Analytical approach to wave and stress analysis of bars made of non linear material with finite length


Thesis Type: Postgraduate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2006

Thesis Language: Turkish

Student: Özkan Bademci

Supervisor: YAŞAR PALA

Abstract:

First of all this study contains an introduction to non-linear eqations. Later,some techniques used for solving non-linear equations are explained by givenexamples.Second of all, the non-linear elastic and elastic-plastic wave motion in a finitebar made of a material obeying non-linear stress-strain relation is analyzed. Non-lineargoverning partial differential equation is separated into two non-linear ordinarydifferential equations using a new method for the separation. Analytical solutionsatisfying boundary and initial conditions are constructed from the proper solutions ofequations. Stresses, wave velocities and displacements in the rod are found for arbitraryconditions. Two methods are developed. While the first method brings a limitation onthe solution, the second one removes this problem by selecting more practically logical conditions.