TY - JOUR

T1 - Thin shells with finite rotations formulated in biot stresses

T2 - Theory and finite element formulation

AU - Wriggers, Peter

AU - Gruttmann, F.

PY - 1993/6/30

Y1 - 1993/6/30

N2 - A bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated work‐conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and, therefore, appropriate for the formulation of constitutive equations. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.

AB - A bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated work‐conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and, therefore, appropriate for the formulation of constitutive equations. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's method.

UR - http://www.scopus.com/inward/record.url?scp=0027607820&partnerID=8YFLogxK

U2 - 10.1002/nme.1620361207

DO - 10.1002/nme.1620361207

M3 - Article

AN - SCOPUS:0027607820

VL - 36

SP - 2049

EP - 2071

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 12

ER -