Control the stability of small-scale non-uniform structures via neural networks applied to partial differential equations

This research uses a numerical technique and a neural network process to investigate the stability management of non-uniform cylindrical constructions with varying sizes. The non-uniform or truncated conical shapes vary in axial length. This complicated geometry results in partial differential equations in the mathematical explanation of stability performance. Furthermore, material distributions vary in the radial direction in functionally graded materials such as metal and ceramic. The governing equations are obtained from beam theory using the energy technique and non-classical size-dependent theory, respectively. These equations are then solved using both a numerical and neural network methodology. This research can potentially be utilized in nanotechnology to build and evaluate size-dependent non-uniform cylindrical structures. As a consequence, it will help to develop sophisticated nanoscale materials and architectures.