Development of shell element with thickness stretch

The finite element method is commonly used to simulate the behavior of sheet forming processes, in order to realize high precision machining. In the conventional shell elements, the plane stress condition which ignores the transverse normal stress is assumed. Thus, the conventional shell elements are not sufficient to simulate the complex behaviors, such as, the deformation of the sheet and the contact force at the sheet-die interface. In this paper, we present a formulation for considering the thickness change and the stress distribution by the surface traction in the shell element. We introduce a displacement variation along the transverse direction to MITC shell element, which is widely used for avoiding the transverse shear locking. Then, we can evaluate the equilibrium equation for the transverse direction by using the introduced variation. Further, we verify the proposed approach to compare the results of the proposed shell with that of the continuum elements. © 2015 The Japan Society For Computational Engineering and Science.