A new element for analyzing large deformation of thin Naghdi shell model. Part 1: Elastic

作者：Ghassemi Aazam^*; Shahidi Alireza; Farzin Mahmoud

来源：Applied Mathematical Modelling, 2010, 34(12): 4267-4277.

DOI：10.1016/j.apm.2010.05.001

• Large deformation
• Cosserat surface
• Thin shell
• Finite element
• Elastic

One of the best approaches for modeling large deformation of shells is the Cosserat surface. However, the finite-element implementation of this model suffers from membrane and shear locking, especially for very thin shells. The basic assumption of this theory is that the mid-surface of the shell is regarded as a Cosserat surface with one inextensible director. In this paper, it is shown that by constraining the director vector normal to the mid-surface, besides very good and accurate results, shear locking is also eliminated. This constraint is in fact a limiting analysis of the Cosserat theory in which Kirichhoff's hypothesis is enforced. Numerical solution is performed using nine-node isoparametric element. The principal of virtual work is used to obtain the weak form of the governing differential equations and the material and geometric stiffness matrices are derived through a linearization process. The validity and the accuracy of the method are illustrated by numerical examples.

• 出版日期2010-12