### Lagrangean-Based Inverse Finite Element Analysis of Shells Using Simple Reduced-Integration Hexahedral Elements

#### Abstract

The Inverse Finite Element Method (IFEM) is basically the Finite Element Method (FEM) applied to the solution of the equilibrium equations when the configuration after large elastic deformations is given. IFEM is usually formulated on an Eulerian or spatial framework taking advantage of the knowledge of the domain of analysis. However, for finite elements affected by spurious locking like beams and shells, remedies were usually developed on a Lagrangean framework, which obliges to formulate a new locking free Eulerian based element prior to IFEM analysis. The Lagrangean based IFEM approach spares this extra work whenever a Lagrangean based FEM exists. Now, the governing equations are identical to those of the classical Lagrangean based FEM for nonlinear geometric problems, enabling the reusability of the available theoretical and algorithmic tools. Using this approach, to transform FEM into IFEM just amounts to interchange knowns and unknowns in the nonlinear equilibrium equations. Here, for the analysis of shells, recourse is made to the finite element proposed by Flores Comput. Methods Appl. Mech. Engrg. 303 260 287 2016) in virtue of its great deal between simplicity and accuracy. This is a trilinear hexahedron that uses reduced integration (RI) and Assumed Natural Strain (ANS) techniques to prevent shear a nd membrane locking together with RI and Enhanced Assumed Strain (EAS to avoid volumetric locking. Like the standard trilinear hexahedron, this solid shell element eight vertex nodes, each one with three displacement degrees of freedom. Further, it has one scalar degree of freedom associated to EAS, which is easily condensed (i.e., eliminated) at the element level.

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Güemes 3450

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**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**