Stability of Structures: Kinematics, Equivalent Single-Layer Theories, and Energy-based Semi-Analytical Methods

Abstract

This part of the course details the fundamental principles of structural stability, focusing on kinematic relations and equivalent single-layer (ESL) theories for composite plates and shells. It derives three-dimensional strain-displacement equations for planar, cylindrical, conical, and spherical geometries. The formulations are systematically reduced to two-dimensional ESL models, specifically the Classical Laminated Plate Theory (CLPT), First-order Shear Deformation Theory (FSDT), and Third-order Shear Deformation Theory (TSDT). The limitations of ESL theories regarding interlaminar stress continuity are analysed, introducing Zig-Zag and Layerwise theories as advanced alternatives. Furthermore, the material covers energy-based formulation frameworks, deriving the principle of minimum potential energy, the semi-analytical Ritz method utilizing Legendre polynomials, and the neutral equilibrium criterion for extracting geometric stiffness matrices and linear buckling equations.