Models and finite elements for thin-walled structures

By Manfred Bischoff, Kai-Uwe Bletzinger, Wolfgang A. Wall, Ekkehard Ramm. 2004

319 citations recorded by the source corpus.

The present study provides an overview of modeling and discretization aspects in finite element analysis of thin-walled structures. Shell formulations based upon derivation from three-dimensional continuum mechanics, the direct approach, and the degenerated solid concept are compared, highlighting conditions for their equivalence. Rather than individually describing the innumerable contributions to theories and finite element formulations for plates and shells, the essential decisions in modeling and discretization, along with their consequences, are discussed. It is hoped that this approach comprises a good amount of the existing literature by including most concepts in a generic format. The contribution focuses on nonlinear finite element formulations for large displacements and rotations in the context of elastostatics. Although application to dynamics and problems involving material nonlinearities is straightforward, these subjects are not taken into account explicitly.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c2a1ede9f0f57da1bb624f521656a4500bd6e9e5

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In Civil and Structural Engineering

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Citations in the corpus

The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches (2010, background): “This theory is appropriate for thin shells (20 ≤ R/t, where R is the shell radius of curvature and t is its thickness)[31].”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, background): “directions, whereas only one quadratic NURBS element is used through the thickness, which has been shown to be adequate to obtain sufficiently accurate results [5, 97].”
Isogeometric shell analysis: The Reissner-Mindlin shell (2010, unknown): “[14].”
Rotation free isogeometric thin shell analysis using PHT-splines (2011, background): “Shell elements can also be classified according to the thickness of the shell and the curvature of the mid-surface [1].”
Isogeometric collocation: Neumann boundary conditions and contact (2015, unknown): “However, one point quadrature with standard basis functions gives rise to zero-energy hourglass modes and rank deficient system matrices [9].”
Modeling of Composite Shells in 6–Parameter Nonlinear Theory with Drilling Degree of Freedom (2011, background): “Since the sixth parameter in the present theory is the drilling rotation, the important effect of Poisson thickness locking (see for instance [9] or [10] and references given therein) does not occur here.”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, methodology): “Based on the Kirchhoff-Love assumptions [64,65], the 3D strain tensor E reduces to the in-plane strain components E = Eαβ G α ⊗ G .”
Stress‐adapted numerical form finding of pre‐stressed surfaces by the updated reference strategy (2005, background): “Geometry and displacements are discretized by standard displacement elements [35, 36], i.”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “In this manner, since we consider a basis of degree p = 2, the bending modes are properly taken into account by the three–dimensional linear elastic model [13]; indeed, three control points exist through the thickness.”
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials (2015, methodology): “shell formulations based on Reissner–Mindlin kinematics requiring only C0 continuity are much more widespread in finite element shell analysis [1].”
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, unknown): “[43].”
Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework (2014, background): “An important choice for C0-Lagrange elements is the definition of nodal directors DI , see a detailed discussion in [1].”