Explicit finite deformation analysis of isogeometric membranes

in Computer Methods in Applied Mechanics and Engineering (2014)

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear ... [more ▼]

NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultrathin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order Ck (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation is demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated. [less ▲]

A cell - based smoothed finite element method for free vibration and buckling analysis of shells

in KSCE Journal of Civil Engineering (2011), 15(2), 347-361

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient ... [more ▼]

This paper further extends a cell-based smoothed finite element method for free vibration and buckling analysis of shells. A four-node quadrilateral Mindlin-Reissner shell element with a gradient smoothing operator is adopted. The membrane-bending and geometrical stiffness matrices are computed along the boundaries of the smoothing cells while the shear stiffness matrix is calculated by an independent interpolation in the natural coordinates as in the MITC4 (the Mixed Interpolation of Tensorial Components) element. Various numerical results are compared with existing exact and numerical solutions and they are in good agreement. The advantage of the present formulation is that it retains higher accurate than the MITC4 element even for heavily distorted meshes without increasing the computational cost. © 2011 Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg. [less ▲]