Warping Elements

Warping elements:

  • are used to model an arbitrarily shaped beam cross-section profile for use with Timoshenko beams;

  • are used in conjunction with the beam section generation procedure described in Meshed Beam Cross-Sections; and

  • model linear elastic behavior only.

This page discusses:

 

See Also
Meshed Beam Cross-Sections
*SOLID SECTION

Typical Applications

Warping elements are special-purpose elements that are used to discretize a two-dimensional model of a beam cross-section. This two-dimensional cross-section model is used in Abaqus/Standard to calculate the out-of-plane and, optionally, the in-plane warping displacements, as well as relevant sectional stiffness and mass properties that are required in a subsequent beam analysis in either Abaqus/Standard or Abaqus/Explicit. Applications include any structure whose overall behavior is beam-like, yet the cross-section is non-standard or includes multiple materials. Examples include the cross-section of a ship for performing whipping analysis, a beam model of an airfoil-shaped rotor blade or wing, a laminated I-beam, etc.

Choosing an Appropriate Element

To mesh an arbitrarily shaped solid beam cross-section Abaqus/Standard offers two element classes:

  • 1-DOF warping elements have one degree of freedom per node representing the out-of-plane warping displacement.
  • 3-DOF warping elements have two additional degrees of freedom per node representing the in-plane warping displacements.

Adjacent elements in the cross-sectional mesh must share common nodes; mesh refinement using multi-point constraints is not allowed. The mesh can contain either 1-DOF warping elements or 3-DOF warping elements; you cannot mix the two element classes in the same analysis.

Naming Convention

Warping elements are named as follows:



For example, WARP2D4 is 4-node warping element in two dimensions.

Defining the Elements Section Properties

You use a solid section definition to define the section properties. You must associate these properties with a region of your model. No additional data are necessary.

Assigning a Material Definition to a Set of Warping Elements

You must associate a linear elastic material definition with each warping element section definition. Optionally, you can associate a material orientation definition with the section (see Orientations).

Only isotropic linear elasticity (Defining Isotropic Elasticity) or orthotropic linear elasticity for warping elements (Defining Orthotropic Elasticity for 1-DOF Warping Elements) are valid material models for 1-DOF warping elements.

For 3-DOF warping elements, you can define the following types of linear elasticity: