Ph.D. Tezi Görüntüleme
In this study, a frictionless contact problem for an elastic layer resting on two quarter planes is considered according to linear elasticity theory, and artificial neural network method is applied to the problem. The concentrated force in the vertical direction is applied to the layer by means of rigid cylindrical stamp. Using the theory of elasticity and integral transform technique, the expressions of displacements and stresses are obtained. Contact lengths and contact stresses are calculated in the case of different loading, material properties and geometry.The study consists of five main chapters.
In the first chapter, the previous studies of contact problems and artificial neural network problems are summarized, fundamental equations related with the problem is obtained and content of the problem is given.In the second chapter, the problem is introduced and general equations are expressed. Using the mixed boundary conditions, two singular integral equations are obtained where the contact lengths and contact stresses are unknowns. The numerical solutions of the integral equations is carried out by the method of Gauss-Jacobi integration formula.
In the third chapter, the numerical applications of the problem are performed for different numerical values of external load, radius of the rigid stamp, height of the layer, the distance between two quarter planes and material constant ratios. The contact lengths and the contact stresses are examined associated with those values. The solutions are demonstrated by tables and graphics.In the fourth chapter, the artificial neural network method is expressed and, which has enough numbers of patterns in the training set, is applied to the problem. Trained artificial neural network is tested and the test results are compared with the theoretical results and a very good approximation is obtained. The results are presented in tables and graphics.
In the fifth chapter, the conclusions obtained from this work and offers are given.Key Words : Theory of Elasticity, Contact Mechanics, Integral Equation, Fourier Transform, Mellin Transform, Contact Length, Contact Stress, Artificial Neural Network