Computational model of the deformation of thin gradient coating lying on nondeformable foundation

As a computational model of deformation of wedge-shaped gradient coatings lying on a non-deformable base, we propose a solution of the contact problem for a wedge non-uniform in thickness rigidly fixed on the lower face. A closed analytic solution of the contact problem is obtained for the case of elastic moduli (Young’s modulus, Poisson’s ratio, shear modulus), which is a continuous differentiable function with respect to the angular coordinate. The influence of the gradient of the wedge on the distribution of contact stresses under the stamp is illustrated. The problem is posed in connection with the need to predict the phenomenon of delamination of modern coatings of a complex structure from a nondeformable substrate.

show abstract

Computational model of the deformation of graded wedge with complicated structure

Trubchik

Евич

Ladosha

2018

MATEC Web Conf.

View full text Add to dashboard Cite

show abstract

Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip

Бобылев

2023

Diff Equat

View full text Add to dashboard Cite

Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip

Bobylev

2023

Differencialʹnye uravneniâ

View full text Add to dashboard Cite

For an isotropic stratified elastic strip we consider the Poincaré–Steklov operator that maps normal stresses into normal displacements on part of the boundary. A new approach is proposed for constructing the transform of the kernel of the integral representation of this operator. A variational formulation of the boundary value problem for the transforms of displacements is obtained. A definition is given and the existence and uniqueness are proved for a generalized solution of the problem. An iteration method for solving variational equations is constructed, and conditions for its convergence are obtained based on the contraction mapping principle. The variational equations are approximated by the finite element method. As a result, at each step of the iteration method, it is required to solve two independent systems of linear algebraic equations, which are solved using the tridiagonal matrix algorithm. A heuristic algorithm is proposed for choosing the sequence of parameters of the iteration method that ensures its convergence. Verification of the developed computational algorithm is carried out, and recommendations on the use of adaptive finite element grids are given

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Computational model of the deformation of thin gradient coating lying on nondeformable foundation

Cited by 3 publications

References 1 publication

Computational model of the deformation of graded wedge with complicated structure

Computational model of the deformation of graded wedge with complicated structure

Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip

Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip

Contact Info

Product

Resources

About