Load History Overview

Static Fatigue Analysis: Linear Superposition of Multiple FEA/Load Time History Load Cases

When there are several load cases at the same time, all of which vary independently of one another, the principle of linear superposition will be used to combine all load cases together to determine the stress variation at each calculation point due to the combination of all loads. The formula is:
Figure 1.
σ i j ( t ) = k = 1 n ( σ i j , k P F E A , k P k ( t ) )

Where n is the total number of load cases, P k ( t ) and σ i j ( t ) are, respectively, the time variation of the kth load time history and the total stress tensor, and P F E A , k and σ i j ( t ) are, respectively, the kth load magnitude and stress tensor from FE analysis.

The following equation depicts how LDM, Scale, and Offset values work together to scale the FEA stress tensor at time t.
Figure 2.
σ ij (t)= σ ij.FEA LDM (P(t)Scale+Offset) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMgacaWGQbaabeaakiaacIcacaWG0bGaaiykaiabg2da 9maalaaabaGaeq4Wdm3aaSbaaSqaaiaadMgacaWGQbGaaiOlaiaadA eacaWGfbGaamyqaaqabaaakeaacaWGmbGaamiraiaad2eaaaGaaiik aiaadcfacaGGOaGaamiDaiaacMcacaWGtbGaam4yaiaadggacaWGSb GaamyzaiabgUcaRiaad+eacaWGMbGaamOzaiaadohacaWGLbGaamiD aiaacMcaaaa@55EB@
Where:
σ i j ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMgacaWGQbaabeaakiaacIcacaWG0bGaaiykaaaa@3C1E@
Results stress tensor at time t
σ i j . F E A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMgacaWGQbGaaiOlaiaadAeacaWGfbGaamyqaaqabaaa aa@3CCF@
Stress tensor from static analysis
P ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacI cacaWG0bGaaiykaaaa@391D@
The y point value of load-time history at time t