SS-V: 1070 Plate with a Hole

Test No. VS08 Find the maximum stress of a plate with a hole.

Definition

Due to symmetry, only ¼ section was analyzed (Figure 1).

The units are SI.

Sliding constraints applied to the left, back, and bottom faces.

The load is 5000N applied to the right face.*

The model parameters are:

The material properties are:

The reference solution is given by:(1)

σ_{m a x} = k σ_{n o m}

$σ_{m a x} = k σ_{n o m}$

With k = 3.

σ_{n o m} = F \frac{h}{h - r} = 166, 7 M P a

$σ_{n o m} = F \frac{h}{h - r} = 166, 7 M P a$

k = 3 - 3.13 (\frac{d}{h}) + 3.66 {(\frac{d}{h})}^{2} - 1.53 {(\frac{d}{h})}^{3} = 2.2357

$k = 3 - 3.13 (\frac{d}{h}) + 3.66 {(\frac{d}{h})}^{2} - 1.53 {(\frac{d}{h})}^{3} = 2.2357$

σ_{\max} = 372.7 M P a

$σ_{\max} = 372.7 M P a$

The following table summarizes the maximum stress.

	Theory	SimSolid	% Difference
Maximum Stress [MPa]	3.7270E+02	3.7775E+02	1.35%

*To determine the load: 100N/mm² x 50mm x 1mm.