Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors

By Wolfgang Dornisch, Bernd Simeon. 2013

184 citations recorded by the source corpus.

An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/8828c5dacc700894094bd00963d2f5ba8a93691d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and B-method (2013, methodology): “Here, rather than solving this problem using a Kirchhoff-Love [4,5] or Reissner-Mindlin [7,32,8] shell structural model, we undertake to solve it using solid-shell elements [33–37].”
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials (2015, unknown): “Keywords: Isogeometric; Kirchhoff–Love; Thin shell; Hyperelastic; Finite strain; Nonlinear material; Incompressibility”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “A recently published approach employs non-uniform rational B-splines (NURBS) as shape functions [37,54,106,107,270,270].”
Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework (2014, methodology): “For all details including the linearization of the weak form we refer to [6].”