A variational formulation for motion design of adaptive compliant structures

TL;DR

This paper introduces a variational finite element method for designing optimal quasi-static motions of adaptive structures, accounting for large deformations and enabling analytical sensitivity analysis.

Contribution

It presents a novel variational formulation combined with dual finite element discretizations for motion design in adaptive structures, including a Newton-Raphson based optimization approach.

Findings

Method successfully handles large deformations and stability issues.

Verifies effectiveness through benchmark examples.

Enables analytical sensitivity analysis for motion optimization.

Abstract

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account. It is based on a variational formulation and the solution by two finite element discretizations, the spatial discretization (the standard finite element mesh) and an additional discretization of the deformation path or trajectory. For the investigations, an exemplary objective function, the minimization of the internal energy, integrated along the deformation path, is used. The method for motion design presented herein uses the Newton-Raphson method as a second order optimization algorithm and allows for analytical sensitivity analysis. The proposed method is verified and its properties are investigated by benchmark examples including rigid body motions, instability phenomena and determination of inextensible deformations of shells.