Pierre Duysinx

Design Sensitivity Analysis for Shape Optimization of Nonlinear Magnetostatic Systems

This paper discusses the sensitivity analysis for the shape optimization of a nonlinear magnetostatic system, evaluated both by direct and adjoint approaches. The calculations rely on the Lie derivative concept of differential geometry, where the flow is the velocity field associated with the modification of a geometrical parameter in the model. The resulting sensitivity formulas can be expressed naturally in a finite-element setting through a volume integral in the layer of elements connected to the surface undergoing shape modification. The accuracy of the methodology is analyzed on a 2-D model of an interior permanent magnet motor and on a 3-D model of a permanent magnet system.

Contributions to handle maximum size constraints in density-based topology optimization

The maximum size formulation in topology optimization restricts the amount of material within a test region in each point in the design domain, leading to a highly constrained problem. In this work the local constraints are aggregated into a single one by p-mean and p-norm functions, classically used for stress constraints. Moreover, a new test region is investigated which is a ring instead of the classical circle around the element. These developments were implemented for compliance minimization with the MBB beam test case. Results indicate that p-mean performs better in the maximum size field than p-norm, because it underestimates the most violated constraint. This gives some relaxation to the problem that allows stiffer connections. Similar effect has been observed for the ring-shaped region which reduces the amount of holes that are introduced in the structure, specially in the connection of solid members. In addition, it is shown that the maximum size formulation allows the definition of the minimum gap between solid members which gives designers more control over the geometry. The developments have been illustrated and validated with compliance minimization tests of 2D-domains.

Shape and topology optimization of electrical machines using lie derivative-based analytical sensitivity analysis

The paper addresses the optimal design of electric machines, through the general setting of both shape and topology optimization. The optimization problems are efficiently solved with a classical gradient-based mathematical programming algorithm. An analytical sensitivity analysis for the nonlinear magnetostatic problem that can handle both shape and topology design variables, based on the Lie derivative is derived and applied to the optimal design of an interior permanent magnet (IPM) machine.

Unilateral contact condition enhanced with squeeze film modelling in automotive differentials

The dynamic behaviour of automotive drivetrains is significantly influenced by contacts occurring between the various parts. In this paper, a three-dimensional formulation is proposed to model unilateral and frictional contact conditions between two rigid planar rings. The magnitude of the contact force is determined by a penalty method. In a second step, a simple squeeze film model is developed to account for the damping effect produced by the lubricating oil filling the gap between the two contacting bodies. The relevance and the accuracy of these models are illustrated through the global multibody modelling of a TORSEN differential.