A large deformation–small strain formulation for the mechanics of geometrically exact thin-walled composite beams

• A large displacement–small strain composite thin-walled beam formulation is presented.
• A pure vectorial small strain measure consistent with finite kinematics is derived.
• The discrete small strain measure results to be objective under rigid body motions.
• A finite element is implemented in a multibody algorithm to test the formulation.
• The formulation results to be very accurate and computationally efficient.

This work presents a new formulation of the geometrically exact thin walled composite beam theory. The formulation assumes that the beam can undergo arbitrary kinematical changes while the strains remain small, thus compatibilizing the hypotheses of the strain measure and the constitutive law of the composite material. A key point of the formulation is the development of a pure small strain measure written solely in terms of scalar products of position and director vectors; the latter is accomplished through the obtention of a generalized small strain vector by decomposition of the deformation gradient. The resulting small strain measure is objective under rigid body motion. The finite element implementation of the proposed formulation is simpler than the finite strain theory implementation previously developed by the authors. Numerical experiments show that the present formulation is very accurate and computationally more efficient than the finite strain formulation, thus it is more convenient for most practical applications.