Claude Blanzé

The variational theory of complex rays for the calculation of medium‐frequency vibrations

A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.

A modular approach to structure assembly computations: application to contact problems

Presents a modular method for obtaining either a quick or a precise calculation for three‐dimensional structure assemblies with local non‐linearities, such as unilateral contact with friction, or technological components, such as prestressed bolt joints. An iterative method, including a domain‐decomposition technique, is proposed to solve such quasi‐static problems in small perturbations. Two types of entities are introduced: sub‐structures and interfaces. A local and a global stage are successively carried out by an iterative algorithm until convergence. The linear problem in the global stage is solved by a FEM (3D case) or by another approach using Trefftz functions (2D axisymmetrical case). Applications developed with AEROSPATIALE‐Les Mureaux are presented and concern the study of structure joints with different types of flanges.

A multiscale computational method for medium-frequency vibrations of assemblies of heterogeneous plates

Abstract A new approach, called the “variational theory of complex rays” has been developed in order to calculate the vibrations of slightly damped elastic plates in the medium-frequency range. The resolution of a small system of equations which does not result from a fine spatial discretization of the structure leads to the evaluation of effective quantities (deformation energy, vibration amplitude,…). Here, we extend this approach, which was already validated for assemblies of homogeneous substructures, to the case of heterogeneous substructures.

Contact problems in the design of a superconducting quadrupole prototype

This paper focuses on the design of a superconducting quadrupole prototype. This structure includes many frictional contact zones, and the loading conditions are complex (mechanical, thermal and magnetic). A dedicated computational strategy, based on both a decomposition of the structure and an iterative resolution scheme, has been applied to solve this problem. A simplified approach is used to take complex loading conditions into account. The initial set of results, which are presented herein, demonstrates the interest of this approach with respect to classical finite element methods. This study was conducted within the framework of a joint research contract between the CEA (DSM/DPANIA/STCM) and LMT‐Cachan.

ANALYSIS OF STRUCTURES WITH STOCHASTIC INTERFACES IN THE MEDIUM-FREQUENCY RANGE

This paper proposes efficient techniques to obtain effective quantities when dealing with complex structures (including stochastic parameters, such as interface parameters) in medium-frequency vibrations. The first ingredient is the use of a dedicated approach — the Variational Theory of Complex Rays (VTCR) — to solve the medium-frequency problem. The VTCR, which uses two-scale shape functions verifying the dynamic equation and the constitutive relation, can be viewed as a means of expressing the power balance at the different interfaces between substructures. The second ingredient is the use of the Polynomial Chaos Expansion (PCE) to calculate the random response. Since the only uncertain parameters are those which appear in the interface equations (which, in this application, are the complex connection stiffness parameters), this approach leads to very low computation costs.

La Théorie Variationnelle des Rayons Complexes pour le calcul des vibrations moyennes fréquences

ABSTRACT A new approach named the “Variational Theory of Complex Rays” is introduced for computing the vibrations of elastic structures weakly damped in the medium frequency range. Emphasis has been placed here on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity…) are evaluated after computing a small system of equations which does not derive from a finite element dicretization of the structure. Numerical examples related to plates show the interest and the possibilities of the VTRC.