Multi-objective shape optimization for axially functionally graded microbeams

Nonuniform microbeams made of functionally graded materials (FGMs) have been studied extensively in literature to predict their mechanical and thermal behavior, those demonstrated that each of material variation, non-uniformity and micro-scale effects have significant influences on the static stability sand dynamic behavior. Therefore, this research exploited the multi-objective shape optimization method to optimize the beam shape and its volume fraction distribution in order to maximize the critical buckling loads and fundamental frequencies while minimizing the mass and cost of the FG microbeam, for the first time. Modified continuum model based on both Euler-Bernoulli beam theory as kinematic assumptions and constitutive equation of modified couple stress theory, is developed to derive equilibrium equations (in static analysis) and equations of motion (in dynamic analysis) of axially FGMs nonuniform microbeam. To control the variation of height and width along the beam length, three different shape functions are proposed in the analysis. The multiobjective particle swarm optimization (MOPSO) is adopted to get the Pareto optimal solutions. In addition to the FGM power index, the shape functions types and parameters are considered as the design variables. Several optimization problems are studied to demonstrate the multi-objective optimal shape design of axially functionally graded microbeams.

Automated summary

This research utilized multi-objective shape optimization method to optimize the shape and volume fraction distribution of functionally graded microbeams, for the first time, to maximize the critical buckling loads and fundamental frequencies while minimizing mass and cost. The modified continuum model based on Euler-Bernoulli beam theory and particle swarm optimization were used to derive equilibrium equations and equations of motion for the nonuniform microbeams. Multiple optimization problems were studied to demonstrate the multi-objective optimal shape design of these microbeams.