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SS-V: 1070 Plate with a Hole
Test No. VS08 Find the maximum stress of a plate with a hole.

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- Introduction
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- Access the Model Files
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- Static Analysis
  - SS-V: 1000 Straight Cantilever Beam
    Test No. VS01 Find tip deflections of a cantilever beam when subjected to extension, shear, and twisting loads.
  - SS-V: 1010 Twisted Cantilever Beam
    Test No. VS02 Find tip deflections of a twisted cantilever beam when subjected to shear loads.
  - SS-V: 1020 Curved Beam
    Test No. VS03 Find tip deflections of a curved beam when subjected to in-plane and out-of-plane loads.
  - SS-V: 1030 Simply Supported Thin Plate
    Test No. VS04 Obtain the displacement at the center of a simple supported thin plate for concentrated load and uniform pressure load.
  - SS-V: 1040 Clamped Thin Plate
    Test No. VS05 Obtain the displacement at the center of a clamped thin plate for concentrated load and uniform pressure load.
  - SS-V: 1050 Tapered Solid Bar
    Test No. VS06 Determine the maximum axial deflection and axial stress at the mid-length for a tapered solid bar.
  - SS-V: 1060 Cantilever Plate
    Test No. VS07 Find bending stress at fixed end for a cantilevered plate subjected to a vertical shear load of 120 lbs.
  - SS-V: 1070 Plate with a Hole
    Test No. VS08 Find the maximum stress of a plate with a hole.
  - SS-V: 1080 Scordelis-Lo Roof
    Test No. VS09 Find the maximum Z displacement for a curved cylindrical dome.
  - SS-V: 1090 Stepped Shaft with Fillet
    Test No. VS10 Find the stress concentration in a filleted notch.
  - SS-V: 1100 Raasch Challenge
    Test No. VS11 Find the tip displacement at the free end of a thick, doubly curved beam.
  - SS-V: 1110 Notched Plate
    Test No. VS12 Find Sx stress in the notch and top face of a notched plate.
  - SS-V: 1120 Simply Supported Beam with Mid-span Load
    Test No. VS13 Find the max displacement and stress for a pinned beam with load at the midpoint.
  - SS-V: 1130 Skew Plate Under Pressure
    Test No. VS14 Find the maximum principle stress at the skew plate center at point E.
  - SS-V: 1140 Stress Concentration of Filleted Bar
    Test No. VS15 Find maximum normal stress for two configurations of a filleted bar.
  - SS-V: 1150 Buckling
    Test No. VS16 Find the critical compression load at which the cantilever beam buckles.
  - SS-V: 1160 Stress Concentration in a Groove Shaft
    Test No. VS17 Find the stress concentration in a grooved shaft.
  - SS-V: 1170 Stress Concentration of a Plate with Eccentric Hole
    Test No. VS18 Find the stress concentration in a plate with eccentric hole.
  - SS-V: 1180 Stress Concentration in a Filleted Notch
    Test No. VS19 Find the stress concentration in a filleted notch when torque is applied.
  - SS-V: 1190 Stress Concentration of a Plate with Semi-circular Holes
    Test No. VS20 Find the stress concentration in a plate with semi-circular holes.
  - SS-V: 1200 Tangential Edge Stress in an Elliptic Membrane
    Test No. VS21 Find the tangential edge stress in an elliptic membrane.
  - SS-V: 1210 Tangential Stress for a Cylindrical Shell
    Test No. VS22 Find outer surface tangential stress for a cylindrical shell.
  - SS-V: 1220 Displacements in Hemispherical Shell
    Test No. VS23 Find displacements in a hemispherical shell.
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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:

Parameters: Value
L: 100mm
H: 50mm
R: 20mm
F: 100N/mm²
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:

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

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

The following table summarizes the maximum stress.


	Theory	SimSolid	% Difference
Maximum Stress [MPa]	3.7270E+02	3.7746E+02	1.28%

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