Finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity

Abstract

This paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range. The problem consists in determining the initial shape of the piece, such that it attains the designed shape under the effect of service loads. The model is particularly focused on the design of parts with a markedly anisotropic behavior, like laminated turbine blades. Although the formulation expresses equilibrium on the distorted configuration, it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration. In this way, the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix. Two examples are given, the first one for validation purposes, while the second is an application which has industrial interest for the design of turbine blades.