Metody Zastosowania Rachunku Tensorowego w Technice - Malecki, Ignacy (Engineering Transactions, 1954)
The author's aim is to determine the degree of utility of the tensor calculus in various branches of technical sciences and to discuss the application of the classical methods of tensor analysis to technical problems.A short historical introduction indicates the ways in which the methods of tensor calculus have been applied to problems of mechanics and electrotechnics. Since the paper is destined for technicians, it has been considered desirable to explain some fundamental notions relating to tensors. The geometrical interpretation of tensor transformations in Cartesian cordinates was taken as the starting point, generalizing the notion to curvilinear co-ordinates and to Riemannian space.The basis of technical applications of tensor analysis is the physical interpretation of the tensor. The tensorial character of physical relations and the use of tensors for detecting invariable features of the investigated object are discussed. The methods of dimensional analysis are com- pared with those of tensor algebra. Next, the physical differences be- tween the notion of the tensor and that of the matrix are investigated.It was found that in technical problems there are three types of tensortransformations: (a) formal transformations, in which the type of the object is not changed,(b) formal transformations changing the type of the object,(c) transformations representing real changes in the object. Each type of transformation is characterised and examples given. The advantages of tensor calculus in technical problems resulting from its general and synthetic character and its suitability for calculations are analysed. The whole of the 'applications discussed is divided into two groups of problems, the first concerning continuous media, and the other systems of many degrees of freedom. The tensorial character of physical quantities relative to the elastic and the electromagnetic fields are discussed, as well as special types of tensors used for investigation of continuous media. It was found that the methods of tensor calculus, when suitably modified, can be applied in the following branches of technics, concerning continuous media:(a) classical theory of elasticity, especially the theory of anisotropic bodies,(b) theory of finite deformations,