A corotational flat triangular element for large strain analysis of thin shells with application to soft biological tissues

摘要

A flat triangular element for the nonlinear analysis of thin shells is presented. The formulation relies on (i) a polar decomposition based corotational framework and (ii) a core-element kinematic description adopting the multiplicative superposition of membrane and bending actions. The resulting element is a refined yet simple three-node displacement-based triangle accounting for thickness extensibility and initial shell curvature, and equipped with a fully consistent tangent stiffness. Numerical tests involving shell structures made of rubber-like materials or fibred biological tissues showthe effectiveness of the proposed element and its suitability to problems characterized by large displacements, large rotations, large membrane strains and bending. AMatlab toolkit implementing the present formulation is provided as supplementary material.