Constitutive Relation Error Method Research Articles

Domain decomposition based finite element verification in linear framework

The objective of this work is to obtain an a posteriori estimate of the discretization error of a reference problem. This reference problem is a mechanical problem solved using a finite element analysis in linear elasticity. We use the constitutive relation error based estimator. The construction of admissible fields, which is a pillar of the constitutive relation error method, is revisited using a domain decomposition method.The originality of the present work is the introduction of a simplifying hypothesis that leads to an approximation of the discretization error. The construction of admissible fields, which is global, is then replaced by resolution of several local problems that conduce to lower CPU costs. The key point of this domain decomposition based error estimation is the fact that no inter-subdomain communication is needed. We present and illustrate this strategy and evaluate its benefits.

Error Assessment in Structural Transient Dynamics

This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates.

Updating 3D acoustic models with the constitutive relation error method: A two-stage approach for absorbing material characterization

In the global framework of improving vibro-acoustic numerical simulations together with the need to decrease the number of prototyping stages, improving the quality for acoustic models becomes increasingly important for many industries such as automotive companies, for instance. This paper focuses on achieving greater accuracy for acoustic numerical simulations by making use of a parametric updating technique, which enables tuning the model parameters inside physically meaningful boundaries. The improved model is used for the next prototyping stages, allowing more accurate results within reduced simulation times. The updating technique used in this paper is based on recent works dealing with the constitutive relation error (CRE) method applied to acoustics. The updating process focuses on improving the acoustic damping matrix related to the absorbing properties of the materials covering the borders of the acoustic domain. The present study proposes a 2-stage optimization process, which exhibits many advantages. Indeed, the computational time decreases, the frequency interpolation of the material absorbing properties outside the studied frequency range is easily performed, and comparing the correlation of several material absorbing constitutive equations with experimental records is fast. Additional originality of the work comes with the application of the CRE updating method to a concrete real-life device, while previous works addressed purely numerical setups without experimental data. The test-case is the TRICARMO setup engineered by LMS International in Leuven, Belgium. The TRICARMO setup is a simplified car cabin with rigid walls and car seats inside. Thanks to the 2-stage approach, the material property characterization of the seat is improved by running the updating simulation process using a physical absorbing material model.

Verification of stochastic models in uncertain environments using the constitutive relation error method

This paper deals with local stress errors which occur in linear elastic FE analysis in an uncertain environment (material, loads, …). The estimation technique described here uses the concept of error in constitutive relation, but it can be adapted to other estimators. First, we review the principle of the method, then extend it to the stochastic case. This approach yields bounds on the stresses associated with a given confidence level. We illustrate this presentation through a test example.

Model validation in the presence of uncertain experimental data

In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics‐based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations.

Updating 2D acoustic models with the constitutive relation error method

Nowadays, the increasing importance of acoustic noise in industry makes it essential to establish reliable simulation tools. Furthermore, many industries need to know the acoustic performances of the products that they achieve or use. Indeed, these components are often parts of larger set-ups (like cars, airplanes, concert halls, theatres, etc.) for which numerical acoustic simulations are run from the earliest design stage. In that framework, this paper proposes a new updating technique for acoustic simulations, which is based on the constitutive relation error (CRE) proposed by Ladevèze in structural dynamics. The technique consists of improving the quality of acoustic models by reducing the constitutive relation error below a prescribed level. The CRE updating method aims at minimizing a cost function with respect to physical parameters of the model. Both modelling error (i.e., the error related to the approximation of physical phenomena) and measurement error are taken into account. Particular attention is paid to the admittance coefficient, which is probably the most important and the least known acoustic parameter, and the application to two-dimensional finite element numerical simulations is presented showing how promising the technique is. The ultimate goal of the approach should be to improve the numerical simulations of the acoustic pressure level of real-life complex set-ups like cars, aircrafts, satellite launchers, etc.