Bernard Peseux

Dynamic inflation of non‐linear elastic and viscoelastic rubber‐like membranes

The present paper deals with the dynamic inflation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooneys model or the non-linear viscoelastic Christensens model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite-difference algorithm for the time-integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas flow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through different examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber-like membranes.

A numerical integration scheme for special finite elements for the Helmholtz equation

The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissae and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved.

Dynamic inflation of hyperelastic spherical membranes

The dynamic inflation of hyperelastic spherical membranes of a Mooney–Rivlin material is analyzed in this study. Various inflation regimes are identified through ranges of the material parameters and driving pressure. In particular, the conditions for oscillatory inflation around the static fixed point are examined. It is found that, for a given material, the frequency of oscillation exhibits a maximum at some pressure level, which tends to increase for materials closer to neo-Hookean behavior.

Structural modal interaction of a four degree-of-freedom bladed disk and casing model

Consideration is given to a very specific interaction phenomenon that may occur in turbomachines due to radial rub between a bladed disk and surrounding casing. These two structures, featuring rotational periodicity and axisymmetry, respectively, share the same type of eigenshapes, also termed nodal diameter traveling waves. Higher efficiency requirements leading to reduced clearance between blade-tips and casing together with the rotation of the bladed disk increase the possibility of interaction between these traveling waves through direct contact. By definition, large amplitudes as well as structural failure may be expected. A very simple two-dimensional model of outer casing and bladed disk is introduced in order to predict the occurrence of such phenomenon in terms of rotational velocity. In order to consider traveling wave motions, each structure is represented by its two n d -nodal diameter standing modes. Equations of motion are solved first using an explicit time integration scheme in conjunction with the Lagrange multiplier method, which accounts for the contact constraints, and then by the harmonic balance method (HBM). While both methods yield identical results that exhibit two distinct zones of completely different behaviors of the system, HBM is much less computationally expensive.

n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities

The harmonic balance method is widely used for the analysis of strongly nonlinear problems under periodic excitation. The concept of hypertime allows for the generalization of the usual formulation to multi-tone excitations. In this article, the method is applied to a system involving a nonlinearity which cannot be explicitly expressed in the multi-frequency domain in terms of harmonic coef_cients. The direct and inverse Discrete Fast Fourier Transforms are then necessary to alternate between time and frequency domains in order to take into account this nonlinearity. The results show the efficiency and the precision of the method.

Dynamic Analysis of a Coupled Fluid Structure Problem With Fluid Sloshing

The present paper is related to the study of a generic linear coupled fluid/structure problem, in which an elastic beam is coupled with an inviscid fluid, with or without sloshing effects. A previous study [18] focussed on added mass effects; the present study is devoted to the coupling effects between fluid sloshing modes and structure with fluid added mass modes. The discretization of the coupled linear equations is performed with an axisymmetric fluid pressure formulated element, expanded in terms of a FOURIER series [14]. Various linear fluid model are taken into account (compressible, uncompressible, with or without sloshing) with the corresponding coupling matrix operator. The modal analysis is performed with a MATLAB program, using the non-symmetric LANCZOS algorithm [16]. The temporal analysis is performed with classical numerical techniques [10], in order to describe the dynamic response of the coupled problem subjected to a simple sine wave shock. The coupling effects are studied in various conditions represented by several non-dimensionnal numbers [12] such as the dynamic FROUDE number and the mass number, based on the geometrical and physical characteristics of the coupled problem. Comparisons are performed on the coupled problem with or without free surface modeling, with a model and temporal analysis. Coupling effects are exhibited and quantified; the numerical results obtained in the modal analysis here are in good agreement with other previous studies, carried out on different geometry [3,15]. The temporal analysis gives another point of view on the importance of the coupling effects and their importance at low dynamic FROUDE numbers. The present study gives and will be completed with a non-linear analysis (for both fluid and structure problems) of the coupled problem, using a finite element and finite volume explicit coupling procedure [19].© 2004 ASME

Prediction of transient engine loads and damage due to hollow fan blade-off

The loss of a fan blade causes serious damages on an engine and can endanger the aircraft integrity and the safety of passengers. Commercial aircraft engines must then meet the FAA (Federal Aviation Administration) and JAA (Joint Aviation Authorities) certification requirements concerning the fan blade containment. The certification is validated through a Fan Blade-Off (FBO) test on a whole engine. The success in this test requires destructive and expensive development tests performed at the different stages of the design process. To reduce the number of these experiments and thus, the costs and the time of development, the engine behaviour under FBO can be understood and even predicted thanks to finite element (FE) analysis. This paper shows a comparison between a FBO simulation of hollow blades, computed with an explicit integration FE code, and experimental data obtained during an intermediate FBO test carried out by Snecma Moteurs. The results of the load levels and the similarity on the sequence of events show good agreement.

Modelling and Simulation of the Three-Dimensional Hydrodynamic Problem

This paper deals with slamming phenomenon (impact between bow ship and water free surface). Slamming loads on ship may be sufficiently important so as to create plastic deformations of the hull external structure. In extreme cases, they have been recognised for being responsible for the loss of ships. The problem to solve is transient and highly non-linear due to the character of the flow. In the present paper, the three-dimensional Wagner problem is solved numerically using a variational formulation together with a Finite Element Method. Three-dimensional results for simple rigid bodies such as a cone and an ellipsoid are successfully compared with analytical results. Results for deformable structure will be presented.

Numerical Modelling of the Three-Dimensional Slamming Problem

This paper deals with the slamming phenomenon for deformable structures. In a first part, a three-dimensional hydrodynamic problem is solved numerically with the Finite Element Method. The results for a rigid body are successfully compared to the analytical solutions. After the numerical analysis, an experimental investigation is presented. It consists in series of free fall drop-tests of rigid, deformable cones shaped models with different deadrise angle and thickness. Distribution of the pressure and its evolution are analyzed. Numerical and experimental results are compared and present good agreement.

Modélisation du contact en implicite: Application à I'interaction rotor/stator

ABSTRACT The two main contact methods in dynamics are firstly studied. The influence of the Newmark implicit time scheme parameter values is then analysed with a special attention to the contact compatibility conditions. A new contact stiffness is proposed to compute interaction forces in a finite element code with a Newmark implicit integration scheme. The contact model is finally used to simulate rotor/stator interaction in an aircraft engine, after a blade-off event.