Emmanuel Pagnacco

Identification from measurements of mechanical fields by finite element model updating strategies

Inverse problem resolution methods are widely used in the determination of material behaviour. The optimisation of the parameters, as inputs into a well-defined system, is obtained from observed outputs such as kinematic field measurements. The aim of this paper is to summarize the research concerning one inverse method, Finite Element Modelling Updating, based on the use of these field measurements. This method is based on a combination of three components, described in the following three sections. First we present the optical field measurements applied to multi-axially loaded objects, together with their performances. Then we outline the use of Finite Element Modelling for achieving a correlation between numerical fields and their experimental counterparts. Finally we describe the identification process, together with cost functions, minimisation procedure and model validation analysis.

Statics and inverse dynamics solvers based on strain-mode disassembly

ABSTRACT The finite element method is widely used in design engineering for modeling and analyzing structural systems. Two approaches have been developed: the force-based method that exploits the equilibrium of forces and moments at nodal joints of the mesh to formulate the assembly of element-level matrices into master mass and stiffness matrices and its dual counterpart, the flexibility-based method. An alternative formulation of stiffness-based finite element assembly is proposed that decomposes element-level matrices even further into strain mode contributions. This decomposition (referred to as finite element disassembly here) allows the derivation of an efficient numerical solver. It is shown that a single matrix factorization is required for analyzing all models characterized by the same topology. This makes finite element disassembly and the associated inverse solver ideal in cases where multiple design analyzes are performed. In the first part, this publication derives a framework for an alternative finite element assembly of mass and stiffness matrices in the context of linear elasticity. Basically, disassembly consists of representing finite element matrices as a matrix product where topology contributions are isolated from constitutive law or inertia law contributions. Application examples are discussed to illustrate the advantages and limitations of this formulation using various meshes typically encountered in the automotive and aerospace industries. The second area of application discussed in the second part of this publication is the correlation between finite element models and test data. It is shown that numerical models can be updated for improving their correlation with measured frequency response functions with minimum computational cost when the model is disassembled.

DESIGN OPTIMIZATION OF A RANDOM SUSPENSION DEVICE CONSIDERING A RELIABILITY CONSTRAINT ON THE FREQUENCY RESPONSE FUNCTION

This work deals with the design of a suspension device, idealized as a spring-mass-damper system. The amplitude of a nominal system is constrained to satisfy certain limitations in a given frequency band and the design is to be done as a reliability-based optimization. This constitutes a major difficulty since the constraint becomes a random process. To concentrate in the main ideas, only the stiffness of the system will be considered random. The stiffness is characterized by a uniform random variable, and its mean and standard deviation are the optimization parameters. The design problem is stated as a two-objective optimization. They are the mean and the standard deviation of the stiffness: one search for the lowest stiffness and the greatest standard deviation, while the amplitude response must be within the acceptable domain of vibration, which is prescribed. To generate the Pareto front, the Normal Boundary Intersection method is used in the RFNM algorithm. Results show that a not-connected Pareto curve can be obtained for some choice of constraint. Hence, in this simple example, one shows that difficult situations can occur in the design of dynamic systems when prescribing an amplitude-response hull. Despite the simplicity of the example treated here, chosen to highlight the main ideas without distraction, the strategy proposed here can be generalized for more complex cases and give valuable results, able to help designers to choose for the best compromise between the mean and the standard deviation in reliability-based designs.

Generation of stationary Gaussian processes and extreme value distributions for high-cycle fatigue models - application to tidal stream Turbines

The operating environment of tidal stream turbines is random due to the variability of the sea flow (turbulence, wake, tide, streams, among others). This yields complex time-varying random loadings, making it necessary to deal with high cycle multiaxial fatigue when designing such structures. It is thus required to apprehend extreme value distributions of stress states, assuming they are stationary multivariate Gaussian processes. This work focus on such distributions, addressing their numerical simulation with an analytical description. For that, we first focused on generating one-dimensional Gaussian processes, considering a band-limited white noise in both the narrow-band and the wide-band cases. We then fitted the resulting extreme value distributions with GEV distributions. We secondly extended the generation method to the correlated two-dimensional case, in which the joint extreme value distribution can be obtained from the associated margins. Finally, an example of application related to tidal stream turbines introduces a Bretschneider spectrum, whose shape is commonly encountered in the field of hydrology. Comparing the empirical calculations with the GEV fits for the extreme value distributions shows a very well agreement between the results.

Topology optimization of structures subject to random excitations with fatigue life constraints

In this paper a topology optimization strategy for randomly excited linear elastic structures with fatigue life constraints is presented. In random vibration it is often convenient to describe the excitation and response in term of function in the frequency domain. The random vibration theory was developed to deal with random excitations and is based on the assumption of excitations fully described by their second order statistical properties: their mean value, their autocorrelation function and also their power spectral density function (PSD). In the light of this, specific frequency formulations [1] of commonly used damage criteria are chosen as fatigue life assessment techniques in the optimization procedure. These frequency formulations are well suited to random vibration problems and give a fast and accurate estimation of the structural fatigue life from the response PSD (stress PSD).

Dedicated procedures for temporal identification in a flexible multi-body system

The aim of this paper is to evaluate forces and torques in flexible joints of a flexible multi-body system (FMS). To represent such a FMS a 2D non-linear model based on finite element method is built. Its numerical form solution based on a stable integration scheme and on the non-linear Newton-Raphson method is described. As the evaluation procedure first requires that some model physical properties are obtained as identified parameters, two procedures are used: direct and indirect identification. They are respectively based on dynamic equilibrium verification and on comparison between simulated and measured kinematics of the proposed model. The development of the two procedures and a performance comparison between them is carried out.

Topological Optimization of Shells with Non Uniform Thicknesses

This work concerns the automatic design of minimum weight spare parts, under geometrical and frequencies constraints. We propose a method of rapid topological optimization which has successfully solved industrial situations involving about 3,000 unknowns. In the considered approach, the topology of the structure is characterized by an unknown thickness distribution and the frequency constraint is treated by a dual method.