VM-WB-MECH-026

VM-WB-MECH-026
Fatigue Analysis of a Rectangular Plate Subjected to Edge Moment

Overview

Reference:	Any standard Machine Design and Strength of Materials book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Fatigue Analysis
Element Type(s):	Shell

Test Case

A plate of length L, width W, and thickness T is fixed along the width on one edge and a moment M is applied on the opposite edge about the z-axis.

Find the maximum Bending Stress (Normal X Stress) and maximum Total Deformation of the plate. Also find the part life and the factor of safety using Goodman, Soderberg, & Gerber criteria. Use the x-stress component. Consider load type as fully reversed and a Design Life of 1e6 cycles, Fatigue Strength factor of 1, and Scale factor of 1.

Figure 29: Schematic for Ansys Mechanical

Material Properties

Geometric Properties

E = 2 x 10¹¹ Pa

ν = 0.0

Ultimate tensile strength = 1.29 x 10⁹ Pa

Endurance strength = 1.38 x 10⁸ Pa

Yield Strenth = 2.5 x 10⁸ Pa

Length L = 12 x 10^-3 m

Width W = 1 x 10^-3 m

Thickness T = 1 x 10^-3 m

Moment M = 0.15 Nm (counterclockwise @ z-axis)

No. of Cycles

Alternating Stresses (Pa)

1000

1.08 x 10⁹

1 x 10⁶

1.38 x 10⁸

Results Comparison for Ansys Mechanical

Results		Target	Mechanical	Error (%)
Maximum normal x-stress (Pa)		9 x10⁸	9 x 10⁸	0.000
Maximum total deformation (m)		6.48 x 10^-4	6.4982 x 10^-4	0.281
SN-Goodman	Safety factor	0.1533	0.15333	0.020
SN-Goodman	Life	1844.3	1844.4	0.005
SN-Soderberg	Safety factor	0.1533	0.15333	0.020
SN-Soderberg	Life	1844.3	1844.4	0.005
SN-Gerber	Safety Factor	0.1533	0.15333	0.020
SN-Gerber	Life	1844.3	1844.4	0.005