermal radiations with uniform and non-uniform fluxes is first analyzed. The creeping flow solutions show that the deformed droplet has a slender or a cardioid shape, which depends on the form of the radiation flux. The deviation from a sphere depends not only on the viscosity and the conductivity ratios of two-phase fluids but also on capillary and thermal radiation numbers. Moreover, in the roles of interfacial rheology on thermocapillary migration of a deformed droplet, only the surface dilatational viscosity and the surface internal energy can reduce the steady migration velocity, but the surface shear viscosity has not any effects on the steady migration velocity. The surface shear and dilatational viscosities affect the deformation of the droplet by increasing the viscosity ratio of two-phase fluids. The surface internal energy directly reduces the deformation of the droplet. However, the deformed droplet still keeps its original shape without the influence of interfacial rheology. Furthermore, it is found that, based on the net force balance condition of the droplet, the normal stress balance at the interface can be used to determine the steady migration velocity, which is not affected by the surface deformation in the creeping flow. From the expressions of the normal/the tangential stress balance, it can be proved that the surface shear viscosity does not affect the steady migration velocity. The results could not only provide a valuable understanding of thermocapillary migration of a deformed droplet with/without the interfacial rheology in a vertical temperature gradient controlled by thermal radiation but also inspire its potential practical applications in microgravity and microfluidic fields.

Vertical performance of rock-socketed pile group in layered saturated rock-soil mass

This paper studies the vertical performance of rock-socketed pile group embedded in layered saturated rock-soil mass. The three-node bar element is utilized to discretize the pile, and the global stiffness matrix equation of rock-socketed pile group is assembled by the finite element method. Based on the solution for the interaction between a rock-socketed single pile and rock-soil mass, the flexibility matrix equation of rock-soil mass for the pile group is derived by the boundary element method. Combination of the force balance and displacement compatibility conditions for the rigid pile cap leads to the solution of rock-socketed pile group embedded in saturated rock-soil mass. The correctness of the proposed method is examined by comparing the solutions predicted by the present paper with the solutions from existing literature and ABAQUS results. The relevant factors affecting the vertical performance of rock-socketed pile group, such as the socketed length, pile spacing, pile-rock mass modulus ratio, length-diameter ratio and the rock mass stratification, are further discussed

A Modeling Method for a 6-SPS Perpendicular Parallel Micro-Manipulation Robot Considering the Motion in Multiple Nonfunctional Directions and Nonlinear Hysteresis

Abstract Precision motion systems that call for an ultrahigh resolution are widely used in ultrahigh-precision engineering applications. In this article, a 6-SPS perpendicular compliant parallel micro-manipulation robot is presented. It is difficult to establish the mapping relationship between the applied voltage and end-effector pose due to the existence of compliant joints and piezoelectric actuators. A modeling method for a 6-SPS perpendicular compliant parallel micro-manipulation robot considering the motion in nonfunctional directions and hysteresis effect is proposed to reflect the characteristic from input voltage to output pose. The motion of the spherical compliant joint is regarded as a spatial six degrees-of-freedom mechanism. This method considers the motion errors in multiple nonfunctional directions of the compliant joints. The internal force and torque are also taken into account based on the spatial force and moment balance condition. The slow, fast dynamic modes, and hysteresis nonlinearity behavior are described using a series and parallel hybrid model structures. The kinematic model and compliance model without considering the motion in nonfunctional directions are conducted for comparison. Simulation results show that the presented modeling method has higher modeling accuracy. Finally, experiments on a 6DOF compliant parallel micro-manipulation robot reveal the fine modeling performance of the developed method for the precision motion systems in the presence of intrinsic hysteresis effect and motion error of compliant joints.

On the differences between periodic domain and fluidized bed

To understand the effects of macroscale constraints on fluidization, we investigate the differences between the periodic domain and realistic bed by using fine-grid simulations. The differences in these two systems are highlighted by identifying three force-balance conditions with respect to the gas-phase, solid-phase and the mixture, respectively. Specifically, these three conditions are not satisfied at the microscale, but satisfied at the macroscale in both systems; Over the mesoscale, the gas-phase force balance is established in the periodic domain and in the fluidized bed at bubbling states, but not at turbulent states, whereas the solid-phase and the mixture force balance conditions are established only in the periodic domain, not in the realistic bed. The influence of the bounding wall can be implicitly included by introducing the gas-phase pressure gradient, turbulent kinetic energies (TKEs) of gas and solids phases, and drift velocity as the markers for the drag force.

Vibration energy flow of main drive system of hot tandem mill

We analyzed the power flow of the vibration transmission of the F2 mill drive system coupled with complex beams using the substructure method. The system was divided into three cylindrical substructures, which were coupled to each other by three spring-dampers. The modal analysis of the substructures was conducted to describe their dynamic characteristics; subsequently, the substructure receiving function under free interface conditions was established. The dynamic characteristics of the transmission coupling system were calculated by synthesizing the force balance conditions and geometric coordination at the coupling interface. The input energy and transmission energy in the system were effectively evaluated. The effects of spring-damper stiffness change, excitation position, and loss factor on the transmission of vibration power flow were studied and verified by field experiments. This study provides an effective theoretical basis for vibration suppression measures for hot tandem rolling mills.

Hard-sphere jamming through the lens of linear optimization.

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres, investigating the transition in finite-dimensional systems poses very difficult and different problems, in particular from the numerical point of view. Soft particles are modeled by continuous potentials; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, the latter methods are inapplicable to hard-sphere (HS) systems since the interaction energy among the particles is always zero by construction. To overcome these difficulties, here we recast the jamming of hard spheres as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed HS packings without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free-energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.

Relative grain boundary energies from triple junction geometry: Limitations to assuming the Herring condition in nanocrystalline thin films

Grain boundary character distributions (GBCD) are routinely measured from bulk microcrystalline samples by electron backscatter diffraction (EBSD) and serial sectioning, and this data can be used to reconstruct relative grain boundary energy distributions (GBED) based on the 3D geometry of triple lines, assuming that the Herring condition of force balance is satisfied. These GBEDs correlate to those predicted from molecular dynamics (MD); furthermore, the GBCD and GBED are found to be inversely correlated. For nanocrystalline thin films, orientation mapping via precession enhanced electron diffraction (PED) has proven effective in measuring the GBCD, but the GBED has not been extracted. Here, the established relative energy extraction technique is adapted to PED data from four sputter deposited samples: a 40 nm-thick tungsten film and a 100 nm aluminum film as-deposited, after 30 and after 150 min annealing at 400 °C. These films have columnar grain structures, so serial sectioning is not required to determine boundary inclination. Excepting the most energetically anisotropic and highest population boundaries, i.e. aluminum Σ3 boundaries, the relative GBED extracted from these data do not correlate with energies calculated using MD nor do they inversely correlate with the experimentally determined GBCD for either the tungsten or aluminum films. Failure to reproduce predicted energetic trends implies that the conventional Herring equation cannot be applied to determine relative GBEDs and thus geometries at triple junctions in these films are not well described by this condition; additional geometric factors must contribute to determining triple junction geometry and boundary network structure in spatially constrained, polycrystalline materials.

An accurate and numerically efficient time-varying mesh stiffness model for modified straight bevel gear under load

Gear time-varying mesh stiffness (TVMS) plays an important role in the analysis accuracy of a gear transmission mechanism. In previous research, the TVMS of a modified straight bevel gear (SBG) was mainly obtained by the finite element method (FEM), whose computation time is usually long to ensure computational accuracy. By contrast, this work proposes a fast calculation method with high accuracy for the TVMS of a modified SBG. First, B-spline surfaces are introduced to reconstruct a modified SBG using discrete tooth surface points. Next, based on the tooth contact analysis and loaded tooth contact analysis, combined with energy conservation principle and infinitesimal method, a semi-analytical instantaneous single mesh stiffness (SMS) model for the modified SBG is derived. Then, using the additional deformation compatibility condition and principle of force balance, the calculation method of the TVMS of the modified SBG is obtained. Finally, a comparison of the mesh stiffness calculation results between the method of this study and that of FEM is completed. The results show that the semi-analytical TVMS model used in this study can be accurately and quickly solved.

An extended Hill’s lemma for non-Cauchy continua based on the modified couple stress and surface elasticity theories

An extended Hill’s lemma is provided for non-Cauchy continua satisfying the modified couple stress theory in the bulk and the surface elasticity theory in the surface layer. Based on the Hill–Mandel condition, four sets of boundary conditions (BCs) are identified. It is shown that each of these four sets of BCs satisfies the admissibility and average field requirements. In addition, the set of kinetic BCs meets the force and moment balance conditions, and the set of modified kinematic BCs satisfies the displacement and micro-rotation compatibility constraint. By applying the newly extended Hill’s lemma, a homogenization analysis of a two-phase composite is performed, in which the average strain energy of the composite is computed using a finite element model constructed using COMSOL. The effective elastic constants obtained in this analysis are found to satisfy the Voigt and Reuss bounds.

Influence of scour on the vertical response of rock‐socketed piles in layered saturated rock–soil mass

AbstractThe influence of scour on the vertical response of rock‐socketed piles in a layered saturated rock–soil mass is studied through the finite element‐boundary element coupling method. By utilizing the theoretical solution of layered saturated media as the kernel function, the boundary element method (BEM) is used to deduce the boundary integral equations of rock–soil mass. Meanwhile, the pile is modelled with the three‐node bar element and the global stiffness matrix of the pile is assembled by the finite element method (FEM). Then according to the scour type, the flexibility matrix of the foundation is recombined and extended, which is consistent with the stiffness matrix dimension of the pile. In consideration of the force balance and continuity conditions at the pile‐soil‐rock interface, the FEM–BEM coupling equation is established to solve the interaction between layered rock–soil mass and rock‐socketed pile that considers different scour types. A corresponding MATLAB program is compiled to verify the correctness of the present theory by comparisons with the existing literature solutions, field tests and the finite element solutions. The influences of the scour type, scour depth, socketed length as well as pile‐rock mass modulus ratio and rock mass stratification on the vertical response of a rock‐socketed single pile are further discussed through several numerical examples.

Experimental study on creep of short performance-based alkali-activated concrete column

Performance-based alkali-activated concrete overcomes the fatal disadvantage of short setting time and poor workability. In this paper, The creep test of this kind of concrete is carried out to explore the influence of strength grade and reinforcement ratio on the creep coefficient under the condition of constant temperature and humidity environment. Results show that specific creep and creep coefficient of alkali activated concrete decrease with strength grade. The ratio of creep coefficients of C30, C50 and C70 is 1:0.89:0.80. The creep coefficients were compared with the creep models adopted by the American Code, the European Code, and the Chinese Code, which are not suitable for predicting the creep coefficient of alkali-activated concrete. At the same time, considering the use of reinforcement in practical applications, the effect of reinforcement ratio on the creep coefficient of alkali-activated concrete is studied. The results show that reinforcement can reduce the creep coefficient. The greater the reinforcement ratio, the smaller the creep coefficient. The creep coefficient of alkali-activated concrete with reinforcement ratio of 1.1% and 2.0% is 11.1% and 18.7% smaller than that of concrete without reinforcement. Based on the aging theory method, according to the force balance condition and deformation coordination condition, the creep coefficient calculation formula considering the influence of the steel bar can be deduced. The theoretically calculated value is in good agreement with the measured data. This formula can be used to predict the creep coefficient of alkali-activated reinforced concrete.

Study on excitation and time-varying mesh characteristics of straight bevel gears considering modification and friction

An accurate and numerically efficient nonlinear coupled excitation model for straight bevel gears (SBG) with linear and point contact is proposed. This model incorporates stiffness, load distribution, and transmission error (TE) models. Considering root fillet and axial mesh force components, energy equivalence principle, accumulated integral potential energy method, and segment coupling theory, single mesh stiffness (SMS) models with and without coupling effect are proposed. On this basis, the formula for calculating SMS under the action of friction is given. Time-varying mesh stiffness (TVMS), load distribution, and TE models were established using the deformation compatibility condition and principle of force balance. The proposed model was verified by comparing the calculation results with those obtained using the finite element method (FEM). The semi-analytical TVMS model used in this study could be solved accurately and quickly. The meshing characteristics and changing rules of SBG under the influence of different modification methods, modification amounts, and friction coefficients were analyzed. This study is expected to help further enrich and develop gear stiffness theory and provide a theoretical tool for gear dynamics research.

Models for calculation of the sideways force due to the kink modes in tokamaks

The solution of the sideways force problem is finally needed for the ITER project. The task became urgent when the extreme danger of such a force was perceived. The predictions were based on the so-called Noll's formula derived under some simplifications. One of them was the prescription of the plasma motion without testing its compatibility with the force balance condition. Later, an alternative approach has been proposed [D. V. Mironov and V. D. Pustovitov, Phys. Plasmas 24, 092508 (2017)], where the key element was the absence of an integral electromagnetic force on the plasma. Another important improvement was a proper treatment of the vacuum vessel wall. Now the extensions of the previously developed models leading to or supporting Noll's formula are proposed with the resistive wall reaction similarly incorporated. The main attributes of those approaches, the plasma displacements, are kept the same as in the original versions. Precisely, these are the plasma tilt or the (1,1) kink mode. Two forces are calculated with such displacements: on the plasma and on the vacuum vessel wall. The former is shown to be far from zero in the analyzed cases, violating thereby the force-free condition. This does not happen when this constraint goes first. It becomes a selection rule for allowable perturbations. These roughly resemble the tilt and (1,1) mode but differ from them, which changes the result dramatically. The maximal force that can be produced by such kink-like modes compatible with the force balance cannot reach even one tenth of Noll's force. The quantitative comparisons of the competing models are provided.

A Cluster Based Algorithm Coupled With Shooting Method for Estimation of Parametric Clusters Yielding Optimal Stable Periodic Solutions in Nonlinear Vibrating Systems

Abstract This work presents a novel cluster based optimization procedure for estimating parameter values that yield stable, periodic responses with desired amplitude in nonlinear vibrating systems. The parameter values obtained by conventional nonlinear optimization schemes, with minimization of amplitude as the objective, may not furnish periodic and stable responses. Moreover, global optimization strategies may converge to isolated optima that are sensitive to parametric perturbations. In practical engineering systems, unstable or isolated optimal orbits are not practically realizable. To overcome these limitations, the proposed method tries to converge to a cluster in the r-dimensional parameter space in which the design specifications including the specified optimality, periodicity, stability and robustness are satisfied. Thus, it eliminates the need for computationally expensive bifurcation studies to locate stable, periodic parameter regimes before optimization. The present method is based on a hybrid scheme which involves the algebraic form of the governing equations in screening phase and its differential form in the selection phase. In the screening phase, force and energy balance conditions are used to rephrase the nonlinear governing equations in terms of the design parameter vector. These rephrased equations are reduced to algebraic form using a harmonic balance procedure which also specifies the desired amplitude and frequency of the response. An error norm based on this algebraic form is defined and is used to contract the search bounds in the parameter space leading to convergence to a cluster. The selection phase of the algorithm uses shooting method coupled with evaluation of Floquet multipliers to retain only those vectors in the arrived cluster yielding stable periodic solutions. The method is validated with Den Hartog's vibration absorbers and is then applied to vibration absorbers with material nonlinearity and vibration isolators with geometric nonlinearity. In both the cases, the converged cluster is shown to yield stable, periodic responses satisfying the amplitude condition. Parametric perturbation studies are conducted on the cluster to illustrate its robustness. The use of algebraic form of governing equations in the screening phase drastically reduces the computational time needed to converge to the cluster. The fact that the present method converges to a cluster in the parameter space rather than to a single parameter value offers the designer more freedom to choose the design vector from inside the cluster. It also ensures that the design is robust to small changes in parameter values.

Balance of osmotic pressures determines the nuclear-to-cytoplasmic volume ratio of the cell

The volume of the cell nucleus varies across cell types and species and is commonly thought to be determined by the size of the genome and degree of chromatin compaction. However, this notion has been challenged over the years by much experimental evidence. Here, we consider the physical condition of mechanical force balance as a determining condition of the nuclear volume and use quantitative, order-of-magnitude analysis to estimate the forces from different sources of nuclear and cytoplasmic pressure. Our estimates suggest that the dominant pressure within the nucleus and cytoplasm of nonstriated muscle cells originates from the osmotic pressure of proteins and RNA molecules that are localized to the nucleus or cytoplasm by out-of-equilibrium, active nucleocytoplasmic transport rather than from chromatin or its associated ions. This motivates us to formulate a physical model for the ratio of the cell and nuclear volumes in which osmotic pressures of localized proteins determine the relative volumes. In accordance with unexplained observations that are a century old, our model predicts that the ratio of the cell and nuclear volumes is a constant, robust to a wide variety of biochemical and biophysical manipulations, and is changed only if gene expression or nucleocytoplasmic transport is modulated.

Balance of osmotic pressures determines the volume of the nucleus

The volume of the cell nucleus varies across cell-types and species, and is commonly thought to be determined by the size of the genome and degree of chromatin compaction. However, this notion has been challenged over the years by multiple experimental evidence. Here, we consider the physical condition of mechanical force balance as a determining condition of the nuclear volume and use quantitative, order-of-magnitude analysis to estimate the forces from different sources of nuclear and cellular pressure.

Out-of-Plane Free Vibration Analysis of Continuous Curved Girders with Combined Linetypes Using Differential Quadrature Element Method

In this study, the out-of-plane free vibration equations of circular curved and clothoid transition curved girders with various boundary conditions were derived. The continuous curved girder with combined linetypes was discretized into separate curved girder elements. Based on the differential quadrature element method (DQEM), the Chebyshev–Gauss–Labatto unequal mesh division was applied to discretize the vibration equations of the continuous curved girder into those of the curved girder elements, along with the boundary conditions, internal geometric compatibility conditions, and force balance conditions. The out-of-plane natural frequency equations were derived considering the boundary conditions by the substitution method. The free vibration was solved for continuous curved girders with combined linetypes of circular and clothoid transition curves. The effectiveness of the DQEM was verified, and the effect of the number of grid points on the accuracy of the solution was evaluated. In addition, the effects of the bending/torsional stiffness ratio, warping coefficient, and boundary conditions on the natural frequencies of continuous curved girders with combined linetypes were investigated. The results showed that the DQEM can be efficiently used to solve the free vibration of multispan continuous curved girders with various linetype combinations. The frequencies of the continuous curved girder with combined linetypes decrease with the weakening of boundary constraints, but increase with increasing warping coefficient and bending/torsional stiffness ratio.