Theoretical and experimental studies of unbraced tubular trusses allowing for torsional stiffness

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.

Influence of nonlinear stiffness on the dynamics of a slender elastic beam under torsional oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

Análise de um veículo todo o terreno do tipo KARTCROSS

O presente trabalho descreve a análise feita a um veículo de todo o terreno. O kartcross/buggy em estudo é usado em provas do tipo Baja, sendo estas provas longas e com traçados sinuosos. O veículo, já construído, foi testado através de softwares, a nível estrutural e ciclístico, pretendendo-se assim efetuar engenharia inversa sobre o mesmo. No decorrer da sua utilização normal o kartcross/buggy sofre vários tipos de solicitações, como sejam aceleração, travagem e força centrípta em curva. Portanto, o veículo deve ser capaz de suportar estes esforços e ter uma boa habilidade. Além dos testes em uso corrente foi analisada também a rigidez torsional do quadro do veículo e do veículo completo, podendo-se assim melhorar estes valores. A nível ciclístico foram analisados os parâmetros das suspensões como o camber, convergência/divergência, caster, entre outros. Da análise destes parâmetros e possível fazerem-se melhorias de forma a que o veículo tenha um melhor desempenho. Para validar os testes computacionais efetuados foi reproduzido experimentalmente o teste da rigidez torsional. No final, compararam-se os valores numéricos com os experimentais e aferir se o modelo se encontra bem representado.

Avaliação da rigidez torcional do chassi de um protótipo Baja SAE através do método de elementos finitos e de ensaio experimental

The torsional stiffness of chassis is one of the most important properties of a vehicle's structure and therefore its measurement is important. For the first time, the torsional stiffness was considered on the design of a prototype Baja SAE of the team from UNESP - FEG, Equipe Piratas do Vale Bardahl. According to the team's opinion, the increase of stiffness on this prototype, called MB1114, made possible a great improvement in its performance during competitions. In this work, the experimental evaluation of the torsional stiffness from this prototype is performed, detailing the analysis of results, as well as, the hysteresis' effect, least-squares regression and uncertainty analysis. It also shows that it is possible to measure the torsional stiffness of chassis with a low experimental uncertainty without expending many resources. The test rig costed R$ 32,50 due the reuse of materials and the use of instrumentation already available on campus. Furthermore, it is simple to produce and can be easily stocked. Those features are important for Baja and Formula SAE teams. Lastly, the measured value is used to validate the finite element analysis performed by the team during this prototype's design, because similar studies will be performed for the new cars. After investigating the finite element analysis, one result 13,5% higher than the measured value was reached. This difference is believed to be occurred due the imperfections of the finite element model, in other words, for not been possible to simulate every phenomena present on the real model

Avaliação da rigidez torcional do chassi de um protótipo Baja SAE através do método de elementos finitos e de ensaio experimental

The torsional stiffness of chassis is one of the most important properties of a vehicle's structure and therefore its measurement is important. For the first time, the torsional stiffness was considered on the design of a prototype Baja SAE of the team from UNESP - FEG, Equipe Piratas do Vale Bardahl. According to the team's opinion, the increase of stiffness on this prototype, called MB1114, made possible a great improvement in its performance during competitions. In this work, the experimental evaluation of the torsional stiffness from this prototype is performed, detailing the analysis of results, as well as, the hysteresis' effect, least-squares regression and uncertainty analysis. It also shows that it is possible to measure the torsional stiffness of chassis with a low experimental uncertainty without expending many resources. The test rig costed R$ 32,50 due the reuse of materials and the use of instrumentation already available on campus. Furthermore, it is simple to produce and can be easily stocked. Those features are important for Baja and Formula SAE teams. Lastly, the measured value is used to validate the finite element analysis performed by the team during this prototype's design, because similar studies will be performed for the new cars. After investigating the finite element analysis, one result 13,5% higher than the measured value was reached. This difference is believed to be occurred due the imperfections of the finite element model, in other words, for not been possible to simulate every phenomena present on the real model

Studio del comportamento flesso-torsionale di un telaio in materiale composito per vettura sportiva

Lo studio svolto in merito alle tecniche di produzione di componenti strutturali in materiale composito ha permesso il raggiungimento di una precisa consapevolezza dello stato dell’arte del settore, in particolare in riferimento ai processi attualmente utilizzati per l’industrializzazione in media-grande serie. Con l’obiettivo di sintetizzare i principali vantaggi delle tecnologie suddette e permettere la realizzazione di forme più complesse, si è proceduto all’analisi di fattibilità, attraverso uno studio funzionale e una prima progettazione di una tecnologia di produzione per nastratura automatizzata di componenti strutturali in materiale composito. Si è voluto quindi dimostrare la flessibilità e la consistenza del processo disegnando un telaio nastrato in carbonio, intercambiabile al telaio FSAE 2009 in tubolare d’acciaio (stessi punti di attacco motore, punti di attacco telaietto posteriore, attacchi sospensioni anteriori) e che garantisca un sostanziale vantaggio in termini di peso, a pari rigidezza torsionale. La caratterizzazione di tale telaio è stata eseguita mediante l'utilizzo del calcolo strutturale, validato da prove sperimentali.

Minimalinvasive Osteosynthese der distalen extraartikulären Radiusfraktur : XSCREW und DorsalNailPlate im biomechanischen Vergleich

Gegenstand der Arbeit: Die distale Radiusfraktur ist der häufigste Bruch des Menschen. Neben etablierten Verfahren wie der dorsalen und palmaren Plattenosteosynthese gibt es seit Kurzem neuartige minimalinvasive Osteosynthesesysteme. Gegenstand der vorliegenden Arbeit ist die Untersuchung der biomechanischen Stabilität von zwei neuartigen Implantaten für die distale extraartikuläre Radiusfraktur. rnMethodik: Es handelt sich einerseits um das System XSCREW (Zimmer, Freiburg i. Br., Deutschland), eine kanülierte Schraube, die über den Processus styloideus eingeführt wird und mit bis zu neun Bohrdrähten im Knochen fixiert werden kann. Das Vergleichsimplantat DorsalNailPlate (HandInnovations, Miami, Florida, USA) ist ein Hybrid aus einer dorsalen Platte und einem Marknagel. Beide Systeme wurden an 8 paarigen frischen unfixierten Leichenradii unter Axialbelastung bis 100 N und Torsionsbelastung bis 1,5 Nm getestet. Die A3-Fraktur wurde durch eine standardisierte Keilosteotomie simuliert. Das Biomaterial wurde prä- und postinterventionell sowie nach einem Dauerbelastungstest unter 1000 Zyklen in Rotation mit 0,5 Hz untersucht. Ein Versagenstest mit steigendem Drehmoment beendete das Experiment. rnErgebnisse: Die XSCREW erreichte eine Axialsteifigkeit von 136 N/mm und eine Torsionssteifigkeit von 0,16 Nm/°. Die DNP erzielte hingegen axial 70 N/mm und torsional 0,06 Nm/°. Der Unterschied zwischen beiden Verfahren war nur für die Torsion eindeutig statistisch auffällig (p=0,012), jedoch nicht für die Axialsteifigkeit (p=0,054). Die ursprüngliche Axial- und Torsionssteifigkeit wurde durch die XSCREW signifikant besser wiederhergestellt als durch die DNP (p=0,012). Beide Verfahren erzielten nach der Intervention signifikant niedrigere Steifigkeiten als die intakten Knochen (p=0,012). Ein Präparat der DNP-Gruppe und vier Präparate der XSCREW-Gruppe überstanden den Dauerbelastungstest. Das Drehmoment bei Versagen war mit der XSCREW höher als mit der DNP, der Unterschied zwischen den Verfahren war signifikant (p=0,043). Die Schwachstellen beider Systeme lagen vorwiegend in der proximalen Verankerung im Knochen. Kirschner-Drähte bzw. Verriegelungsschrauben führten unter andauernder Belastung zu einer Spaltung der Kortikalis im Schaftbereich. Bedingt durch die Ausrichtung der distalen Verriegelungen können mit beiden Implantaten Schäden an der radiocarpalen bzw. radioulnaren Gelenkfläche entstehen. rnZusammenfassung: Die XSCREW ermöglicht insgesamt eine höhere mechanische Stabilität als die DNP. Beide Verfahren sind jedoch einer winkelstabilen palmaren Plattenosteosynthese insbesondere unter rotatorischer Dauerbelastung unterlegen und erreichen nicht die Stabilität eines anderen neuartigen minimalinvasiven Systems.

Biomechanical analysis of torsion and shear forces in lumbar and lumbosacral spine segments of nonchondrodystrophic dogs

OBJECTIVE: To determine stiffness and load-displacement curves as a biomechanical response to applied torsion and shear forces in cadaveric canine lumbar and lumbosacral specimens. STUDY DESIGN: Biomechanical study. ANIMALS: Caudal lumbar and lumbosacral functional spine units (FSU) of nonchondrodystrophic large-breed dogs (n=31) with radiographically normal spines. METHODS: FSU from dogs without musculoskeletal disease were tested in torsion in a custom-built spine loading simulator with 6 degrees of freedom, which uses orthogonally mounted electric motors to apply pure axial rotation. For shear tests, specimens were mounted to a custom-made shear-testing device, driven by a servo hydraulic testing machine. Load-displacement curves were recorded for torsion and shear. RESULTS: Left and right torsion stiffness was not different within each FSU level; however, torsional stiffness of L7-S1 was significantly smaller compared with lumbar FSU (L4-5-L6-7). Ventral/dorsal stiffness was significantly different from lateral stiffness within an individual FSU level for L5-6, L6-7, and L7-S1 but not for L4-5. When the data from 4 tested shear directions from the same specimen were pooled, level L5-6 was significantly stiffer than L7-S1. CONCLUSIONS: Increased range of motion of the lumbosacral joint is reflected by an overall decreased shear and rotational stiffness at the lumbosacral FSU. CLINICAL RELEVANCE: Data from dogs with disc degeneration have to be collected, analyzed, and compared with results from our chondrodystrophic large-breed dogs with radiographically normal spines.

Papain-induced in vitro disc degeneration model for the study of injectable nucleus pulposus therapy

BACKGROUND CONTEXT Proteolytic enzyme digestion of the intervertebral disc (IVD) offers a method to simulate a condition of disc degeneration for the study of cell-scaffold constructs in the degenerated disc. PURPOSE To characterize an in vitro disc degeneration model (DDM) of different severities of glycosaminoglycans (GAG) and water loss by using papain, and to determine the initial response of the human mesenchymal stem cells (MSCs) introduced into this DDM. STUDY DESIGN Disc degeneration model of a bovine disc explant with an end plate was induced by the injection of papain at various concentrations. Labeled MSCs were later introduced in this model. METHODS Phosphate-buffered saline (PBS control) or papain in various concentrations (3, 15, 30, 60, and 150 U/mL) were injected into the bovine caudal IVD explants. Ten days after the injection, GAG content of the discs was evaluated by dimethylmethylene blue assay and cell viability was determined by live/dead staining together with confocal microscopy. Overall matrix composition was evaluated by histology, and water content was visualized by magnetic resonance imaging. Compressive and torsional stiffness of the DDM were also recorded. In the second part, MSCs were labeled with a fluorescence cell membrane tracker and injected into the nucleus of the DDM or a PBS control. Mesenchymal stem cell viability and distribution were evaluated by confocal microscopy. RESULTS A large drop of GAG and water content of the bovine disc were obtained by injecting >30 U/mL papain. Magnetic resonance imaging showed Grade II, III, and IV disc degeneration by injecting 30, 60, and 150 U/mL papain. A cavity in the center of the disc could facilitate later injection of the nucleus pulposus tissue engineering construct while retaining an intact annulus fibrosus. The remaining disc cell viability was not affected. Mesenchymal stem cells injected into the protease-treated DDM disc showed significantly higher cell viability than when injected into the PBS-injected control disc. CONCLUSIONS By varying the concentration of papain for injection, an increasing amount of GAG and water loss could be induced to simulate the different severities of disc degeneration. MSC suspension introduced into the disc has a very low short-term survival. However, it should be clear that this bovine IVD DDM does not reflect a clinical situation but offers exciting possibilities to test novel tissue engineering protocols.

Mechanical restoration and failure analyses of a hydrogel and scaffold composite strategy for annulus fibrosus repair

Unrepaired defects in the annulus fibrosus of intervertebral disks are associated with degeneration and persistent back pain. A clinical need exists for a disk repair strategy that can seal annular defects, be easily delivered during surgical procedures, and restore biomechanics with low risk of herniation. Multiple annulus repair strategies were developed using poly(trimethylene carbonate) scaffolds optimized for cell delivery, polyurethane membranes designed to prevent herniation, and fibrin-genipin adhesive tuned to annulus fibrosus shear properties. This three-part study evaluated repair strategies for biomechanical restoration, herniation risk and failure mode in torsion, bending and compression at physiological and hyper-physiological loads using a bovine injury model. Fibrin-genipin hydrogel restored some torsional stiffness, bending ROM and disk height loss, with negligible herniation risk and failure was observed histologically at the fibrin-genipin mid-substance following rigorous loading. Scaffold-based repairs partially restored biomechanics, but had high herniation risk even when stabilized with sutured membranes and failure was observed histologically at the interface between scaffold and fibrin-genipin adhesive. Fibrin-genipin was the simplest annulus fibrosus repair solution evaluated that involved an easily deliverable adhesive that filled irregularly-shaped annular defects and partially restored disk biomechanics with low herniation risk, suggesting further evaluation for disk repair may be warranted. Statement of significance Lower back pain is the leading cause of global disability and commonly caused by defects and failure of intervertebral disk tissues resulting in herniation and compression of adjacent nerves. Annulus fibrosus repair materials and techniques have not been successful due to the challenging mechanical and chemical microenvironment and the needs to restore biomechanical behaviors and promote healing with negligible herniation risk while being delivered during surgical procedures. This work addressed this challenging biomaterial and clinical problem using novel materials including an adhesive hydrogel, a scaffold capable of cell delivery, and a membrane to prevent herniation. Composite repair strategies were evaluated and optimized in quantitative three-part study that rigorously evaluated disk repair and provided a framework for evaluating alternate repair techniques.

Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks

This paper presents a multi-stage algorithm for the dynamic condition monitoring of a gear. The algorithm provides information referred to the gear status (fault or normal condition) and estimates the mesh stiffness per shaft revolution in case that any abnormality is detected. In the first stage, the analysis of coefficients generated through discrete wavelet transformation (DWT) is proposed as a fault detection and localization tool. The second stage consists in establishing the mesh stiffness reduction associated with local failures by applying a supervised learning mode and coupled with analytical models. To do this, a multi-layer perceptron neural network has been configured using as input features statistical parameters sensitive to torsional stiffness decrease and derived from wavelet transforms of the response signal. The proposed method is applied to the gear condition monitoring and results show that it can update the mesh dynamic properties of the gear on line.