The Transfer-Matrix Method (TMM) is an original and relatively simple mathematical approach for the calculus of thin-walled cylindrical tubes presented in this work. Calculation with TMM is much less used than calculation with the Finite Elements Method (FEM), even though it is much easier to apply in different fields. That is why it was considered imperative to present this original study. The calculus is based on Dirac’s and Heaviside’s functions and operators and on matrix calculation. The state vectors, the transfer-matrix, and the vector corresponding to the external efforts were defined, which were then used in the calculations. A matrix relation can be written, which gives the state vector of the last section depending on the state vector of the first section, a relation in which the conditions of the two end supports can be set. As an application, a heat exchanger was studied, with a large cylinder subjected to a uniformly distributed internal load, and from the inner cylinder bundle, a cylinder subjected to both uniform internal and external loads was considered. For the second cylinder, two possibilities of action for the external forces were considered, a successive action and a simultaneous action, achieving the same results in both situations. The TMM is intended to be used for iterative calculus in optimization problems where rapid successive results are required. In the future, we want to expand this method to other applications, and we want to develop related programs. This is an original theoretical study and is a complement to the research in the field on thin-walled cylinder tubes and their applications in heat exchangers.

This work presents the Transfer-Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements, using an iterative calculation for future applications in vehicle industry. Plate calculus is important in construction, in medicine, in orthodontics and in many other fields too. This work is original and new. The plate is discretized along its length in unitary beams, which have the width of the rectangular plate. The unitary beam can also be discretized into parts. As applications, they are studied long rectangular plates, embedded on the two long borders and charged with a vertical uniform load that acts on a line parallel to the long borders. It is associated with each side a state vector. For each of the four cases studied, a matrix relationship was written for some side, based on a transfer matrix, the state vector corresponding to origin side and the vector due to the action of external forces acting to the considered side. After, it is possible to calculate all the state vectors for all sides of the unity beam. Now, the efforts, deformations and stress can be calculated in any section of the beam, respectively for the long rectangular plate. This calculus will serve as calculus of resistance for different pieces of components of vehicles.

This article presents the Transfer Matrix Method as a mathematical approach for the calculus of different structures that can be discretized into elements using an iterative calculus for future applications in the vehicle industry. Plate calculus is important in construction, medicine, orthodontics, and many other fields. This work is original due to the mathematical apparatus used in the calculus of long rectangular plates embedded in both long borders and required by a uniformly distributed force on a line parallel to the long borders. The plate is discretized along its length in unitary beams, which have the width of the rectangular plate. The unitary beam can also be discretized into parts. As applications, the long rectangular plates embedded on the two long borders and charged with a vertical uniform load that acts on a line parallel to the long borders are studied. A state vector is associated with each side. For each of the four cases studied, a matrix relationship was written for each side, based on a transfer matrix, the state vector corresponding to the origin side, and the vector due to the action of external forces acting on the considered side. After, it is possible to calculate all the state vectors for all sides of the unity beam. Now, the efforts, deformations, and stress can be calculated in any section of the beam, respectively, for the long rectangular plate. This calculus will serve as a calculus of resistance for different pieces of the components of vehicles.