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.

Citing this course

In many slides, you can find the original references, which should be cited in case you want to reproduce some of the equations or methods. If you are using the images for plate, cylindrical, conical or shell domains, or any of the examples, please cite as shown below:

G. P. Castro, S. (2025, July 8). Stability of Structures: Kinematics, Equivalent Single-Layer Theories, and Energy-based Semi-Analytical Methods. Zenodo. https://doi.org/10.5281/zenodo.18957062