Inverse finite element modeling of shells using the degenerate solid approach

•Inverse Finite Element Method (IFEM) for degenerate solid shells.•Cost-effective method for the design of compliant mechanisms and structures.•Cure for shear locking using Mixed Interpolation of Tensorial Components (MITC).•Multiplicative scheme for the update of the director vector under large rotations.

The Inverse Finite Element Method (IFEM) for degenerate solid shells is introduced. IFEM allows determining the undeformed shape of a body (in this case, a shell-like body) such that it attains a desired shape after large elastic deformations. The model is based on the degenerate solid approach, which enables the use of the standard constitutive laws of Solid Mechanics. First, IFEM is applied to three popular benchmarks for validation purposes. Then, the capabilities of IFEM for inverse design are demonstrated by means of its application to the design of a microvalve.