Simple Rigid Body Research Articles

High strain rate elasto‐plasticity identification using the image‐based inertial impact (IBII) test part 1: Error quantification

AbstractCurrent high strain rate testing procedures generally rely on the split Hopkinson bar (SHB). In order to gain accurate material data with this technique, it is necessary to assume the test sample is in a state of quasi‐static equilibrium so that inertial effects can be neglected. During the early portion of an SHB test, it is difficult to satisfy this assumption making it challenging to investigate the elastic–plastic transition for metals. With the development of ultra‐high speed imaging technology, the image‐based inertial impact (IBII) test has emerged as an alternative to the SHB. This technique uses full‐field measurements coupled with the virtual fields method to identify material properties without requiring the assumption of quasi‐static equilibrium.The purpose of this work is to develop the IBII method for the identification of elasto‐plasticity in metals. In this paper (part 1), the focus is on using synthetic image deformation simulations to analyse identification errors for two plasticity models, a simple linear hardening model and a modified Voce model. Additionally, two types of virtual fields are investigated, a simple rigid body virtual field and the recently developed sensitivity‐based virtual fields. The results of these simulations are then used to select optimal processing parameters for the experimental data analysed in part 2.

Mechanisms of ligand binding.

Many processes in chemistry and biology involve interactions of a ligand with its molecular target. Interest in the mechanism governing such interactions has dominated theoretical and experimental analysis for over a century. The interpretation of molecular recognition has evolved from a simple rigid body association of the ligand with its target to appreciation of the key role played by conformational transitions. Two conceptually distinct descriptions have had a profound impact on our understanding of mechanisms of ligand binding. The first description, referred to as induced fit, assumes that conformational changes follow the initial binding step to optimize the complex between the ligand and its target. The second description, referred to as conformational selection, assumes that the free target exists in multiple conformations in equilibrium and that the ligand selects the optimal one for binding. Both descriptions can be merged into more complex reaction schemes that better describe the functional repertoire of macromolecular systems. This review deals with basic mechanisms of ligand binding, with special emphasis on induced fit, conformational selection, and their mathematical foundations to provide rigorous context for the analysis and interpretation of experimental data. We show that conformational selection is a surprisingly versatile mechanism that includes induced fit as a mathematical special case and even captures kinetic properties of more complex reaction schemes. These features make conformational selection a dominant mechanism of molecular recognition in biology, consistent with the rich conformational landscape accessible to biological macromolecules being unraveled by structural biology.

A Simplified Model, Dynamic Analysis and Force Estimation for a Large-scale Orinthopter in Forward Flight Based on Flight Data

Similarities and differences of a large-scale flapping-wing robot with fixed-wing UAVs in equations of motion, trim curves, and aerodynamic forces in forward flight are discussed in this paper and a simplified model for flapping flight is presented. Due to the high Wing to Total Weight (WTW) ratio of large-scale ornithopters, simple rigid body dynamics is not accurate enough for flight dynamics modeling. On the other hand, the multi-body dynamics associated with flapping gives little insight into the behavior of the resulting model due to complexity of equations. It is also difficult to design proper controllers for such complicated models. In this paper, the effects of different terms of multi-body equations of ornithopter on the estimated aerodynamic forces are studied via experimental flight data. A simpler but yet accurate set of equations is obtained by removing less effective terms from original relations. The presented model is in the form of normal aircraft equations plus some additional terms which can be used in different control and estimation processes. In addition, trim conditions of forward flight are extracted using several flight tests, and corresponding periodic behavior of states and forces are studied. These studies are applicable for identifying time-periodic models.

CUPyDO - An integrated Python environment for coupled fluid-structure simulations

CUPyDO, a fluid-structure interaction (FSI) tool that couples existing independent fluid and solid solvers into a single synchronization and communication framework based on the Python language is presented. Each coupled solver has to be wrapped in a Python layer in order to embed their functionalities (usually written in a compiled language) into a Python object, that is called and used by the coupler. Thus a staggered strong coupling can be achieved for time-dependent FSI problems such as aeroelastic flutter, vortex-induced vibrations (VIV) or conjugate heat transfer (CHT). The synchronization between the solvers is performed with the predictive block-Gauss-Seidel algorithm with dynamic under-relaxation. The tool is capable of treating non-matching meshes between the fluid and structure domains and is optimized to work in parallel using Message Passing Interface (MPI). The implementation of CUPyDO is described and its capabilities are demonstrated on typical validation cases. The open-source code SU2 is used to solve the fluid equations while the solid equations are solved either by a simple rigid body integrator or by in-house linear/nonlinear Finite Element codes (GetDP/Metafor). First, the modularity of the coupling as well as its ease of use is highlighted and then the accuracy of the results is demonstrated.

Multi-point vibration measurement and mode magnification of civil structures using video-based motion processing

Abstract Image-based vibration measurement has gained increased attentions in civil and construction communities. A recent video-based motion magnification method was developed to measure and visualize small structure motions. This new approach presents a potential for low-cost vibration measurement and mode shape identification. Pilot studies using this approach on simple rigid body structures were reported. Its validity on complex outdoor structures has not been investigated. In this study, a non-contact video-based approach for multi-point vibration measurement and mode magnification is introduced. The proposed approach can output a full-field vibration map that increases the efficiency of the current structural health monitoring (SHM) practice. The multi-point approach is developed based on the local phases which also fill the gap of the existing intensity-based multi-point vibration measurement. As an extension of the phase-based motion magnification, the multi-point measurement result is then integrated with the maximum likelihood estimation (MLE) to estimate the magnified frequency bands at each identified structure mode for operational deflection shape (ODS) visualization. This proposed method was tested in both indoor and outdoor environments for validation. The results show that using the developed method, mode frequencies and mode shapes of multiple points in complex structures can be simultaneously measured. And vibrations in each mode can be visualized separately after magnification.

Application of energy derivative method to determine the structural components' contribution to deceleration in crashes

ABSTRACTObjective: For occupant protection, it is important to understand how a car's deceleration time history in crashes can be designed using efficient of energy absorption by a car body's structure. In a previous paper, the authors proposed an energy derivative method to determine each structural component's contribution to the longitudinal deceleration of a car passenger compartment in crashes. In this study, this method was extended to 2 dimensions in order to analyze various crash test conditions. The contribution of each structure estimated from the energy derivative method was compared to that from a conventional finite element (FE) analysis method using cross-sectional forces.Method: A 2-dimensional energy derivative method was established. A simple FE model with a structural column connected to a rigid body was used to confirm the validity of this method and to compare with the result of cross-sectional forces determined using conventional analysis. Applying this method to a full-width frontal impact simulation of a car FE model, the contribution and the cross-sectional forces of the front rails were compared. In addition, this method was applied to a pedestrian headform FE simulation in order to determine the influence of the structural and inertia forces of the hood structures on the deceleration of the headform undergoing planar motion.Result: In an oblique impact of the simple column and rigid body model, the sum of the contributions of each part agrees with the rigid body deceleration, which indicates the validity of the 2-dimensional energy derivative method. Using the energy derivative method, it was observed that each part of the column contributes to the deceleration of the rigid body by collapsing in the sequence from front to rear, whereas the cross-sectional force at the rear of the column cannot detect the continuous collapse. In the full-width impact of a car, the contributions of the front rails estimated in the energy derivative method was smaller than that using the cross-sectional forces at the rear end of the front rails due to the deformation of the passenger compartment. For a pedestrian headform impact, the inertial and structural forces of the hood contributed to peaks of the headform deceleration in the initial and latter phases, respectively.Conclusions: Using the 2-dimensional energy derivative method, it is possible to analyze an oblique impact or a pedestrian headform impact with large rotations. This method has advantages compared to the conventional approach using cross-sectional forces because the contribution of each component to system deceleration can be determined.

Homogenized modeling methodology for 18650 lithium-ion battery module under large deformation.

Effective lithium-ion battery module modeling has become a bottleneck for full-size electric vehicle crash safety numerical simulation. Modeling every single cell in detail would be costly. However, computational accuracy could be lost if the module is modeled by using a simple bulk material or rigid body. To solve this critical engineering problem, a general method to establish a computational homogenized model for the cylindrical battery module is proposed. A single battery cell model is developed and validated through radial compression and bending experiments. To analyze the homogenized mechanical properties of the module, a representative unit cell (RUC) is extracted with the periodic boundary condition applied on it. An elastic–plastic constitutive model is established to describe the computational homogenized model for the module. Two typical packing modes, i.e., cubic dense packing and hexagonal packing for the homogenized equivalent battery module (EBM) model, are targeted for validation compression tests, as well as the models with detailed single cell description. Further, the homogenized EBM model is confirmed to agree reasonably well with the detailed battery module (DBM) model for different packing modes with a length scale of up to 15 × 15 cells and 12% deformation where the short circuit takes place. The suggested homogenized model for battery module makes way for battery module and pack safety evaluation for full-size electric vehicle crashworthiness analysis.

Investigation of optimal bipedal walking gaits subject to different energy‐based objective functions

AbstractOptimal bipedal walking gaits subject to different energy‐based objective functions are investigated using a simple planar rigid body model of a bipedal robot with upper body, thighs and shanks. The robot's segments are connected by revolute joints actuated by electric motors. The actuators' torques are generated by a trajectory tracking controller to produce periodic walking gaits. A numerical optimization routine is used to find optimal reference trajectories for average speeds in the range of 0.3 – 2.3 m/s to investigate the influence of different objective functions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Understanding hind limb lameness signs in horses using simple rigid body mechanics

Hind limb lameness detection in horses relies on the identification of movement asymmetry which can be based on multiple pelvic landmarks. This study explains the poorly understood relationship between hind limb lameness pointers, related to the tubera coxae and sacrum, based on experimental data in context of a simple rigid body model. Vertical displacement of tubera coxae and sacrum was quantified experimentally in 107 horses with varying lameness degrees. A geometrical rigid-body model of pelvis movement during lameness was created in Matlab. Several asymmetry measures were calculated and contrasted. Results showed that model predictions for tubera coxae asymmetry during lameness matched experimental observations closely. Asymmetry for sacrum and comparative tubera coxae movement showed a strong association both empirically (R2≥0.92) and theoretically. We did not find empirical or theoretical evidence for a systematic, pronounced adaptation in the pelvic rotation pattern with increasing lameness. The model showed that the overall range of movement between tubera coxae does not allow the appreciation of asymmetry changes beyond mild lameness. When evaluating movement relative to the stride cycle we did find empirical evidence for asymmetry being slightly more visible when comparing tubera coxae amplitudes rather than sacrum amplitudes, although variation exists for mild lameness. In conclusion, the rigidity of the equine pelvis results in tightly linked movement trajectories of different pelvic landmarks. The model allows the explanation of empirical observations in the context of the underlying mechanics, helping the identification of potentially limited assessment choices when evaluating gait.

A new model for pore formation by cholesterol-dependent cytolysins.

Cholesterol Dependent Cytolysins (CDCs) are important bacterial virulence factors that form large (200–300 Å) membrane embedded pores in target cells. Currently, insights from X-ray crystallography, biophysical and single particle cryo-Electron Microscopy (cryo-EM) experiments suggest that soluble monomers first interact with the membrane surface via a C-terminal Immunoglobulin-like domain (Ig; Domain 4). Membrane bound oligomers then assemble into a prepore oligomeric form, following which the prepore assembly collapses towards the membrane surface, with concomitant release and insertion of the membrane spanning subunits. During this rearrangement it is proposed that Domain 2, a region comprising three β-strands that links the pore forming region (Domains 1 and 3) and the Ig domain, must undergo a significant yet currently undetermined, conformational change. Here we address this problem through a systematic molecular modeling and structural bioinformatics approach. Our work shows that simple rigid body rotations may account for the observed collapse of the prepore towards the membrane surface. Support for this idea comes from analysis of published cryo-EM maps of the pneumolysin pore, available crystal structures and molecular dynamics simulations. The latter data in particular reveal that Domains 1, 2 and 4 are able to undergo significant rotational movements with respect to each other. Together, our data provide new and testable insights into the mechanism of pore formation by CDCs.

Spinning Janus doublets driven in uniform ac electric fields

We provide an experimental proof of concept for a robust, continuously rotating microstructure-consisting of two metallodielectric (gold-polystyrene) Janus particles rigidly attached to each other-which is driven in uniform ac fields by asymmetric induced-charge electro-osmosis. The pairs (doublets) are stabilized on the substrate surface which is parallel to the plane of view and normal to the direction of the applied electric field. We find that the radius of orbit and angular velocity of the pair are predominantly dependent on the relative orientations of the interfaces between the metallic and dielectric hemispheres and that the electrohydrodynamic particle-particle interactions are small. Additionally, we verify that both the angular and linear velocities of the pair are proportional to the square of the applied field which is consistent with the theory for nonlinear electrokinetics. A simple kinematic rigid body model is used to predict the paths and doublet velocities (angular and linear) based on their relative orientations with good agreement.

Design Tradeoffs of Wind Turbine Preview Control

Recent work demonstrated the benefits of preview wind measurements for turbine control. This paper investigates the basic design tradeoffs between turbine performance, preview time, and pitch actuator rate limits. A Region 3 rotor-speed tracking problem is formulated in continuous-time as an optimal control problem using a simple one-state rigid body turbine model. The exact analytical solution to this problem provides insight into the fundamental performance limits. These analytical results are compared with the performance of an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> preview controller simulated on a higher fidelity, nonlinear turbine model with realistic wind sensor models. The performance versus preview time characteristics of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controllers are in agreement with the predictions from the lower fidelity model. Thus, the analytical results obtained with the low-order model can provide design guidelines for the use of preview information in turbine control.

Dynamics of a Milkshaker – Passage Through Resonance and Frequency Transformation

AbstractRotor dynamics is a fascinating subject both from an experimental and a theoretical point of view. Most often experiments on various phenomena require more or less sophisticated test rigs, either because the experiments are dangerous or because the effects are difficult to reproduce. In teaching it is, however, beneficial to have experiments that are simple and can be performed by the students themselves. One of these examples is a standard milkshaker, which at a closer look, exhibits rich dynamical phenomena. The first phenomenon that can be observed and studied is the passage through resonance. Depending on the eccentricity of the rotor, the driving torque of the motor is strong enough or not to reach supercritical speeds. If for a given torque the eccentricity is too large, the system gets stuck in the resonance with a rather large amplitude. A second phenomenon that can be observed is the following: When the milkshaker is placed on an even surface it starts to move on the surface. The movement is caused by a wobbling motion of the system due to the eccentricity. Although the angular velocity of the rotor is high, the motion on the surface is quite slow in comparison. This is an interesting phenomenon that can be related to mechanical frequency transformation which occurs in the contact between the milkshaker and the ground. Depending on whether the rotor is running in a supercritical range or stuck below the resonance frequency, different motions can be observed. The system can be analyzed with a relatively simple nonlinear rigid body model. In this paper we study both phenomena mentioned above from a theoretical point of view. The equations of motion are derived in analytical form and their nonlinear behavior is investigated. Due to its relatively simple nature, the system has been used in lectures as a demonstrator and for student tutorial projects.

Structural Relationships Between Retaining and Inverting GT-B Glycosyltransferases as Revealed by Structure Analysis of Sucrose Synthase-1 from Arabidopsis Thaliana

Sucrose synthase-1 from Arabidopsis thaliana (AtSus1) is a member of the retaining GT-4 glycosyltransferase subfamily (i.e. the product sucrose has the same alpha configuration as the sugar donor UDP-glucose) within the larger family of metal-independent GT-B glycosyltransferases. A typical GT-B fold comprises of two structurally similar Rossmann folds (GT-BN and GT-BC) connected by two hinge regions. We have determined the structure of AtSus1 in catalytically competent closed state with UDP-glucose or fructose and UDP bound at the active site. Active site analysis provides future evidence for SNi-like reaction mechanism and functions of conserved residues His438, Glu675, Lys585 and Arg580. Structural Comparison of AtSus1 with inverting and retaining GTs of known structures revealed two interesting features of GT-B glycosyltrasferase. First, three loop regions have distinct lengths and differing positions between the inverting and retaining GTs and play an important role in determining the direction of attack on the anomeric carbon of the sugar moiety by the sugar acceptor. Second, a simple rigid body motion of GT-BN domain relative to GT-BC domain may be sufficient for the movement of the loops to open or close the attacking route. This domain motion suggests the two hinge regions connecting the two individual Rossmann folds in a particular orientation will stabilize either retaining or inverting reaction outcome over the other. Further understanding of the hinge region will provide new insights for glycosyltransferase engineering and may open up a broader substrate spectrum for glycosyltransfer reactions.The work was supported in part by grants from the NIH (GM65501) and Michigan State University (REF03-016) to RMG.

How to Change the Oligomeric State of a Circular Protein Assembly: Switch from 11-Subunit to 12-Subunit TRAP Suggests a General Mechanism

BackgroundMany critical cellular functions are performed by multisubunit circular protein oligomers whose internal geometry has evolved to meet functional requirements. The subunit number is arguably the most critical parameter of a circular protein assembly, affecting the internal and external diameters of the assembly and often impacting on the protein's function. Although accurate structural information has been obtained for several circular proteins, a lack of accurate information on alternative oligomeric states has prevented engineering such transitions. In this study we used the bacterial transcription regulator TRAP as a model system to investigate the features that define the oligomeric state of a circular protein and to question how the subunit number could be manipulated.Methodology/Principal FindingsWe find that while Bacillus subtilis and Bacillus stearothermophilus TRAP form 11-subunit oligomers, the Bacillus halodurans TRAP exclusively forms 12-subunit assemblies. Significantly, the two states of TRAP are related by a simple rigid body rotation of individual subunits around inter-subunit axes. We tested if such a rotation could be induced by insertion or deletion mutations at the subunit interface. Using wild type 11-subunit TRAP, we demonstrate that removal of five C-terminal residues at the outer side of the inter-subunit axis or extension of an amino acid side chain at the opposite, inner side, increased the subunit number from 11 to 12. Our findings are supported by crystal structures of TRAP oligomers and by native mass spectrometry data.Conclusions/SignificanceThe subunit number of the TRAP oligomer can be manipulated by introducing deletion or addition mutations at the subunit interface. An analysis of available and emerging structural data on alternative oligomeric states indicates that the same principles may also apply to the subunit number of other circular assemblies suggesting that the deletion/addition approach could be used generally to engineer transitions between different oligomeric states.

이중 블록 계통의 비선형 지진응답 특성

This paper discusses about modeling method to simulate a nonlinear behavior like sliding or rocking of two stacked body system under earthquake condition. A double body system design can be an option to reduce seismic response of a component in comparison to a single body system for free standing structures. Therefore, according to the priority of components, the structure is to be designed by proper ratio of partition in their height for improvement of seismic capability and structural integrity. Nonlinear modeling and analysis using simple rigid body and dynamic system has been performed to check the trend in such cases. As a result, one of the two bodies can be chosen to reduce the seismic response from energy absorption of the other one by appropriate application of friction ratios not only in slip-slip condition but in slip-rock condition. 기호설명 b : 블록(block)의 폭 c : 감쇠계수(damping coefficient) d : 무게중심의 이격 e : 반발계수(coefficient of restitution) f : 마찰력 g : 중력가속도 [m/s

Study of rocking motion of rigid body with slide contact

The purpose of this study is to formulate the motion of a rigid body with unilateral contact problems by applying techniques of multibody dynamics and to analyze the issue of rocking condition of rigid bodies with slide contact. In To investigate rocking motion with slide contact, we formulate for dynamics of a simple rigid body system with a unilateral contact model. Judgment for the occurrence of contact between a rigid body and a base is applied. The planar motion of a rigid body system having a simple shape and both with and without slide cases is assumed. Using constraint conditions for the contact as algebraic equations, the rocking motion of the rigid body, including slide and frictional force, is analyzed. The differential algebraic equation is solved by the augmented method with Lagrange multipliers, using generalized coordinates and independent variables that describe the contact points. The influence of the frequency and amplitude of disturbance given to the base is discussed.

The Dynamics of Multiple Pair-Wise Collisions in a Chain for Designing Optimal Shock Amplifiers

The major focus of this work is to examine the dynamics of velocity amplification through pair-wise collisions between multiple masses in a chain, in order to develop useful machines. For instance low-cost machines based on this principle could be used for detailed, very-high acceleration shock-testing of MEMS devices. A theoretical basis for determining the number and mass of intermediate stages in such a velocity amplifier, based on simple rigid body mechanics, is proposed. The influence of mass ratios and the coefficient of restitution on the optimisation of the system is identified and investigated. In particular, two cases are examined: in the first, the velocity of the final mass in the chain (that would have the object under test mounted on it) is maximised by defining the ratio of adjacent masses according to a power law relationship; in the second, the energy transfer efficiency of the system is maximised by choosing the mass ratios such that all masses except the final mass come to rest following impact. Comparisons are drawn between both cases and the results are used in proposing design guidelines for optimal shock amplifiers. It is shown that for most practical systems, a shock amplifier with mass ratios based on a power law relationship is optimal and can easily yield velocity amplifications of a factor 5–8 times. A prototype shock testing machine that was made using above principles is briefly introduced.

The Dynamics of Multiple Pair-Wise Collisions in a Chain for Designing Optimal Shock Amplifiers

The major focus of this work is to examine the dynamics of velocity amplification through pair-wise collisions between multiple masses in a chain, in order to develop useful machines. For instance low-cost machines based on this principle could be used for detailed, very-high acceleration shock-testing of MEMS devices. A theoretical basis for determining the number and mass of intermediate stages in such a velocity amplifier, based on simple rigid body mechanics, is proposed. The influence of mass ratios and the coefficient of restitution on the optimisation of the system is identified and investigated. In particular, two cases are examined: in the first, the velocity of the final mass in the chain (that would have the object under test mounted on it) is maximised by defining the ratio of adjacent masses according to a power law relationship; in the second, the energy transfer efficiency of the system is maximised by choosing the mass ratios such that all masses except the final mass come to rest following impact. Comparisons are drawn between both cases and the results are used in proposing design guidelines for optimal shock amplifiers. It is shown that for most practical systems, a shock amplifier with mass ratios based on a power law relationship is optimal and can easily yield velocity amplifications of a factor 5-8 times. A prototype shock testing machine that was made using above principles is briefly introduced.

2304 すべりを伴う車輪・レール系のロッキングに関する研究(OS4-1 接触問題とトライボロジ(その1),OS4 接触問題とトライボロジ,オーガナイズド・セッション)

The purpose of this study is to formulate a motion of a rigid body with unilateral contact problems by applying techniques of multibody dynamics and to analyze the issue of rocking condition of the rigid bodies with slide contact. In order to deal with rocking motion with slide contact, we formulate for dynamics of simple rigid body system with unilateral contact model. Judgment for occurrence of the contact between a rigid body and a base are applied. A planar motion of the rigid body system having a simple shape and both cases with and without slide are assumed. We analyze rocking motion of the rigid body including slide and frictional force. We solve the differential algebraic equation by augmented method with Lagrange multipliers, using generalized coordinates and independent variables which describe contact points. The influence of the frequency and amplitude of disturbance given to the base are discussed.