Force Equilibrium Research Articles

Design of a deployable aerodynamic decelerator based on a tensegrity structure

Deployable aerodynamic decelerators are more suitable for planetary exploration missions than rigid aerodynamic decelerators. Their sizes are less limited by the launch vehicle shroud, allowing heavier payloads to be delivered to the surfaces of planets. Aiming at the problem of lightweight designs in deployable aerodynamic decelerators, a deployable tensegrity structure composed of two frustum tensegrity units and a prism tensegrity unit is proposed. To design the deployable tensegrity structure, a self-equilibrium model that is especially suitable for the structure with rotational symmetry is established according to prestressability conditions and force equilibrium equations. Based on the deployable tensegrity structure, the deployment mechanism, with the action of drive units, is designed to realize the transformation from the stowed state to the deployed state of the decelerator. The tensegrity structure always has rotational symmetry to make the deployment process highly synchronized due to the fact that drive units can work simultaneously. During the deployment process, the transverse distance and longitudinal distance are used to measure the deployment degree of the tensegrity structure. The types of axial forces for members are used to determine whether the tensegrity structure is stable. The result shows that the deployment process has continuity and that the tensegrity structure always stays stable.

A Modern Approach to the Complicated Line Integrals in Linear Elastic Dislocation Theory

The standard textbook analysis of dislocations is generally limited to the case of infinitely straight screw or edge dislocations, which do not exist. This is due to the complexity of the formulas for arbitrary dislocation loops, i.e., Burger’s equation for the displacement field, the Peach-Köhler equation for the stress field and Blin’s equation for the interaction energy, which involve line integrals along the dislocation loop. The integrands are complex, and integration often involves non-elementary functions. Elaboration of the integrands with symbolic mathematical software produces tensor formulas which can be reused at will. By formulating convenient parametric expressions for the configuration studied and using superposition, mathematical software can be used to perform the integrations for arbitrary Burgers vectors. Often, the resulting expressions for the tensorial fields are very long, but they can be easily incorporated as user-defined formulas for plotting, parametric analysis, and incorporation into routines for energy minimisation or the non-linear equations for force equilibrium. The effectiveness of this approach will be illustrated by the example of short straight dislocations, circular dislocations, the interaction between a pileup and dissociated dislocations in the grain boundary, and the nucleation of dislocations at grain boundaries.

Lateral earth pressure of granular backfills on retaining walls with expanded polystyrene geofoam inclusions under limited surcharge loading

Existing studies have focused on the behavior of the retaining wall equipped with expanded polystyrene (EPS) geofoam inclusions under semi-infinite surcharge loading rather than limited surcharge loading. In this paper, the failure mode and the earth pressure acting on the rigid retaining wall with EPS geofoam inclusions and granular backfills (henceforth referred to as EPS-wall), under limited surcharge loading are investigated through two- and three-dimensional model tests. The testing results show that different from the sliding of almost all the backfill in the EPS-wall under semi-infinite surcharge loading, only an approximately triangular backfill slides in the wall under limited surcharge loading. The distribution of the lateral earth pressure on the EPS-wall under limited surcharge loading is non-linear, and the distribution changes from the increase of the wall depth to the decrease with the increase of the limited surcharge loading. An approach based on the force equilibrium of a differential element is developed to predict the lateral earth pressure behind the EPS-wall subjected to limited surcharge loading, and its performance was fully validated by the three-dimensional model tests.

Failure mode discrimination and theoretical prediction method for unequal span bonded prestressed concrete substructures against progressive collapse

Unequal-span prestressed concrete (USPC) structures have unequal spans on the left and right sides and are configured with prestressed steel strands on both spans. However, research on the progressive collapse resistance of these structures is lacking. The strength of the asymmetry of the USPC structure varies depending on the span ratio and reinforcement configuration, resulting in two distinct failure modes in progressive collapse. A parametric analysis was conducted using finite element software to determine how the resistance to progressive collapse and failure modes of USPC structures under middle column failure are affected by variables such as the span ratio, reinforcement configuration, and proportion of prestressing. Accordingly, a discrimination criterion for determining the failure modes of USPC structures was proposed. A theoretical approach for predicting the ultimate displacement and resistance of the progressive collapse of USPC structures was presented for different failure modes. This theoretical approach proposes an innovative stiffness combination and tension path method to establish displacement coordination and force equilibrium conditions, respectively. The theoretical prediction method was deemed valid after comparing it with finite element simulation results.

Towards Homological Methods in Graphic Statics

Recent developments in applied algebraic topology can simplify and extend results in graphic statics – the analysis of equilibrium forces, dual diagrams, and more. The techniques introduced here are inspired by recent developments in cellular cosheaves and their homology. While the general theory has a few technical prerequisites (including homology and exact sequences), an elementary introduction based on little more than linear algebra is possible. A few classical results, such as Maxwell's Rule and 2D graphic statics duality, are quickly derived from core ideas in algebraic topology. Contributions include: (1) a reformulation of statics and planar graphic statics in terms of cosheaves and their homology; (2) a new proof of Maxwell's Rule in arbitrary dimensions using Euler characteristic; and (3) derivation of a novel relationship between mechanisms of the form diagram and obstructions to the generation of force diagrams. This last contribution presages deeper results beyond planar graphic statics.

Hybrid simulation framework with mixed displacement and force control for fully compatible displacements

AbstractA novel framework for hybrid simulation of the seismic response of structures is presented that employs a mixed displacement and force control strategy. A key feature of this framework is a controller‐based displacement‐to‐force transformation that enables compatible displacements between the numerical and experimental model for force‐controlled degrees of freedom. The framework can be applied within conventional displacement‐based time‐integration algorithms allowing for implementation across a variety of software and hardware architectures; it is demonstrated here using OpenSees software with detailed nonlinear numerical models. This study includes numerical verification of the proposed force control strategy and actual implementation in a hybrid simulation of special moment frames with full‐scale beam‐column subassemblies. In the hybrid tests, the experimental column axial load is applied in force control due to the large stiffness and when combined with lateral seismic loads, results in column local buckling with significant axial shortening. The hybrid simulation results verify that the proposed mixed displacement and force control strategy effectively enforces displacement compatibility and force equilibrium between the numerical and experimental structures at the boundary degrees of freedom.

A novel separation density model based on force analysis of coal-based oil shale in pulsed fluidized beds

ABSTRACT It is important to study the theory and technology of coal-based oil shale dry beneficiation in China. Traditional separation density models are obtained through particle force analysis, but most studies tend to ignore the influence of medium resistance and bubble disturbance, which seriously limit the predicted accuracy of the separation density model. Therefore, the force on simulated mineral particles (steel balls) in pulsed fluidized bed (PFB) under different operating conditions was tested. It was found that the force decreases with the increase of gas velocity and distance from the distributor. The change of pulsation frequency has less influence on force. The force equilibrium equation was established and verified to be within 10% error; Finally, we obtain a new separation density model of PFB. This is of great importance for the industrialization and scale-up of dry beneficiation.

Interaction between basal edge/mixed dislocations and point defects in zirconium

Zirconium alloys are widely used in nuclear reactors. Due to frequent displacement cascade events under irradiation, a large number of point defects are generated in zirconium alloys. In this work, the interactions between edge/mixed dislocations and point defects (vacancies and SIAs (self-interstitial atoms)) are studied by molecular dynamics (MD) simulations. The simulation results indicate that vacancies are not absorbed by edge dislocations but by mixed dislocations. Compared with their weak pinning effect on edge dislocation motion, vacancies have an intermediate pinning effect on the motion of mixed dislocation. In contrast, SIAs are all absorbed by edge and mixed dislocations and have a strong pinning effect. Then, force equilibrium is established on point defects to explain the absorption of point defects. The attractive force between dislocations and point defects is calculated from the binding energy, and the friction force of point defects is calculated from the migration energy. We found that the friction force of vacancies on edge dislocations is larger than the attractive force, and thus the vacancies cannot be absorbed. For the other three cases, the attractive force is large enough to overcome the friction force, and the point defects are absorbed.

Direct spatio-temporal stress field determination combining full-field deformation measurements and explicit finite element method: Concept verification

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.

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.