Optimal Cellular Core Topologies for One-Dimensional Morphing Aircraft Structures

Boundary conditions applied to the model. (a) Compliant structure with periodic unit cells and (b) quarter of periodic unit.

Determination of the clusters. (a) Only elements in grey are considered neighbors of the element in black and (b) connectivity analysis process.

Illustration of the open filter and close filter

Example of weights for a two-dimensional problem

Flow chart describing the hybrid multi-objective algorithm. The global search block corresponds to the ɛ-NSGA2 algorithm for one single run.

Triangular scatter plot matrix showing solutions located near the Pareto front of the 1D morphing problem

Linear solutions for the topology optimization of a cellular structure for 1D morphing

Comparison of objectives’ values obtained with a linear and a nonlinear FEA (group 1: ×, group 2: □, group 3: ○). (a) Maximum local equivalent strains with linear and nonlinear FEA and (b) strain energy in deformed configuration with linear and nonlinear FEA.

Selected solution

Effect of the number of cells on the nondimensionalized transverse displacement, δ¯, for a 0.2 m × 0.2 m × 0.01 m panel under an out-of-plane pressure

Deformed shape and equivalent Von Mises strain contours for 33% of global strain with linear or nonlinear deformation. (a) Von Mises strain distribution with a linear deformation, (b) Von Mises strain distribution with a nonlinear extension (ɛmorph  = 33%), and (c) Von Mises strain distribution with a nonlinear compression (ɛmorph  = −21%).

Influence of the applied pressure and morphing strain (20 × 20 cells). (a) Nondimensionalized out of plane displacement, δ¯, for p0  = 9500 Pa, (b) strain ratio, LGS, and (c) equivalent nondimensionalized stiffness, Emorph.