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2D or not 2D? That is Often the FEA Modeling Question

Plane Stress Modeling of Stent Balloon Expansion | FEA Consulting
January 29, 2016 By: Peter Barrett

Two-D, or not Two-D: that is the question: Whether ’tis nobler in the mind to suffer the slings and arrows of outrageous CPU time from 3D analyses; or to take arms against a sea of data, and by opposing, gain valuable results in a short period of time with a 2D simulation!

Most FEA simulations start with importing the CAD geometry. Since the geometry file is almost always three dimensional, the analyst will often start by creating a complex 3D finite element model. Yet for many problems, a two dimensional simulation will provide quicker, more accurate results allowing for design iterations and even design optimization in the same time required to perform a single 3D analysis.  At a minimum, when the required simulations are highly nonlinear, lessons learned from 2D simulations can help streamline the input assumptions and convergence efficiency of the future 3D run.

Two dimensional analyses can be used to model thin walled parts using a plane stress assumption; very long parts using a plane strain assumption; and parts of revolution using an axisymmetric solution.  All three simulation types use the same 2D FEA mesh, but different element stiffness formulations to simulate the physical differences as summarized below.

Plane Stress Modeling:

Plane stress is applicable for thin to moderately thick walled parts, where zero normal and shear stress perpendicular to the body surface is assumed. The 2D plane stress FEA model has to lie in a single plane at Z=0 in most codes, but the geometry it represents does not have to be flat. Modeling of a stent using an unwrapped representation of the 3D geometry can be an efficient method for simulating the large deformation and the highly nonlinear material response of stent balloon expansion (see Figure 1, above). The simplification of the stent 2D model is ignoring any out-of-plane deformation which for the best stent designs is minimal.

Plane stress simulations also allow for variable thickness input that can be combined with plane strain and axisymmetric models. When combining plane stress and axisymmetric elements in ANSYS, the thickness must represent the full 360-degree combination of all planar surfaces. For example, if one were modeling a bladed disk, the plane stress blade thickness would be approximated by the combined thickness of all the blades (Figure 2).  2D Loading can be applied in the form of in-plane forces, pressures, accelerations, temperatures and contact induced snap-fits. 

Figure 2 Plane Stress + Axisymmetric 2d Model Modeling Blade-Disk Thermal Stress Response

Plane Strain Modeling:

Plane strain assumes the out-of-plane geometry is large and/or constrained and that loading does not vary in the out-of-plane direction (Z) such that Z displacements are neglected. Common applications of plane strain include the analysis of dams, tunnels, rollers, seals, etc. The out-of-plane strain is either prescribed to be zero or held at a constant value in the special case of “generalized plane strain”. The physical geometry does not have to be rectangular, but it must be defined by a zero or constant rate of out-of-plane response. The generalized plane strain (constant out-of-plane strain) is typically required for temperature loads which would create near infinite normal stresses with the zero Z plane strain modeling assumption. Figure 3 illustrates a generalized plane strain simulation of a simplified air-cooled turbine blade.

Figure 3: Generalized Plane Strain Modeling of Gas Turbine Blade

Axisymmetric Modeling:

For structures of revolution including pressure vessels, pipes, piles, wheels, bottles, cans, disks etc. subjected to axisymmetric loading, the 2D axisymmetric element formulation can save considerable computational time with increased stress accuracy. Axisymmetric analyses of pressure vessels can accurately predict local fillet stresses without the need for submodeling that is often required for more complex 3D analyses. Threaded connections, strictly speaking are not exactly axisymmetric, but can be approximated if the helix angle is small - as illustrated in Figure 4.

So, are you the analyst that will continue “to grunt and sweat under a weary life, but that the dread of something after death for not giving that 2D analysis a try”? I welcome others prose on performing 2D FEA simulations.

Figure 4: Axisymmetric Bolted Connection Model