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Linear 2D Element Analysis: Modelling implications

Some structures can only be adequately modelled using 2D elements. For examples cores (where deformations in the plane of the element dominate) or floor slabs (where deflections normal to the plane of the element dominate). This section gives an introduction to 2D elements for linear analysis. Nonlinear analysis using 2D elements is discussed later.

Modelling using 2D elements is less intuitive than modelling with skeletal elements, and very different results can be obtained for the same problem, by changing mesh size for example.

Structure types​

There are a number of different types of 2D analysis available in GSA depending on the structure type set in the General Specification

  • Space – allowing 2D elements to be combined with other element types in 3D space.
  • Plane stress – where a condition of plane stress (in-plane stresses only) is required, for example a shear wall.
  • Plane strain – where a condition of plane strain (in-plane strains only) is required, for example a tunnel section.
  • Axisymmetric – where a radial slice of an axisymmetric structure is required, for example a cylindrical tank.

Plane stress, plane strain and axisymmetric analyses are restricted to 2 dimensions (x and y only).

Elements​

There are two aspects of 2D elements that need to be considered: the geometrical aspects (element shapes and mesh) and the appropriate properties.

In skeletal analysis the element mesh is defined by the structure, while in 2D analysis the user needs to provide a mesh of 2D elements which will give an adequate representation of the structural behaviour in the region. This will usually be done using the option for generating 2D element meshes.

The type of element chosen will depend on the type of structure and the analysis method that will be used. 2D elements can be either quadrilateral or triangular and linear (nodes at the corners) or quadratic (nodes at corners and at mid-sides). The recommended elements for linear analysis are quadratic quad (Quad8) elements. However it is often more convenient to generate a mesh of Quad4 elements and use the Modify elements command on the Sculpt toolbar to convert the elements from linear to quadratic before analysis. Internally the elements are mapped onto simpler shapes, so for example, a Quad8 element regardless of its shape is mapped to a square. The further the shape of the element departs from a square the less accurate the elements are likely to be.

The properties of 2D elements are defined in the 2D Element Properties table. For plane stress, plane strain and axisymmetric structures no type is required as this is implied by the structure type. For space elements there is a choice of:

  • Plane stress – an element which has only in-plane stiffness
  • Fabric – not available for linear analysis
  • Flat plate – an element which has only out-of-plane stiffness
  • Flat shell – an element which has both in-plane and out-of-plane stiffness
  • Curved shell – not available at present in the solver

So to model a shear wall the plane stress type may be appropriate, while for a slab the flat shell may be the best choice.

It is useful to be able to assign a set of axes to 2D elements that applies to a whole group of elements irrespective of the individual orientations. This can be done by setting the axis in the property table.

The added mass allows for an extra non-structural mass, such as a screed, to be included when gravity loads as being considered.

Loading​

Loading can be applied to 2D elements in a similar way to loading on beam elements, on individual or lists of elements. The 2D element loading modules are accessible from the 2D Element Loading table. The loading types are:

  • Face Loads
  • Edge Loads
  • Prestress
  • Thermal

As with beam elements gravity loads can be applied to lists of 2D elements.

The loading that can be applied will depend on the type of element, so for example face loads cannot be applied to plane stress elements and edge loads cannot be applied to flat plate elements. In general it is preferable to apply loads to elements than to the nodes around the elements as the nodal forces resulting from 2D loads are far from intuitive.