Stress analysis of the contact problem in a functionally graded layer loaded with a distributed load and two rigid circular punches resting on an elastic two quarter planes

In this study, the solution of the contact problem in a functionally graded (FG) layer resting on elastic two quarter planes was done using the finite element method (FEM). The contact problem consists of two rigid circular punches loaded FG and two elastic quarter planes. P and Q loads are transmitted to the FG layer by two rigid circular punches. All surfaces in the problem were considered as frictionless and the weight effect is also taken into account. The two-dimensional model of the contact problem was created with the ANSYS package program based on FEM and the stress analyzes were performed. All operations of quarter planes and circular punches are done with standard ANSYS menus. However, defining the material properties of the FG layer and dividing into meshes in finite elements cannot be done with standard menus. For this reason, a special macro was added to the program in order to define the material properties of the FG layer and to perform the mesh division, and the necessary parameters were applied to the layer by this macro. In the study, the effects of external load, stiffness parameter (βh), density parameter (γh) and contact stresses of distributed load change, normal stresses, and stresses along the depth were investigated.