A Finite Element Model for Inverse Design Problems in Large Deformations Anisotropic Hyperelasticity

VÍCTOR FACHINOTTI; ALBERTO CARDONA; PHILIPPE JETTEUR

Santa Fe

Congreso; 15 Congreso sobre Métodos Numéricos y sus Aplicaciones, ENIEF 2006; 2006

Asociación Argentina de Mecánica Computacional

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 pieces with a markedly anisotropic behavior, like laminated turbine blades. The formulation expresses equilibrium on the distorted configuration. However, it uses the standard constitutive equation library, which is usually expressed for measures attached to the undistorted configuration. Modifications in standard finite elements codes are then restricted to the routines for the computation of the finite element internal forces and tangent matrix. Two application examples are given, the first one for validation purposes, while the second application has industrial interest for the design of turbine blades.