Part I. - Principles and Methods of NLTE

Abstract

This chapter discusses principles and methods of Non-Linear Theory of Elasticity (NLTE). The principles underlying the non-linear theory arise from a body of existing scientific knowledge. Inferences from this knowledge serve as the foundation for new knowledge and new principles. NLTE is constructed in accordance with certain logical principles that facilitate the solution of practical problems. NLTE also provides a complete adequate description. The complete description has a mathematical-logical system consisting of a basic equation and a derivative equation. It can be used to solve a majority of practical problems with a degree of mathematical certainty. NLTE uses two methods of logical reasoning leading to reliable conclusions—namely, inductive method and deductive method. They are used whenever there are appropriate conditions that these methods can resolve. The methods are distinct with respect to their means for reaching conclusions. Deductive method in physics is based on inference with strict mathematical rules, such as from propositional function to derivative function. Inductive method is used for connecting the theoretical concepts and particular laws with universal laws and definitions, and thus to justify these particulars. It is possible to make a reliable inference from general to particular.