Question

c) Describe the boundary conditions needed to impose a symmetry plane when using shell elements.

FEA

FEA question

Answer 1

The finite element method is used for computing displacements and stresses for a wide
variety of problems. Consider an example as shown below:

30 MPa 30 mm 30 MPa 15 mm 30 mm Y 60 mm (b)

Figure. 1

A plate with such a loading can exist anywhere in space.Here we are interested in the deformation of the body, therefore symmetry of the geometry and the symmetry of the loading can be used effectively.Let x and y represent the axes of symmetry as shown in Figure. 1 The points along the x-axis move along x and are constrained in the y direction and points along the y-axis are constrained along the x direction. This suggests that the part, which is one-quarter of the full area, with the loading and boundary conditions as shown is all that is needed to solve
the deformation and stresses.

A linearly distributed load symmetric with respect to a plane can be divided into symmetric-symmetric and symmetric-antisymmetric loading as shown in Fig. 2. The symmetric-symmetric part can be treated as discussed above. While symmetric-antisymmetric part can be treated with boundary condition as shown. Displacements and stresses need to be computed using the principle of superposition. The values for the entire body need to consider the geometry of deformation for symmetry and antisymmetry.

40 MPa 40 MPa 20 MPa 20 MPa 40 + 20 30 MPa 30 MPa zir 2/10 MPa 10 MPa (40 – 30) -10 MPa -10 MPa (20 - 30) Symmetric-Antisymmetric Symmetric-Symmetric U = 0 U = 0 v=0 v = 0 CS Scanned with CamScanner

Figure. 2