Rigid-body Analysis Research Articles

Structural Assessment of Late Neolithic Sa Covaccada Dolmen, Sardinia, Italy

ABSTRACT The application of structural engineering tools to archaeological sites is unusual, while architects, archaeologists, and restorers are more commonly involved in these scenarios. Nevertheless, it can provide valuable indications for conservation and repair. This paper presents the structural assessment of the late Neolithic Sa Covaccada Dolmen, in Sardinia, Italy, regarded as a unicum in the Region and one of the most important megalithic monuments in the Mediterranean area. Due to severe material deterioration and extensive crack pattern, structural stability is a primary concern, yet it has not been assessed to date. To address this, both analytical rigid body analyses and 2D and 3D discrete element simulations were performed, contributing to an as challenging as fascinating multidisciplinary restoration project.

Test and numerical analysis for water entry of elastic cabin from amphibious aircraft

Water-entry performance of amphibious aircraft is one of the main factors affecting the structural design. However, it is analyzed by rigid models in general, which is difficult to reflect the elastic characteristics of the structure. And it is difficult to obtain sufficient guidance for structural design from rigid-body analysis. In this study, water-entry model of an elastic cabin from amphibious aircraft was developed using the Arbitrary Lagrangian-Eulerian (ALE) method and validated by a designed 1:1 cabin water-entry test. Analysis under various conditions revealed the cabin's dynamic response in three steps: (1) the keel of the cabin section touches the water, (2) the bottom skin is wetted, and (3) the bottom skin is submerged. This study also compares the rigid-surface crashes and water-entry impacts of the cabin from the point of view of load and energy analysis. The results show that rigid-surface crash mainly affects bulkhead and keel, whereas water-entry energy is mainly absorbed by the skin, connectors, and stringers. Additionally, varying skin thicknesses showed a negative correlation with back surface deformation. The methodologies and conclusions presented in this study can offer valuable references for researchers in the field of water entry.

A hybrid statistical morphometry free-form deformation approach to 3D personalized foot-ankle models

Foot and ankle joint models are widely used in the biomechanics community for musculoskeletal and finite element analysis. However, personalizing a foot and ankle joint model is highly time-consuming in terms of medical image collection and data processing. This study aims to develop and evaluate a framework for constructing a comprehensive 3D foot model that integrates statistical shape modeling (SSM) with free-form deformation (FFD) of internal bones. The SSM component is derived from external foot surface scans (skin measurements) of 50 participants, utilizing principal component analysis (PCA) to capture the variance in foot shapes. The derived surface shapes from SSM then guide the FFD process to accurately reconstruct the internal bone structures. The workflow accuracy was established by comparing three model-generated foot models against corresponding skin and bone geometries manually segmented and not part of the original training set. We used the top ten principal components representing 85 % of the population variation to create the model. For prediction validation, the average Dice similarity coefficient, Hausdorff distance error, and root mean square error were 0.92 ± 0.01, 2.2 ± 0.19 mm, and 2.95 ± 0.23 mm for soft tissues, and 0.84 ± 0.03, 1.83 ± 0.1 mm, and 2.36 ± 0.12 mm for bones, respectively. This study presents an efficient approach for 3D personalized foot model reconstruction via SSM generation of the foot surface that informs bone reconstruction based on FFD. The proposed workflow is part of the open-source Musculoskeletal Atlas Project linked to OpenSim and makes it feasible to accurately generate foot models informed by population anatomy, and suitable for rigid body analysis and finite element simulation.

A Distributed Impact Model for Seismic Analysis of Planar Rocking Body

ABSTRACT The problem of a planar rigid rocking block subject to dynamic loading is of significant interest to the earthquake engineering community due to its wide application. Despite its simple configuration, rocking itself is a highly nonlinear phenomenon which exhibits non-smooth dynamic behavior. The non-smoothness in dynamics comes from the sudden impact of the rocking body with ground when the sign of rotation angle reverses. Therefore the impact model used in the simulation for rocking problem has a profound influence on the dynamic behavior. Most of existing impact models assume that the impulse during impact is concentrated at the pivot point of the block, ignoring the potential distribution of impulses. This study proposes a distributed impact model for dynamic analysis of planar rigid rocking body. The distributed impulses are achieved through the integration of normal forces induced by penetration over a dummy time period during impact. The distributed impact model is subsequently used to evaluate the post-impact quantities of interest. Numerical simulations suggest Housner’s impact model is a special case of the proposed model. The developed impact model is also compared with published experimental result, showing good accuracy. Finally, evaluation of overturning spectra under analytical pulse excitations suggests that using the distributed impact model can give substantially different results compared to the classic concentrated impact model for relatively stocky blocks. Similar observations can also be made when evaluating rocking responses under seismic excitations.

Mechanical energy flow analysis in athletes with and without anterior cruciate ligament reconstruction during single-leg drop landing

Techniques that reduce mechanical energy have been linked to lower chances of experiencing an Anterior Cruciate Ligament (ACL) injury. Although there is evidence that movement patterns are altered in athletes who have undergone Anterior Cruciate Ligament Reconstruction (ACLR), energy transfer mechanisms have not been examined. This study aimed to compare energy flow mechanisms during single-leg drop landing between athletes with and without history of ACLR. A total of 20 female athletes were included in this study. Ten participants underwent ACLR 12 months ago (mean age, 21.57 ± 0.41 years) and 10 were healthy controls (mean age, 20.89 ± 0.21 years). Participants executed the single-leg drop landing (SLL) maneuver by descending from a 30 cm wooden box and landing on the tested leg on an embedded force plate. Information collected during the SLL trials was refined using rigid-body analysis and inverse dynamics within Nexus software, ultimately allowing construction of skeletal models of the athletes. Ankle and knee mechanical energy expenditure (MEE) was higher in the control participants during landing. However, the result for the hip MEE demonstrated that MEE of the control group was significantly lower compared with the ACLR group, but MEE of the control subjects was higher as compared to ACLR group (p ˂ 0.05). Results suggest the avoidant use of the quadriceps muscle post ACLR leads to knee-avoidant mechanics and loss of knee joint power generation during a SLL task.

Global Attitude Synchronization for Networked Rigid Bodies Under Directed Topologies

This paper is devoted to dealing with global attitude synchronization problems for networked rigid bodies subjected to directed topologies and arbitrary initial orientations. To avoid the asynchronous pitfall where only vector parts of rigid bodies reach agreement on some identical value but scalar parts do not, multiplicative quaternion errors are incorporated to develop attitude synchronization protocols for rigid bodies with absolute attitude measurements. It is shown that global synchronization of networked rigid bodies is achieved if and only if the directed topology is quasi-strongly connected. Simultaneously, a novel double-energy-function analysis method, equipped with an ordering permutation technique for the scalar parts and a coordinate transformation mechanism, is constructed for the quaternion behavior analysis of networked rigid bodies. In particular, global synchronization works well with our analysis method, regardless of the highly nonlinear and strongly coupling problems resulting from multiplicative quaternion errors, which seriously hinder the traditional analysis of global synchronization for networked rigid bodies. Simulations for networked spacecraft are presented to validate global synchronization performances under different directed topologies.

Homogenization of plane ring mesh under static loading

AbstractPlane ring meshes can be produced in large dimensions for various applications, for example, in architecture or protective systems. The numerical simulation of all individual rings of ring meshes is very costly, which is why methods to abstract the structure have been sought in the past. In this paper, a method for determining the strain parameters of a representative ring mesh section under in‐plane tensile loads is presented. Methods of rigid body analysis and representative volume elements with periodic boundary conditions are used. Green Lagrangian strain tensors are determined for both an exemplary representative ring mesh section under different tensile load cases and an experimental ring mesh under one load case. The comparison of the Green Lagrangian strain tensors of the ring meshes between numerical simulations and experiments shows a very good agreement.

Experimental and Mathematical Study of Flexible–Rigid Rail Vehicle Riding Comfort and Safety

This paper analyses the dynamic behavior of a rail vehicle using experimental and simulation analysis on a multi-rigid–flex body model. The mathematical models are developed considering the car body, bogie frame, and wheel axle for rail vehicles of rigid–flexible and multi-rigid formulations, taking the car body as rigid for the rigid body analysis and the flexible car body for flex–rigid analysis. A finite element model of the car body was developed in ANSYS, and substructure and modal analyses were performed. The mathematical model is validated through an experiment conducted by the Research Design and Standards Organization. Then, the validated model is further analyzed to evaluate the running comfort, using the Sperling ride index and the running safety, by investigating the derailment coefficient and wheel load reduction rate. The impact of flexibility on the vehicle’s running stability is investigated using the rigid body dynamics model and experimental data. Compared to experimental data, the simulation results reveal that elastic vibration cannot be neglected in vehicle dynamics, since the rigid–flexible coupling model is slightly more significant than the rigid-body model for ride comfort and safety.

Ride analysis of railway vehicle considering rigidity and flexibility of the carbody

ABSTRACT In this paper, a twenty-one degrees of freedom mathematical model of a railway vehicle is formulated, considering its main components (i.e. carbody, bolster, bogie frame, and wheel axle) as rigid for the rigid body analysis of ride behavior of the vehicle. The ride comfort of the vehicle is analyzed and optimized using ISO 2631 criteria. Further, vertical flexibility of the carbody is accounted for with few modifications in the model, and the effect of vertical stiffness on ride behavior is analyzed and compared with a rigid carbody analysis using the Spering ride index. The carbody bending frequencies are investigated using the covariance method, and it is found that the reduction in stiffness of carbody beyond a specific frequency introduces significant carbody acceleration and declines the vehicle ride. The increased carbody bending frequencies can achieve higher vehicle speed and adequate isolation from track excitations.

Accuracy Evaluation of an Alternative Approach for a CAD-AM Mandibular Reconstruction with a Fibular Free Flap via a Novel Hybrid Roto-Translational and Surface Comparison Analysis

Although the fibula free flap represents the gold standard for mandibular reconstructions, when implanted as a single barrel, this flap does not have the cross-sectional requisites to restore the native mandibular height, which is in turn required for the implant-supported dental rehabilitation of the patient. Our team has developed a design workflow that already considers the predicted dental rehabilitation, positioning the fibular free flap in the correct craniocaudal position to restore the native alveolar crest. The remaining height gap along the inferior mandibular margin is then filled by a patient-specific implant. The aim of this study is to evaluate the accuracy in transferring the planned mandibular anatomy resulting from said workflow on 10 patients by means of a new rigid body analysis method, derived from the evaluation of orthognathic surgery procedures. The analysis method has proved to be reliable and reproducible, and the results obtained show that the procedure already has satisfactory accuracy (4.6° mean total angular discrepancy, 2.7 mm total translational discrepancy, 1.04 mm mean neo-alveolar crest surface deviation), while also pointing out possible improvements to the virtual planning workflow.

Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles

<p style='text-indent:20px;'>Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid body dynamics in the geometric mechanics framework and a novel development of U-K formulation for use on nonlinear manifolds, namely the special Euclidean group <inline-formula><tex-math id="M1">\begin{document}$ {\mathsf{SE}(3)}$\end{document}</tex-math></inline-formula> and its second order tangent bundle <inline-formula><tex-math id="M2">\begin{document}${\mathsf{T}^2\mathsf{SE}(3)} $\end{document}</tex-math></inline-formula>, is proposed in addition to the formulation development on Euclidean spaces. Then, a Morse-Lyapunov based tracking controller using backstepping is applied to capture disturbed initial conditions that the U-K formulation cannot account for. This theoretical development is then applied to fully-constrained and underconstrained scenarios of rigid-body spacecraft motion in a lunar orbit, and the translational and rotational motions of the spacecraft and the control inputs obtained using the proposed methodologies to achieve and maintain those constrained motions are studied.</p>

RESPONSE OF A HIGH-SPEED WAVE-PIERCING CATAMARAN TO AN ACTIVE RIDE CONTROL SYSTEM

Ride control systems on high-seed vessels are an important design features for improving passenger comfort and reducing motion sickness and dynamic structural loads. To investigate the performance of ride control systems a 2.5m catamaran model based on the 112m INCAT catamaran was tested with an active centre bow mounted T-Foil and two active stern mounted trim tabs. The model was set-up for towing tank tests in calm water to measure the motions response to ride control step inputs. Heave and pitch response were measured when the model was excited by deflections of the T-Foil and the stern tab separately. Appropriate combinations of the control surface deflections were then determined to produce pure heave and pure pitch response. This forms the basis for setting the gains of the ride control system to implement different control algorithms in terms of the heave and pitch motions in encountered waves. A two degree of freedom rigid body analysis was undertaken to theoretically evaluate the experimental results and showed close agreement with the tank test responses. This work gives an insight into the motions control response and forms the basis for future investigations of optimal control algorithms.

Precision Assembly Simulation of Skin Model Shapes Accounting for Contact Deformation and Geometric Deviations for Statistical Tolerance Analysis Method

Tolerance analysis methods, which are important to achieve a balance between manufacturing costs and functional requirements, have been studied and improved over the last 30 years. This paper proposes a new method to improve the precision of assembly simulation for statistical assembly simulation; by investigating the effect of the geometric deviations and mechanical behaviors of assembly contact on the stack-up assembly deviation by combining the recent theories on the tolerance analysis of rigid bodies and local contact deformation. To improve the precision of the tolerance analysis, real parts with form defects were simulated with the help of non-nominal skin model shapes. The SMSs were first considered to be rigid, and a quadratic optimization-based method for the rigid body displacement was used to calculate the initial contact points of all the SMSs. Next, contact deformation, following Hertzian contact theory, occurred at the initial contact points, which changed the relative positions of the SMSs in the subsequent interactions. The iteration process was convergent, and the final simulation for tolerance analysis could be generated after several iterations. Case studies demonstrated the practicality of the proposed method. Their actual assembly deviations were simulated by combining the effects of geometric deviations and local surface deformations. Since the proposed tolerance analysis framework based on statistical assembly simulation, it is expected to control the functional requirements of mechanical assemblies with much rough tolerance design and help optimize the tolerance in the future.

Aero-Propulso-Elastic Analysis of a Supersonic Transport

An aeroelastic modeling capability of a flexible aircraft with gas turbine engines is developed using a computational fluid dynamics tool as an integration platform. The new modeling capability allows for the typical aeroelastic analysis to include a nonlinear dynamic model of the turbomachinery that is capable of capturing relevant gas dynamics. An example case of the aero-propulso-elastic (APE) modeling capability is explored for a supersonic transport vehicle with turbofan engines. An overview of the methodology for integrating the propulsion system and elastic vehicle is provided. This is followed by a study to explore coupling sensitivities compared against typical aeroelastic analysis. Dynamic and static vehicle responses are considered across key flight conditions and vehicle-level angles of attack, where the inclusion of the propulsion system has a 10% increase in vehicle wing tip deformations. It is found that the propulsion system is stable at various operating conditions, with structural oscillations having little impact on propulsion system performance. Perceived loudness, a key performance metric for a supersonic transport, is investigated using the APE model. Results lead to an approximately 4 dB increase in noise over a rigid body analysis that neglects the propulsion system. The greatest impacts are shown during off-nominal conditions.

Changes in inertial parameters of the lower limb during the impact phase of dynamic tasks

Mechanical analysis at the whole human body level typically assumes limbs are rigid bodies with fixed inertial parameters, however, as the human body consists mainly of deformable soft tissue, this is not the case. The aim of this study was to investigate changes in the inertial parameters of the lower limb during landing and stamping tasks using high frequency three-dimensional motion analysis. Seven males performed active and passive drop landings from 30 and 45 cm and a stamp onto a force plate. A sixteen-camera 750 Hz Vicon system recorded markers for standard rigid body analysis using inverse kinematics in Visual 3D and 7 × 8 and 7 × 9 marker arrays on the shank and thigh. Frame by frame segment volumes from marker arrays were calculated as a collection of tetrahedra using the Delaunay triangulation method in 3D and further inertial parameters were calculated using the method of Tonon (2004). Distance between the centres of mass (COM) of the rigid and soft tissues changed during impact in a structured manner indicative of a damped oscillation. Group mean amplitudes for COM motion of the soft tissues relative to the rigid body of up to 1.4 cm, and changes of up to 17% in moment of inertia of the soft tissue about the rigid body COM were found. This study has shown that meaningful changes in inertial parameters can be observed and quantified during even moderate impacts. Further examination of the effects these could have on movement dynamics and energetics seems pertinent.

Interactive fluid flow simulation in computer graphics using incompressible smoothed particle hydrodynamics

AbstractInteractive simulations of fluids flow play an important role in several computer graphics‐based applications such as computer games, computer animation, movie industry, and virtual realities. The incompressible smoothed particle hydrodynamics (ISPH) model is a promising numerical scheme for large‐scale and large‐deformation simulations, where the pressure can be determined precisely by solving pressure Poisson equation (PPE). The three main shortcomings of the ISPH scheme are oscillating pressure, particles disorders, and particles penetrations through rigid boundary. In this paper, the stable pressure is obtained from modifications in the source term of PPE, in which the divergence‐free velocity condition plus density‐invariance condition multiply by a relaxation coefficient are included. The particles disorders are solved via utilizing a shifting technique with the current treatment of source term in PPE. Additionally, the dummy boundary particles are used for the rigid boundary treatment. For getting enough pressure on the boundary, the Neumann boundary condition is satisfied during the implicit solving processes. The performance of the stabilized ISPH model is tested on various numerical simulations with largely distorted free surface including liquid sloshing problems, fluid–fluid and fluid–structure interactions, and dam‐break flows. To extend the applicability of the stabilized ISPH model, the post process including visual realism with a highly rendering scheme is coupled. The coupled scheme introduces several simulations including free falling of a rigid body, water splashes, and dam break analysis. Furthermore, the proposed ISPH‐based method enables efficient and viscous fluid simulations with large time steps, higher viscosities, and resolutions, and it is a robust scheme in long interval simulations of nonlinear free‐surface flows.

Mechanics of rigid body and structural calculus interconnection in applications

Mechanical structural calculus can be a complex task, considering quality and quantity of treated aspects. Mechanics of rigid body and structural analysis are two mechanical engineering well defined fields. Amazing, and in many cases favorable, calculus aspects of rigid body mechanics and strength of materials are interconnecting one each other, and so they validate the problem formulation and the solution. A complex application, floating crane, illustrates the above mentioned aspects.

Study on kinematics and inverse dynamics of legged mobile manipulator for determining feet-terrain reaction forces and joint torques

Legged mobile manipulator is a robotic system that consists of a serial manipulator rigidly mounted on a multi-legged platform. Its high mobility and dexterity makes this robotic system more suitable to be used in disaster management and space applications, where there will be an uneven and unstructured terrain. However, its high power consumption and low stability under external disturbances are the challenges to be solved. In this paper, an attempt is made to determine the feet-terrain reaction forces and joint actuating torques, which ensures the minimum power consumption. Initially, the kinematic model of the robotic system is developed using general-purpose rigid body analysis. Newton–Euler approach is then utilized to formulate the coupled dynamics of this multi-body system. The developed inverse dynamics model considers the inertial effects of the manipulator and moving legs on the trunk body and stationary legs. However, it has no unique solution due to its high redundancy. Therefore, it has been formulated as an optimization problem in order to minimize the power consumption after satisfying some functional constraints. The performance of the developed approach has been tested on computer simulations. The results show that the developed model can efficiently study the kinematics and dynamics of the legged mobile manipulator and also explain the nature of shifting of center of gravity of the combined robotic system due to the movement of the manipulator links. The developed model is a generalized one and it can be used for carrying out stability analysis and designing suitable controller for the combined robotic system.

On the Stability Analysis of a Coupled Rigid Body

In this research article, we investigate the stability of a complex dynamical system involving coupled rigid bodies consisting of three equal masses joined by three rigid rods of equal lengths, hinged at each of their bases. The system is free to oscillate in the vertical plane. We obtained the equation of motion using the generalized coordinates and the Euler-Lagrange equations. We then proceeded to study the stability of the dynamical systems using the Jacobian linearization method and subsequently confirmed our result by phase portrait analysis. Finally, we performed MathCAD simulation of the resulting ordinary differential equations, describing the dynamics of the system and obtained the graphical profiles for each generalized coordinates representing the angles measured with respect to the vertical axis. It is discovered that the coupled rigid pendulum gives rise to irregular oscillations with ever increasing amplitude. Furthermore, the resulting phase portrait analysis depicted spiral sources for each of the oscillating masses showing that the system under investigation is unstable.

FEA integration in the tolerance analysis using Skin Model Shapes

Many research works on tolerance analysis have been carried out in the last thirty years. In this paper, a new idea is proposed, aiming to investigate the effect of form error and mechanical behavior of parts on the stack-up result by combining the recent novelties on the tolerance analysis of rigid and flexible bodies. The real parts are simulated considering the non-nominal Skin Model Shape and the mechanical properties in order to simulate the assembly of a realistic case study. A manufacturing signature model to generate the features with geometric deviations and Finite Element Analysis (FEA) are used.