Question

4. What are the material properties to be input in 2-D stress-strain analysis?

5. What are the two sources of errors in FEA modeling? Explain.

Answer 1

4. The material properties that are input to the 2D stress problems are Young's Modulus, cross-sectional area of element, length of the element and poisson's ratio.

5. In general, we can decompose errors in FEA—Finite Element Analysis—into three main groups:

• Modeling errors due to simplifications
• Discretization errors that arise from the creation of the mesh
• Numerical errors of the solution of the FEA equations

Furthermore, it must be kept in mind that the Finite Element Method, in addition to the other numerical methods (FVM, FDM, BEM) consists of approximations.

Modelling Errors in FEA:

The finite element description is a boundary value problem (BVP), which means there is a differential equation with a number of constraints called boundary conditions.

The solution to a BVP must resolve the differential equation and satisfy the boundary condition.

Errors of this type can include:

• the wrong geometric description: for instance, we use axial symmetry or rotational symmetry, but often forget that we are dealing with an antisymmetric load
• the wrong definition of the material: for example, the limit of Poisson’s ratio in isotropic materials
• the wrong definition of the load: trying to simplify complex load states or a number of loads with one load (depends on the case). But often “the difference between the effects of two different but statically equivalent loads becomes very small at sufficiently large distances from load” as Saint-Venant’s Principle expresses
• the wrong boundary conditions: if you forget to fix model (rigid body motion) or set boundary conditions, you might inadvertently falsify the results.
• the wrong type of analysis.

Numerical Errors in FEA:

1. Integration errors in FEA caused by Gauss integration lead to numerical instabilities. However, a large number of Gauss points is far too expensive.
2. Rounding errors in FEA can be caused by adding or subtracting very large and very small numbers, or when dividing by small numbers.
3. Matrix conditioning errors.

Discretization Errors:

Here the user has set up the problem correctly, properly approximated the real world situation and entered all the correct information, but the density of the mesh is insufficient to capture the correct solution. Ansys and other FEA codes offer tools for the user to investigate how much error is being introduced by inadequate mesh density.