Jean-Pierre Coyette

Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties

This paper presents two efficient modal approaches as an alternative to direct formulations for the time-harmonic dynamic analysis of structures with random material and shape parameters. In both approaches, the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters. The modal perturbation stochastic finite element method (SFEM) then condenses the response sensitivities to assess the response variability. The mixed perturbation/Monte-Carlo SFEM assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions (PDFs). Geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis. Two numerical applications examine both approaches in terms of accuracy, variability level and computational requirements. The applications involve a plate bending problem with random Young modulus or edge length and a plate with a random flatness default. Particular observations related to the influence of the parameter PDFs in simulation-based methods are also provided.

APPLICATION OF A DOMAIN DECOMPOSITION METHOD WITH LAGRANGE MULTIPLIERS TO ACOUSTIC PROBLEMS ARISING FROM THE AUTOMOTIVE INDUSTRY

The Finite Element Tearing and Interconnecting method for the Helmholtz equation is a recent nonoverlapping domain decomposition method for solving linear systems arising from the finite element discretization of Helmholtz problems in bounded domains. This method was validated on two-dimensional external problems with first-order absorbing boundary conditions. The purpose of this paper is to study the robustness and efficiency of iterative methods for the solution of the associated interface problem for three-dimensional interior problems arising from the automotive industry.

An efficient method for evaluating diffuse field joint acceptance functions for cylindrical and truncated conical geometries

The evaluation of the response of elastic structures subjected to distributed random excitations is usually performed in the modal space. Random excitations (like acoustic diffuse fields) are usually modeled as weakly stationary random processes and are assumed to be homogeneous. Their characterization basically relies on the power spectral density (PSD) function of the pressure at a particular reference position and a suitable spatial correlation function. In the modal space, the distributed random excitation is characterized by a modal PSD matrix made from the joint acceptance functions related to the mode pairs. The joint acceptance function is a double surface integral involving the product of the considered mode shapes and the spatial correlation function. The paper shows how to evaluate efficiently this quadruple integral for cylindrical and truncated conical structures excited by an acoustic diffuse field. Basically, the procedure relies on the derivation of alternative expressions for the spatial correlation function. The related expressions prove to be more convenient for these geometries and are leading to a reduction of the double surface integral to a combination of simple integrals. A very substantial breakdown of the computational cost can be achieved using the resulting expressions. (c) 2005 Acoustical Society of America.

Connection and comparison between frequency shift time integration and a spectral transformation preconditioner

The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large-scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a connection between a spectral transformation preconditioner and a frequency shift time integration. This preconditioner is close to the shifted Laplace preconditioner. The preconditioned iterative method appears to be faster than time integration. Copyright

Sound Propagation in a Sheared Flow Based on Fluctuating Total Enthalpy as Generalized Acoustic Variable

Noise propagation mechanisms in presence of a rotational flow are currently receiving some attention from the aircraft industry. Different methods are used in order to compute the acoustic wave propagation in sheared flows in terms of pressure perturbations (e.g. Linearized Euler Equations (LEE), Lilley’s and Galbrun’s equations). Nevertheless, they have drawbacks in terms of computational performance (high number of DOFs per node, inadequacies of classical numerical schemes like standard FE). In contrast with other studies, in this work, the fluctuating total enthalpy is selected as the main variable in order to describe the acoustic field, which obeys to a convected wave equation obtained by linearization of momentum (Crocco’s form), energy and continuity equations and with coefficients depending on flow variables. The resulting 3D convected wave operator is an extension of the Mohring acoustic analogy which is able to predict the sound propagation through rotational flows in the subsonic regime and is well adapted to FE discretization. A 2D convected wave equation is generated from the previous operator. This is followed by a numerical solution based on FEM with two types of boundary conditions: non reflecting BC and incident plane wave excitation. The numerical results are used to estimate the reflection coefficient generated by the shear flow. The new acoustic wave operator is compared to well-known theories of flow acoustics (Pridmore-Brown wave operator) and shows promising results. Finally additional development steps are presented so further improvements on the new operator can be carried out.Copyright

An oriented finite element model for shearwall analysis

Abstract Generally, loadbearing wall structures exhibit some regularity along the height. This regularity is exploited by cutting the building into typical slices. Each slice is obtained from the assemblage of basic structural units. The finite element method supports the calculation of the boundary stiffness matrices of these components which are stored in a user-defined structural library. Evaluation of structural response is based on a frontal process. The resulting program is runable on a minicomputer at low cost. Torsion of a model core illustrates the application of the method.

Use of the student edition of ACTRAN in acoustics education

The power of computation has changed the way problems are solved in acoustics, and students should be trained to have an adequate background in modern techniques and software packages to simulate noise and vibration. Universities often cannot provide industrial-grade packages for their students due to the cost limitations. But recently a student version of a modern acoustics computation package was released, Student Edition of ACTRAN. This tool lets students solve a wide variety of problems using finite elements and infinite elements. This talk will describe the software and how it was used in a graduate level course in computational acoustics. Two examples that will be shown include finding the modes of an irregularly shaped room and computing the acoustic radiation from a gearbox. But it is clear that this software can be used in many different ways, for both undergraduate and graduate acoustics education. Instructors can demonstrate acoustical phenomena for students not adept at using the software them...

An energy‐based updated modal approach for the efficient analysis of large trimmed models

Large trimmed models, widely encountered in the automotive industry, generally involve a body‐in‐white structure coupled to an acoustic cavity and covered by a set of trim components. Due to the large number of degrees of freedom of such models, the direct analysis in physical coordinates, though theoretically correct, is not feasible on current computers. The paper presents an alternative and efficient solution strategy in modal coordinates that relies on an update of the modal parameters of the car body and the acoustic cavity, based on the energetic behaviour of the trim components. The description of the trim component in terms of an energetic database simplifies the data exchange between the automotive manufactor and the trim provider. Furthermore, it enables a fast frequency analysis of various loadcases/trim scenarios and makes optimisation possible. The updated modal approach implemented in Actran/Trim is applied on a simplified car model on which various trim components are applied. The applicati...

Noise Transmission Characteristics of Stiffened/Unstiffened Cylindrical Shells Subjected to Random Excitations at High Frequencies: Computational performances of an extended modal model

The present study is related to the evaluation of the computational performances of an extended analytical modal representation for the evaluation of the noise transmission characteristics of stiffened or unstiffened cylindrical shells subjected to random distributed excitations (acoustic diffuse fields or turbulent boundary layer excitations). The development of such a capability is requested in order to cover the wide frequency band related to noise transmission studies on real-life aircraft fuselage structures. The main ingredients of this model are summarized and computational results produced for various configurations are compared to test results. Computational performances of the related QUIET software are also demonstrated.