Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Development of beam and plate finite elements based on the absolute nodal coordinate formulation

The focus of this dissertation is to develop finite elements based on the absolute nodal coordinate formulation. The absolute nodal coordinate formulation is a nonlinear finite element formulation, which is introduced for special requirements in the field of flexible multibody dynamics. In this formulation, a special definition for the rotation of elements is employed to ensure the formulation will not suffer from singularities due to large rotations. The absolute nodal coordinate formulation can be used for analyzing the dynamics of beam, plate and shell type structures. The improvements of the formulation are mainly concentrated towards the description of transverse shear deformation. Additionally, the formulation is verified by using conventional iso-parametric solid finite element and geometrically exact beam theory. Previous claims about especially high eigenfrequencies are studied by introducing beam elements based on the absolute nodal coordinate formulation in the framework of the large rotation vector approach. Additionally, the same high eigenfrequency problem is studied by using constraints for transverse deformation. It was determined that the improvements for shear deformation in the transverse direction lead to clear improvements in computational efficiency. This was especially true when comparative stress must be defined, for example when using elasto-plastic material. Furthermore, the developed plate element can be used to avoid certain numerical problems, such as shear and curvature lockings. In addition, it was shown that when compared to conventional solid elements, or elements based on nonlinear beam theory, elements based on the absolute nodal coordinate formulation do not lead to an especially stiff system for the equations of motion.

A computationally efficient shear deformable beam element for large deformation multibody applications

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Absoluuttisten solmukoordinaattien menetelmä kuorimaisten kappaleiden mallinnuksessa

Työn tavoitteena oli kehittää nopeasti konvergoiva kuorielementti epälineaarisesti joustavien kappaleiden analysointiin. Kuorielementti perustuu absoluuttisten solmukoordinaattien menetelmään ja se hyödyntää kaarevuuden kuvausta elastisten voimien määrityksessä. Kehitettyä elementtiä verrattiin kontinuumimekaniikalla kehitettyyn kuorielementtiin ja kaupallisen elementtimenetelmän kuorielementtiin. Yksinkertaisimman kuormitustapauksen tuloksia verrattiin teknisen taivutusteorian mukaiseen analyyttiseen ratkaisuun. Staattisten testien tulokset tässä työssä kehitetyllä kuorielementillä vastasivat hyvin kaupallisella elementtimenetelmällä saatuja tuloksia. Deformaatioiden ollessa geometrisesti lineaarisella alueella, kehitetyllä kuorielementillä saadut tulokset vastasivat paremmin sekä analyyttistä ratkaisua että kaupallisella elementtimenetelmällä saatuja tuloksia kuin aiemman kontinuumimekaniikkaan perustuvan kuorielementin tulokset. Kehitetyn kuorielementin ongelmana verrattuna kontinuumimekaniikkaan perustuvaan elementtiin on monimutkaisempi kinematiikan kuvaus. Tästä on seurauksena laskenta-ajan huomattava kasvaminen. Jatkossa kannattaisi keskittyä numeeristen ratkaisumenetelmien kehittämiseen.

Development of finite elements for analysis of biomechanical structures using flexible multibody formulations

The absolute nodal coordinate formulation was originally developed for the analysis of structures undergoing large rotations and deformations. This dissertation proposes several enhancements to the absolute nodal coordinate formulation based finite beam and plate elements. The main scientific contribution of this thesis relies on the development of elements based on the absolute nodal coordinate formulation that do not suffer from commonly known numerical locking phenomena. These elements can be used in the future in a number of practical applications, for example, analysis of biomechanical soft tissues. This study presents several higher-order Euler–Bernoulli beam elements, a simple method to alleviate Poisson’s and transverse shear locking in gradient deficient plate elements, and a nearly locking free gradient deficient plate element. The absolute nodal coordinate formulation based gradient deficient plate elements developed in this dissertation describe most of the common numerical locking phenomena encountered in the formulation of a continuum mechanics based description of elastic energy. Thus, with these fairly straightforwardly formulated elements that are comprised only of the position and transverse direction gradient degrees of freedom, the pathologies and remedies for the numerical locking phenomena are presented in a clear and understandable manner. The analysis of the Euler–Bernoulli beam elements developed in this study show that the choice of higher gradient degrees of freedom as nodal degrees of freedom leads to a smoother strain field. This improves the rate of convergence.

Sekaelementit absoluuttisten solmukoordinaattien menetelmässä

Tässä lisensiaatintyössä käsitellään sekaelementtien sovellusmahdollisuuksia absoluuttisten solmukoordinaattien menetelmässä. Absoluuttisten solmukoordinaattien menetelmä on uudentyyppinen lähestymistapa elementtimenetelmän elementtien koordinaattien määrittämiseksi ja sen yhtenä tavoitteena on tehostaa suuria siirtymiä tai kiertymiä sisältävien elementtien laskentatehokkuutta. Tässä työssä absoluuttisten solmukoordinaattien menetelmä esitellään pääpiirteittäin sekä annetaan esimerkkejä muutamista tyypillisimmistä elementeistä lausuttuna edellä mainittujen koordinaattien perusteella. Sekaelementeiksi kutsutaan elementtityyppejä, missä tuntemattomien muuttujien joukkoja on aina enemmän kuin yksi. Sekaelementit erottavat redusoitumattomista elementeistä siirtymäkentän sisältyminen muuttujaryhmään ja hybridielementeistä muuttujien identtiset ulottuvuudet. Sekaelementtejä käytetään esimerkiksi kokoonpuristumattomien materiaalien rakenneanalyyseissä, alentamaan elementiltä vaadittavia jatkuvuusehtoja tai mallintamaan ilmiöitä, missä fysikaaliset ominaisuudet ovat jostain syystä voimakkaasti toisistaan riippuvaisia. Tämän lisensiaatintyön kirjoittamiseksi on tehty tutkimusta sekaelementtien mahdollisuuksista toimia absoluuttisten solmukoordinaattien menetelmässä. Tutkimuksen tuloksena on saatu aikaan kaksi tässä työssä esiteltävää, varsin rajatun toimintakyvyn omaavaa sekaelementtityyppiä, joiden siirtymäkentät on määritelty globaalien koordinaattien suhteen sisältäen myös orientaatiotermit. Tutkimusaihe vaatii kuitenkin vielä paljon lisätyötä, ennen kuin sekaelementtityyppejä voidaan kauttaaltaan soveltaa absoluuttisten solmukoordinaattien menetelmällä toteutetuissa rakenneanalyyseissä.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Development of a subject-specific musculoskeletal shoulder model : inverse and forward dynamics applications

A prevalência de pessoas que referem dor no complexo articular do ombro, com concomitante limitação na capacidade para realizar atividades da vida diária, é elevada. Estes níveis de prevalência sobrecarregam quer os utentes, como a própria sociedade. A evidência científica atual indicia a existência de uma relação entre as alterações da articulação escápulo-torácica e as patologias associadas à articulação gleno-umeral. A capacidade de quantificar, cinemática e cineticamente, as disfunções ao nível das articulações escápulo-torácica e gleno-umeral, é algo de enorme importância, quer para a comunidade biomecânica, como para a clínica. No decorrer dos trabalhos desta tese foi desenvolvido, através do software OpenSim, um modelo tridimensional músculo-esquelético do complexo articular do ombro que inclui a representação do tórax/coluna, clavícula, omoplata, úmero, rádio, cúbito e articulações que permitem os movimentos relativos desses segmentos, assim como, 16 músculos e 4 ligamentos. Com um total de 11 graus de liberdade, incluindo um novo modelo articular escápulo-torácico, os resultados demonstram que este é capaz de reconstruir de forma precisa e rápida os movimentos escápulo-torácicos e glenoumerais, recorrendo para tal, à cinemática inversa, e à dinâmica inversa e direta. Conta ainda com um método de transformação inovador para determinar, com base nas especificidades dos sujeitos, os locais de inserção muscular. As principais motivações subjacentes ao desenvolvimento desta tese foram contribuir para o aprofundar do atual conhecimento sobre as disfunções do complexo articular do ombro e, simultaneamente, proporcionar à comunidade clínica uma ferramenta biomecânica de livre acesso com o intuito de melhor suportar as decisões clínicas e dessa forma concorrer para uma prática mais efetiva.

Dynamic analysis of the motorcycle chattering behaviour by means of symbolic multibody modelling

Aim of this research is the development and validation of a comprehensive multibody motorcycle model featuring rigid-ring tires, taking into account both slope and roughness of road surfaces. A novel parametrization for the general kinematics of the motorcycle is proposed, using a mixed reference-point and relative-coordinates approach. The resulting description, developed in terms of dependent coordinates, makes it possible to efficiently include rigid-ring kinematics as well as road elevation and slope. The equations of motion for the multibody system are derived symbolically and the constraint equations arising from the dependent-coordinate formulation are handled using a projection technique. Therefore the resulting system of equations can be integrated in time domain using a standard ODE algorithm. The model is validated with respect to maneuvers experimentally measured on the race track, showing consistent results and excellent computational efficiency. More in detail, it is also capable of reproducing the chatter vibration of racing motorcycles. The chatter phenomenon, appearing during high speed cornering maneuvers, consists of a self-excited vertical oscillation of both the front and rear unsprung masses in the range of frequency between 17 and 22 Hz. A critical maneuver is numerically simulated, and a self-excited vibration appears, consistent with the experimentally measured chatter vibration. Finally, the driving mechanism for the self-excitation is highlighted and a physical interpretation is proposed.

Role and extent of lymphadenectomy during radical cystectomy for invasive bladder cancer

There is substantial variability in the extent of the node dissection performed during radical cystectomy for bladder cancer. Here, we review the diagnostic assessment of lymph node metastasis and the prognostic and therapeutic benefit for pelvic node dissection for bladder cancer. A review of the applicable urologic literature regarding the topics of lymphadenectomy for bladder cancer was conducted. Nodal metastasis above a limited or standard template is not uncommon, with up to 16% of all nodal metastasis detected proximal to the aortic bifurcation. However, skip metastasis is extremely rare. Proteins associated purely with epithelial tissue such as cytokeratin (CK)-19, CK-20, and uroplakin II have been observed in reportedly negative nodal specimens, which indicates that routine microscopic analysis of nodal tissue may miss small foci of metastatic cancer. In addition to the surgical technique, the total number of lymph nodes removed is influenced by patient anatomy and pathologic processing and therefore may be unsuitable as a procedural quality statement. Consecutively, meticulous removal of tissue within a defined and uniformly applied template may be more relevant than absolute nodal count. Observational cohort series indicate an improved oncologic outcome for patients undergoing extensive nodal dissection. The results of two randomized controlled trials addressing the extent of nodal dissection for bladder cancer are forthcoming.

Multibody systems formulation

"Series: Solid mechanics and its applications, vol. 226"

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

A comparison between joint coordinate system and attitude vector for multi-segment foot kinematics.

The joint angles of multi-segment foot models have been primarily described using two mathematical methods: the joint coordinate system and the attitude vector. This study aimed to determine whether the angles obtained through these two descriptors are comparable, and whether these descriptors have similar sensitivity to experimental errors. Six subjects walked eight times on an instrumented walkway while the joint angles among shank, hindfoot, medial forefoot, and lateral forefoot were measured. The angles obtained using both descriptors and their sensitivity to experimental errors were compared. There was no overall significant difference between the ranges of motion obtained using both descriptors. However, median differences of more than 6° were noticed for the medial-lateral forefoot joint. For all joints and rotation planes, both descriptors provided highly similar angle patterns (median correlation coefficient: R>0.90), except for the medial-lateral forefoot angle in the transverse plane (median R=0.77). The joint coordinate system was significantly more sensitive to anatomical landmarks misplacement errors. However, the absolute differences of sensitivity were small relative to the joints ranges of motion. In conclusion, the angles obtained using these two descriptors were not identical, but were similar for at least the shank-hindfoot and hindfoot-medial forefoot joints. Therefore, the angle comparison across descriptors is possible for these two joints. Comparison should be done more carefully for the medial-lateral forefoot joint. Moreover, despite different sensitivities to experimental errors, the effects of the experimental errors on the angles were small for both descriptors suggesting that both descriptors can be considered for multi-segment foot models.