Optimal design and optimal control of structures undergoing finite rotations and elastic deformations

TL;DR

This paper develops advanced methods for the optimal design and control of structures experiencing large rotations and elastic deformations, using a geometrically exact beam model and exploring both gradient-based and genetic algorithm solutions.

Contribution

It introduces a novel formulation for optimal design and control problems in large deformation mechanics, employing Lagrange multipliers for variable independence and comparing two solution strategies.

Findings

Gradient-based response surface method shows fast convergence.

Genetic algorithm effectively handles complex, non-convex problems.

Numerical examples demonstrate the strengths and limitations of each approach.

Abstract

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.