ME3602 – ME3692

FEA Assignment 2013 – 2014

Introduction

The magnitude of stress concentrations around holes in plates used as components of structures has long been an important design consideration.

The localized stress around a hole is usually obtained by multiplying the nominal stress by a factor called a stress concentration factor. For example, the localized stress or stress concentration

maxσ at

the edge of a relatively small hole, at the center of a wide plate that resists and axial load P is

0max σσ KAPK ==

in which K is the stress concentration factor and AP

=0σ is the (nominal) stress that would occur

at the same point if the bar did not contain the hole; A is the gross area including the area which is removed at the hole. If the diameter of the hole is relatively large, the net area of cross section is frequently used in calculating the nominal stress

0σ , hence the value of the stress concentration

factor for a given discontinuity will depend on the method of calculating the nominal stress.

The below assignment brief is limited to small holes in plates that is, holes which are relatively small in comparison to the plate size such that boundary conditions do not affect the results. An exception to this is the case when holes are near a free edge of a plate.

Procedure

The general layout of the problem is shown in Figure 1. You are required to determine the “stress concentration” and peak stresses that will be introduced as a result of each particular configuration you are to investigate. The elastic modulus is E = 210 GPa, Poisson’s ratio is 0.32 and the yield stress is 250 MPa.

Figure 1: Sheet with double row of holes, under tension

Figure 1 shows a semi-finite plate with a double row of staggered holes subject to tension. Hereby, a problem arises in identifying the critical the stress concentration areas, as K depends on the ratio

ab and θ . The staggered holes are centrally placed on plate.

a diameter of holes (mm) Variable (given)

b horizontal pitch (mm) Variable (given)

c distance between rows in a double row of holes (mm) Variable (given)

c = [0, 10, 15, 20, 25, 30, 35, 40, 45] mm

t plate thickness (mm) Variable (given)

t = [3, 5, 7] mm

l length of plate (mm) Constant = 250 mm

θ angle of stagger between holes in double row of holes (deg), bc2tan 1−=θ

w width of plate (mm) Constant = 100 mm

σ stress applied as function of total tensile load P = 1.2kN normally distributed along the

horizontal edge of plate

There is only one load case to consider. Each student has his/her own data. This will be given to each individual in the class or laboratory session.

You are required to carry out/produce/determine:

• A finite element analysis using the ANSYS package to show the effect of the staggered holes, radius, etc.. in the plate. You should investigate the effect of varying meshes on the results. (At least three different meshes should be used). You may use an “auto-mesh” routine for one of these meshes only – the other two should be user-specified mesh densities.

• The calculated numerical stress concentrations K along with the theoretical values tK (see

references above) for each attempt should be clearly plotted in a graph K and tK vs θ (deg) and presented in the conclusions.

• A recommendation for the best set of variables a , b , c and t if a revised design is to be suggested.

• A report on the investigation (see specification above).

You should sign in at your staffed sessions in TC 402. At least 4 “sign-ins” will be expected.