Introduction to Mechanics and Structures

TL;DR

This paper offers a comprehensive overview of continuum mechanics, covering elastic and plastic behaviour, and discusses the design and analysis of pressure vessels and shells under various loads.

Contribution

It integrates fundamental concepts with practical design principles for pressure vessels and shells, emphasizing their mechanical behaviour and stability.

Findings

Elastic and plastic behaviours are distinguished by atomic and macroscopic perspectives.

Shell theory simplifies stress analysis for thin, axisymmetric structures.

Design provisions for pressure vessels include buckling and secondary stress considerations.

Abstract

This work provides a comprehensive overview of the fundamental concepts in continuum mechanics, focusing on the behaviour of materials under mechanical loads. It discusses the distinction between elastic and plastic, highlighting their atomic origins and macroscopic implications. Elastic behaviour is examined via Hooke's law and constitutive matrices, while plasticity is treated through yield surfaces, flow rules, and hardening laws, including isotropic and kinematic hardening. In addition, the theoretical foundations and design principles of pressure vessels and thin axisymmetric shells, focusing on their mechanical behaviour under internal or external pressure, is discussed. The analysis is based on shell theory, assuming thin walls and axisymmetric geometry, which simplifies the stress distribution into membrane stresses. The work also addresses buckling phenomena under external pressure, secondary stresses at geometric discontinuities, and design provisions from the EN 13445 standard.