Applications of the Calculus by the Transfer Matrix Method for Long Rectangular Plates Under Uniform Vertical Loads

The aim of this work is to present an original, relatively simple, and elegant approach to the analysis of long rectangular plates subjected to uniformly distributed vertical loads acting on various surfaces. Plate analysis is important in many fields, especially where components are either rectangular plates or can be approximated as such. The Transfer Matrix Method is increasingly used in research, as evidenced by the references cited. The advantages of this method lie in the simplicity of its algorithm, the ease of implementation in programming, and its straightforward integration into optimization software. The approach consists of discretizing the rectangular plate by sectioning it with planes parallel to the short sides—i.e., perpendicular to the two long edges. This results in a set of beams, each with a length equal to the width of the plate, a height equal to the plate’s thickness, and a unit width. Each unit beam has support at its ends that replicate the edge conditions of the plate along its long sides. In the study presented, the rectangular plate is embedded along its two long edges, meaning the unit beam is considered embedded at both ends. The Transfer Matrix Method is particularly valuable because it lends itself well to iterative calculations, making it easy to develop software capable of analyzing long rectangular plates quickly. This makes it especially useful for shape optimization applications, which we intend and hope to pursue in future studies.