Polar decomposition based corotational framework for triangular shell elements with distributed loads

Abstract

A polar decomposition based corotational formulation for deriving geometrically nonlinear triangular shell elements is proposed. This formulation is novel in two aspects. (1) Original formulas for the projector operator and its variation are presented, leading to simple algorithms for the computation of the nodal residual vector and of the consistent tangent stiffness tensor. (2) For the first time in the context of a corotational kinematic description, a rigorous treatment of distributed dead and follower loads is performed, thoroughly accounting for the various contributions entailed in the residual vector and in the tangent stiffness. Numerical simulations of popular benchmark problems are reported, showing the effectiveness of the proposed approach. An accessible and adaptable MATLAB toolkit implementing the present formulation is provided as supplementary material

Mixed Tetrahedral Elements for the Analysis of Structures with Material and Geometric Nonlinearities

“…Geometric nonlinearities are treated by means of the polar decomposition based corotational formulation proposed in [5].…”

Effective computational modeling of erythrocyte electro-deformation

“…The derivation of the corotational approach presented in [7,8] is here briefly reviewed for triangular elements. Let u i , i = 1, 2, 3, denote the displacement vector of the typical node V i in the reference configuration.…”

“…In particular, such choices ensure conditions (49) to be satisfied. Further details, including the derivation of Π and K Π T are provided in references [7,8].…”

Corotational flat triangular elements for the nonlinear analysis of thin shell structures

“…By resorting to the corotational formulation, it is possible to adopt constitutive models formulated in the small strain regime, which are simpler and computationally less expensive with respect to finite strain approaches. In particular, a small strain plane-stress SMA model based on the formulation proposed in [2] is considered here, in conjunction with the corotational framework developed in [3].…”

“…In addition, a suited kinematic description of the core-element displacement field is required. In this work, the corotational framework developed in [3] is adopted, along with a multiplicative (instead of additive) superposition of membrane and bending actions [7], accounting for the effect of the membrane-straininduced thickness variation on the bending behaviour. The cantilever has square cross section, thickness h = 1 mm, length L = 10 mm, Young's modulus E = 1.2 GPa, zero Poisson's ratio, and is clamped at one end.…”