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 three dimensional solid structures

in KSCE Journal of Civil Engineering (2012), 16(7), 1230-1242

This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded ... [more ▼]

This paper extends further the strain smoothing technique in finite elements to 8-noded hexahedral elements (CS-FEM-H8). The idea behind the present method is similar to the cell-based smoothed 4-noded quadrilateral finite elements (CS-FEM-Q4). In CSFEM, the smoothing domains are created based on elements, and each element can be further subdivided into 1 or several smoothing cells. It is observed that: 1) The CS-FEM using a single smoothing cell can produce higher stress accuracy, but insufficient rank and poor displacement accuracy; 2) The CS-FEM using several smoothing cells has proper rank, good displacement accuracy, but lower stress accuracy, especially for nearly incompressible and bending dominant problems. We therefore propose 1) an extension of strain smoothing to 8-noded hexahedral elements and 2) an alternative CS-FEM form, which associates the single smoothing cell issue with multi-smoothing cell one via a stabilization technique. Several numerical examples are provided to show the reliability and accuracy of the present formulation. [less ▲]

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

in Engineering Fracture Mechanics (2008), 75(16), 4740-4758

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept ... [more ▼]

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data. [less ▲]