### Finite Element Fatigue Deformation Model using Matrix-Eigen Value Method and Calculus of Variation for Varying Load Amplitudes

Mr. Anwar Wali Gutti

#### Abstract

Fatigue loads vary in amplitude and frequency, i.e., on a body, loads of varying amplitude will act with a frequency which can vary. Deformations are created in the body due to these loads which eventually initiates the crack formation. In this paper, fatigue load analysis is done using the finite element theory by dividing the body in finite Isoparametric elements which are the elements that are capable of representing the boundary curvature which helps us to incorporate in the analysis the irregular curved boundaries developed during the formation of crack. Then for the same isoparametric element, a mathematical model of varying amplitude loads is prepared using the spring mass model from which the Eigen frequency values, displacement, stress, strain and curvature equations are derived and finally using the calculus of variation method the path of deformation is predicted for the isoparametric element.

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