ELASTICITY: FUNDAMENTAL THEORIES, ASSUMPTIONS, AND ENGINEERING APPLICATIONS

Abstract

 Elasticity theory constitutes a foundational pillar of solid mechanics, providing the mathematical framework for analyzing stress, strain, and displacement fields in deformable bodies under external loads. This review article systematically presents the fundamental principles of linear elasticity, tracing its historical development from early empirical observations to the rigorous continuum theory established in the 19th century. The core assumptions of the theory—continuity, homogeneity, isotropy, and small-strain behavior—are elucidated, highlighting their critical role in linearizing the governing equations. Furthermore, the paper extensively explores the theory's applications across civil, mechanical, and aerospace engineering, demonstrating its necessity for accurate stress analysis in structures, machine components, and geomechanical systems. A comparative analysis with elementary mechanics of materials underscores the superior accuracy of elasticity solutions in problems involving stress concentrations and complex geometries, affirming its indispensable role in modern engineering design and analysis.