Test No. VS08Find 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:
 Parameters
 Value
 L
 100mm
 H
 50mm
 R
 20mm
 F
 100N/mm^2
 Thickness
 1mm
The material properties are:
 Properties
 Value
 Modulus of Elasticity
 2.1e+11
 Poisson's Ratio
 0.3
Results
The reference solution is given by:
(1)
$${\sigma}_{max}=k{\sigma}_{nom}$$
With k = 3.
${\sigma}_{nom}=F\frac{h}{hr}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}166,\text{\hspace{0.33em}}7MPa$
$k=3\text{\hspace{0.17em}}\text{\hspace{0.17em}}3.13\left(\frac{d}{h}\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}3.66{\left(\frac{d}{h}\right)}^{2}\text{\hspace{0.17em}}1.53{\left(\frac{d}{h}\right)}^{3}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}2.2357$
${\sigma}_{\mathrm{max}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}372.7MPa$
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/mm^2 x 50mm x 1mm.