Investigation of the Frictionless Contact Problem in A Rigidly Supported Homogeneous Layer by Using FEM

In this study, the continuous contact problem of a homogeneous layer of constant thickness perfectly bonded to a rigid support on its bottom surface and loaded a rigid stamp is investigated using the finite element method (FEM). It is assumed that the all contact surfaces are frictionless. The homogenous layer is loaded by rigid circular stamp with external load P. Two-dimensional finite element analysis of the problem is performed using ANSYS software. Also, normal stresses and shear stresses are investigated along the depth of the layer for different shear modulus ratios. Besides, contact length and contact stress between rigid block and homogenous layer are determined. The obtained results are compared to analytical solution and they are shown in graphs and tables.

Anahtar Kelimeler:

Contact problem, Finite element method, Homogenous layer, Rigid stamp

Rijit Olarak Mesnetlenmiş Homojen Tabakada Sürtünmesiz Temas Probleminin Sonlu Elemanlar Metodu ile İncelenmesi

Bu çalışmada, alt yüzeyinden rijit olarak mesnetlenmiş ve rijit bir dairesel blok ile yüklenmiş sabit yükseklikli bir homojen tabakada sürekli temas problemi sonlu elemanlar yöntemi kullanılarak incelenmiştir. Bütün yüzeylerin sürtünmesiz olduğu kabul edilmiştir. Homojen tabaka, dış yükü P olan bir rijit dairesel blok vasıtasıyla yüklenmiştir. Problemin iki boyutlu sonlu elemanlar analizi ANSYS yazılımı kullanılarak gerçekleştirilmiştir. Ayrıca farklı yükleme durumları için tabakanın derinliği boyunca normal gerilmeler ve kayma gerilmeleri incelenmiştir. Bunun yanı sıra rijit blok ile homojen tabaka arasındaki temas mesafeleri ve temas gerilmeleri belirlenmiştir. Elde edilen sonuçlar analitik sonuçlarla kıyaslanarak grafik ve tablo halinde gösterilmiştir.

Keywords:

Temas problemi, Sonlu elemanlar yöntemi, Homojen tabaka, Rijit zımba,

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