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Incompressible modelling in finite elements has been a major concern since its early developments and has been extensively studied. However, incompressibility in meshfree methods is still an open topic. Thus, instabilities or locking can preclude the use of mesh-free approximations in such problems. Here, a novel mesh-free formulation is proposed for incompressible flow. It is based on defining a pseudo-divergence-free interpolation space. That is, the finite dimensional interpolation space approaches a divergence-free space when the discretization is refined. Note that such an interpolation does not include any overhead in the computations. The numerical evaluations are performed using the inf-sup numerical test and two well-known benchmark examples for Stokes flow.

In this study, the issue of reconstructing the gradients of noisy full-field data is addressed within the framework of solid mechanics. Two approaches are considered, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). For both approaches, it is proposed to monitor locally the filtering effect in order to adapt the uncertainty to the local signal to noise ratio. Both approaches are applied to a case study which is commonly considered as difficult in solid mechanics (open-hole tensile test on a composite laminate). Both DA and FEA are successful for detecting local subsurface damage from the measured noisy displacement fields. Indications are also provided about the compared performances of DA and FEA. It is shown that DA is more robust, but the downside is that it is also more CPU time consuming.

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In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures.

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RÉSUMÉ. Cette étude s'intéresse à la reconstruction de champs de déformation à partir de me-