# Numerical solution of axisymmetric shells under bilateral contact constraints

## Palavras-chave:

Axisymmetric Shells, Soil, finite difference method, Contact Constraints, Coordinate Systems## Resumo

In structural analysis, the possible geometrical configurations of the structure are fundamental for the

choice of the coordinate system to be used and, consequently, for the determination of solutions. The structural

problem description through an appropriate coordinate system allows us to visualize aspects that would not neces-

sarily be observed in another coordinate system. In this sense, the correct specification of the coordinate system

is important and necessary. The most general coordinate system, of which all others are particular cases, is the

general curvilinear coordinate system. Simultaneously, differential equations are widely used to model problems

in structural engineering. In the solution of a differential equation, the finite difference method plays an important

role, promoting the discretization of space by a mesh of discrete points, with the unknown functions and their

derivatives being replaced by approximations at the grid points through difference quotients. In particular, the

analysis of contact problems between a structure and a deformable foundation is an essential task in civil engineer-

ing, with crucial use in different support systems. Undoubtedly, thin axisymmetric shells are structural elements

widely used in structural engineering, especially when interacting with elastic or inelastic means. The main objec-

tive of this work is to develop a computational tool for the study and analysis of problems under bilateral contact

constraints, involving axisymmetric shells and elastic means, using the approximations derived from Sander’s the-

ory for slender shells. General equations applicable to any coordinate systems are developed. As an application

example, a slender cylindrical shell supported on soil (elastic foundation) is used.