Comments and remarks on symmetry and asymmetry problems in the design of plated/shell composite structures–Laminates, nanostructures and functionally graded materials

Symmetry requires that the material configuration, geometry, restraints, loads, and material properties are symmetrical. It is generally not recommended to use symmetry for buckling and frequency studies. Symmetry can be used to model a portion of a construction instead of the entire model. Results in unmodeled fragments are derived from modeled fragments. In justified situations, the use of symmetry can reduce the size of the problem and increase the accuracy of the results. The analysis of symmetry of composite plated/shell 2D structures is connected with the description of deformations, failure modes and the scale of considerations (nano-, micro-, meso‑ and macro/global scale). For composites made with the use of filament winding method the cyclic symmetry is usually adopted.

Due to the anisotropy of composite materials, the assumption of symmetry is related to the accuracy of the description of deformation and damage of the structure in relation to the results obtained experimentally. Typically, the analysis of composite structures is associated with the introduction of high values ​​of safety factors. It is necessary to determine how and when it is necessary and possible to introduce material property dispersion values ​​even when using a linear approach in geometric or physical approach. The description options are related to the use of statistical analysis, fuzzy set methods or the introduction of anti-optimization.