Department of Civil and Environmental Engineering, The University of Melbourne Finite Element Modelling – Element Types and Boundary Conditions (Notes prepared by A. Hira – modified by N. Haritos)

Modelling Requirements Correct Loads Correct Material properties Correct Geometrical properties Correct BOUNDARY CONDITIONS

Consider Simple Beam Simply supported beamFully fixed beam Simply Supported Rotationally Fixed

Boundary Conditions Simple example exemplifies the importance of correct boundary conditions Results differ significantly Recognise the difference For more complex problems difficult to identify mistakes due to incorrect boundary conditions

Constraints Boundary conditions have two primary functions The ensure that the structure is stable in space in the six degrees of freedom To duplicate the restraint offered to the structural system by external systems. All six degrees of freedom need to be considered. ie translational movement in x,y, and z direction rotation about the x,y, and z axis

Rectangular Slab (5kPa Loading)

Bending Moment (Max 12.0kNm) Vertical support on all 4 sides

Deflection – Max 2.0mm Vertical support on all 4 sides

Bending Moment (Max 6kNm) Vertical and rotational fixity on all 4 sides

Deflection – Max 0.6mm Vertical and rotational fixity on all 4 sides

Quarter of Slab

Vertical and rotational about y restrained Vertical and rotational about x restrained

Compare BMs  Identical

Compare Deflections  Identical

Use of Symmetry Problem can be reduced in size if the following is satisfied Symmetry in geometry Symmetry in Boundary Conditions Symmetry in Loading

Element Types 2D Plane Stress A plane stress analysis assumes a thin two- dimensional sheet of material. All stresses are in the plane and the stress through the thickness is zero. The only active degrees of freedom are those associated with displacement in the XY plane (DX and DY)

2-D Plane stress

Element Type 2D Plane Strain A plane strain element is used to model the cross section of a very thick or long structure. Plane strain assumes that the strain normal to the plane is zero. That is the structure is assumed infinitely long so that no strain is possible in the third direction. The only active degrees of freedom are those associated with displacement in the XY plane (DX and DY)

2-D Plane strain

Element Type Axisymmetric - A structure is said to be axisymmetric when it may be represented by a two dimensional section that can be extruded in a polar direction by 360 degrees about some axis to generate the structure. It should be noted that in addition to any geometric symmetry, the loading must also be symmetric around the axis symmetry. The only active degrees of freedom are those associated with displacement in the XY plane (DX and DY). The Y axis is assumed to be the axis of rotational symmetry. The X axis is the radial direction

Axisymmetrical

Element Types Plate/Shell The plate/shell element is the most general type of plate element in that it is a three-dimensional membrane and bending element. It is the only plate element that permits out of plane displacements associated with bending behaviour. This includes the analysis of flat plates and general three-dimensional shells. The default freedom condition should be set free in all directions. This element is the most commonly used plate element.

Plate/Shell Element Drilling degrees of freedom – normally inactive

Plate/Shell Element

Element Types 3D Membrane The 3D membrane is a plate element that has in-plane (membrane) stiffness only; that is it can carry direct stress and in-plane shear stress. It has no bending stiffness. The 3D membrane plate element is designed to be run using the nonlinear solver. The type of structures that this element would be used to model, typically undergo large deflections and develop significant membrane stresses to support the applied loads. Uses of this element include the modelling of elastic membrane balloon type structures, fabric roofs etc.