José M. Goicolea

Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy–momentum schemes

Abstract A multibody formulation for the nonlinear dynamics of mechanical systems composed of both rigid and deformable bodies is proposed in this work, focusing on its conservation properties for basic magnitudes such as total energy and momentum. The approach is based on the use of dependent variables (cartesian coordinates of selected points) and the enforcement of the constraints through the penalty method. This choice has the advantage of providing a simple overall structure that allows the inclusion of both rigid bodies (discrete model) and elastic bodies (continuum model discretised with the finite element method) under the same framework, in order to build a single set of ordinary differential equations. The elastic bodies are represented by general hyperelastic models and may undergo large displacements, rotations and strains. An energy–momentum time integration method has been employed, achieving remarkable stability and robustness with exact conservation of total energy. This approach effectively overcomes drawbacks associated with penalty formulations in other time integration algorithms. This important result in fact proves to be the main conclusion of this work. Some representative numerical simulations are presented for mechanical systems comprised of rigid and deformable bodies.

[Influence of shear stress on in-stent restenosis: in vivo study using 3D reconstruction and computational fluid dynamics].

INTRODUCTION AND OBJECTIVES Local factors may influence neointimal proliferation following conventional stent implantation. In this study, the relationship between wall shear stress and luminal loss after coronary stenting was assessed using a combination of angiography, intravascular ultrasound, and computational fluid dynamics. PATIENTS AND METHOD Seven patients with de novo right coronary lesions treated with conventional (i.e., bare metal) stents were included. Realistic three-dimensional geometric reconstructions were generated offline from angiographic and intravascular ultrasound data both immediately after stenting and at 6-month follow-up. A finite-volume model was used to calculate local wall shear stress within the stent and 4 mm proximally and distally to the stent. The mean coronary ostium entry flow velocity was assumed to be 25 cm/s in all cases. RESULTS The mean neointimal thickness was 0.29 (0.21) mm. In five cases, weak negative correlations between wall shear stress and neointimal thickness were found: maximum r value = -0.34, minimum r value = -0.11 (P < .001). The neointimal thickness in segments in which the level of wall shear stress was in the lowest quartile was greater than that in segments in which it was in highest quartile, at 0.34 (0.21) mm and 0.27 (0.24) mm (P < .001) for quartiles 1 and 4, respectively. CONCLUSIONS Low wall shear stress after stenting favors neointimal proliferation both within the stent and at the stents edges.

Conserving Properties in Constrained Dynamics of Flexible Multibody Systems

The context of this work is the non-linear dynamics ofmultibody systems (MBS). The approach followed for parametrisation ofrigid bodies is the use of inertial coordinates, forming a dependent setof parameters. This approach mixes naturally with nodal coordinates in adisplacement-based finite element discretisation of flexible bodies,allowing an efficient simulation for MBS dynamics. An energy-momentumtime integration algorithm is developed within the context of MBSconstraints enforced through penalty methods. The approach follows theconcept of a discrete derivative for Hamiltonian systems proposed byGonzalez, achieving exact preservation of energy and momentum. Thealgorithm displays considerable stability, overcoming the traditionaldrawback of the penalty method, namely numerical ill-conditioning thatleads to stiff equation systems. Additionally, excellent performance isachieved in long-term simulations with rather large time-steps.

Mechanical characterisation of the human thoracic descending aorta: experiments and modelling

This work presents experiments and modelling aimed at characterising the passive mechanical behaviour of the human thoracic descending aorta. To this end, uniaxial tension and pressurisation tests on healthy samples corresponding to newborn, young and adult arteries are performed. Then, the tensile measurements are used to calibrate the material parameters of the Holzapfel constitutive model. This model is found to adequately adjust the material behaviour in a wide deformation range; in particular, it captures the progressive stiffness increase and the anisotropy due to the stretching of the collagen fibres. Finally, the assessment of these material parameters in the modelling of the pressurisation test is addressed. The implication of this study is the possibility to predict the mechanical response of the human thoracic descending aorta under generalised loading states like those that can occur in physiological conditions and/or in medical device applications.

Quadratic and Higher-Order Constraints in Energy-Conserving Formulations of Flexible Multibody Systems

The treatment of constraints is considered here within the framework ofenergy-momentum conserving formulations for flexible multibody systems.Constraint equations of various types are an inherent component of multibodysystems, their treatment being one of the key performance features ofmathematical formulations and numerical solution schemes.Here we employ rotation-free inertial Cartesian coordinates of points tocharacterise such systems, producing a formulation which easily couples rigidbody dynamics with nonlinear finite element techniques for the flexiblebodies. This gives rise to additional internal constraints in rigid bodies topreserve distances. Constraints are enforced via a penalty method, which givesrise to a simple yet powerful formulation. Energy-momentum time integrationschemes enable robust long term simulations for highly nonlinear dynamicproblems.The main contribution of this paper focuses on the integration of constraintequations within energy-momentum conserving numerical schemes. It is shownthat the solution for constraints which may be expressed directly in terms ofquadratic invariants is fairly straightforward. Higher-order constraints mayalso be solved, however in this case for exact conservation an iterativeprocedure is needed in the integration scheme. This approach, together withsome simplified alternatives, is discussed.Representative numerical simulations are presented, comparing the performanceof various integration procedures in long-term simulations of practicalmultibody systems.

Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model

The vertical dynamic actions transmitted by railway vehicles to the ballasted track infrastructure are evaluated taking into account models with different degrees of detail. In particular, this matter has been studied from a two-dimensional finite-element model to a fully coupled three-dimensional multibody finite-element model. The vehicle and track are coupled via a nonlinear Hertz contact mechanism. The method of Lagrange multipliers is used for the contact constraint enforcement between the wheel and rail. Distributed elevation irregularities are generated based on power spectral density distributions, which are taken into account for the interaction. Due to the contact nonlinearities, the numerical simulations are performed in the time domain, using a direct integration method for the transient problem. The results obtained include contact forces, forces transmitted to the infrastructure (sleeper) by railpads, and envelopes of relevant results for several track irregularities and speed ranges. The main contribution of this work is to identify and discuss coincidences and differences between discrete two-dimensional models and continuum three-dimensional models, as well to assess the validity of evaluating the dynamic loading on the track with simplified two-dimensional models.

Factors influencing the mechanical behaviour of healthy human descending thoracic aorta

In recent times, significant effort has been made to understand the mechanical behaviour of the arterial wall and how it is affected by the different vascular pathologies. However, to be able to interpret the results correctly, it is essential that the influence of other factors, such as aging or anisotropy, be understood. Knowledge of mechanical behaviour of the aorta has been customarily constrained by lack of data on fresh aortic tissue, especially from healthy young individuals. In addition, information regarding the point of rupture is also very limited. In this study, the mechanical behaviour of the descending thoracic aorta of 28 organ donors with no apparent disease, whose ages vary from 17 to 60 years, is evaluated. Tensile tests up to rupture are carried out to evaluate the influence of age and wall anisotropy. Results reveal that the tensile strength and stretch at failure of healthy descending aortas show a significant reduction with age, falling abruptly beyond the age of 30. This fact places age as a key factor when mechanical properties of descending aorta are considered.

Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework

The evaluation of running safety of railway vehicles on viaducts requires the study of lateral dynamics for the coupled vehicle-bridge system. This includes the structural deformation of the bridge, the vehicle multibody dynamics, and the consideration of wheel to rail contact. In this work, a fully nonlinear coupled method for such study is presented. The model is developed in a modular way using finite element models for the structure and multibody dynamics models for the vehicles in an absolute reference, and implemented within an existing finite element commercial code. A key feature is the consideration of the kinematics and dynamics of nonlinear wheel to rail interface, considering elastic-frictional contact. This contact is based on a global geometric constraint between wheelset and track and tangential forces at local level of each contact point. Some elementary applications are presented for the behavior of the model for stable and unstable hunting motion when subjected to transient lateral loads such as a wind gust. These results show the relevance of considering nonlinear effects and in particular wheel to flange contact.

Bridge Damage Identification from Moving Load Induced Deflection Based on Wavelet Transform and Lipschitz Exponent

The wavelet transform and Lipschitz exponent perform well in detecting signal singularity. With the bridge crack damage modeled as rotational springs based on fracture mechanics, the deflection time history of the beam under the moving load is determined with a numerical method. The continuous wavelet transformation (CWT) is applied to the deflection of the beam to identify the location of the damage, and the Lipschitz exponent is used to evaluate the damage degree. The influence of different damage degrees, multiple damage, different sensor locations, load velocity and load magnitude are studied. Besides, the feasibility of this method is verified by a model experiment.

Robust analysis of flexible multibody systems and joint clearances in an energy conserving framework

Flexible multibody systems (MBS) appear in a number of mechanical applications, in which the model must consider the deformation of some or all of the bodies. A classical method for considering flexibility has been the floating frame technique (25), generally limited to small strains. A more general approach based on inertial coordinates may be formulated by nonlinear finite element methods (27; 28; 11), which are versatile and computationally efficient. Furthermore, employing energy-momentum time integration algorithms they prove to be extremely stable for nonlinear stiff behaviours which frequently arise in such systems. We present briefly the overall dynamic formulation, but we focus mainly on the formulation of constraints for joints with or without clearances. Integration algorithms that conserve both momentum and energy have been proposed in (29; 26; 16; 15), attracting considerable attention in the last few years. One of the main benefits of their robustness is their ability to perform stable long-term simulations in nonlinear systems. The approach followed here, in contrast to other energy-momentum formulations (29; 16; 8; 5; 9; 23), differs in two key aspects: 1) a rotation-free parametrisation for rigid bodies, based on inertial cartesian coordinates of body points, forming a dependent set which is subject to constraints; 2) a penalty formulation for constraints. As will be explained below, this allows for a simple, efficient and robust numerical implementation. Penalty methods are associated to a non-exact fulfilment of constraints, and in order to ensure sufficient numerical accuracy, large enough penalty parameters must be employed. These may lead to a stiff behaviour and further difficulties in the numerical solution of the problem. Their effect on the system is analogous to introducing very stiff elements between the constrained degrees of freedom. As a consequence, a penalty approach introduces high-frequency components in addition to the already existing ones in flexible multibody systems, due to wave propagation in the deformable bodies. This causes severe numerical difficulties for most time integration algorithms (8), being the main drawback of penalty formulations. However,