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Structural Engineering and Mechanics
  Volume 54, Number 4, May25 2015, pages 607-622
DOI: http://dx.doi.org/10.12989/sem.2015.54.4.607
 


Analytical solution of a contact problem and comparison with the results from FEM
Erdal Oner, Murat Yaylaci and Ahmet Birinci

 
Abstract
    This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.
 
Key Words
    contact problem; finite element model; rigid punch; semi-infinite plane; singular integral equation
 
Address
Erdal Oner: Department of Civil Engineering, Bayburt University, 69000, Bayburt, Turkey
Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdoğan University, 53100, Rize, Turkey
Ahmet Birinci: Department of Civil Engineering, Karadeniz Technical University, 61080, Trabzon, Turkey
 

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