Assessment of different solution methods for receding contact problems in functionally graded layered mediums

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

“…The (N/2 + 1)th equation is established automatically [47], and can be safely deleted. Thus, Equations ( 35)- (38) only contains 2N + 1 equations, as well as 2N + 1 unknowns, i.e., the contact pressure p 2 (s k ), q 2 (s k ), (k = 1, 2, • • • , N) and the half-length of receding contact b. It is worth noting that, among all the unknowns in Equations ( 35)- (38), only b is non-linear.…”

“…Thus, Equations ( 35)- (38) only contains 2N + 1 equations, as well as 2N + 1 unknowns, i.e., the contact pressure p 2 (s k ), q 2 (s k ), (k = 1, 2, • • • , N) and the half-length of receding contact b. It is worth noting that, among all the unknowns in Equations ( 35)- (38), only b is non-linear. We can initialize b with a random value and substitute it into Equations ( 35)- (38); the remaining unknowns p 2 (s k ) and q 2 (s k ), (k = 1, 2, • • • , N) can then be solved iteratively.…”

“…It is worth noting that, among all the unknowns in Equations ( 35)- (38), only b is non-linear. We can initialize b with a random value and substitute it into Equations ( 35)- (38); the remaining unknowns p 2 (s k ) and q 2 (s k ), (k = 1, 2, • • • , N) can then be solved iteratively. The numerical results of the iteration method can be verified by Equation (38), if the absolute error δ satisfies:…”

“…Çömez et al [37] investigated the problem of frictional receding contact of an FG layer resting on a homogeneously coated half-plane. Recently, Yaylacı et al [38] used the semianalytical method, the finite element method (FEM), and the multi-layer perceptron method to analyze the receding contact problem between an FG layer and a homogeneous elastic layer resting on a Winkler foundation which loaded with a rigid cylindrical indenter. Öner et al [39] used the semi-analytical method, FEM, and an artificial neural network to study the double receding contact problem of multi-layered FGM structures under a distributive compressive traction field.…”

Application of Artificial Neural Networks to Predict Inhibition in Probiotic Experiments

“…In recent years, artificial neural networks (ANNs), which can describe nonlinear and complex relationships between data without any assumptions, have become an alternative to traditional regression models [32][33]. These are used to predict the outcome of any problem or situation in different disciplines by using some input values and relations [34]. ANNs imitate the functioning of the human brain.…”