Cosserat rods are models for long slender objects. Let SE(3) = R3 SO(3) be the 13 group of orientation-preserving rigid body motions of R3 (the special Euclidean 14 group). A configuration of a Cosserat rod is a map φ : [0,1] → SE(3). For each 15 s ∈ [0,1], the value φ(s) = (φr(s),φq(s)) is interpreted as the position φr(s)∈R and 16 orientation φq(s)∈ SO(3) of a rigid rod cross section. Strain ...

We analyze the shape semiderivative of the solution to an asymptotic nonlinear adaptive elastic rod model, derived in Figueiredo and Trabucho [Math. Mech. Solids, 9 (2004), pp. 331–354], with respect to small perturbations of the cross section. The rod model is defined by generalized Bernoulli–Navier elastic equilibrium equations and an ordinary differential equation with respect to time. Takin...

Sometimes the need for non-circular ducts arises in many heat transfer applications because of lower pressure drop of non-circular cross section such as square duct compared to circular tube, particularly in compact heat. But square cross section has poor heat transfer performance and it is expected that using a nanofluid as a new heat transfer media may improve the heat transfer performance of...

We carry out the asymptotic analysis of the following shape optimization problem: a given volume fraction of elastic material must be distributed in a cylindrical design region of infinitesimal cross section in order to maximize the resistance to a twisting load. We derive a limit rod model written in different equivalent formulations and for which we are able to give necessary and sufficient c...