Advanced mechanical engineering : (with elements of numerical engineering analysis)

Abstract

[...] The book is divided into three parts: the first one contains the foundations of mechanics of solids (particularly of the theory of elasticity) including the stress and strain analysis (concept of the stress and strain tensor in the rectangular co-ordinate system, as well as constitutive stress-strain relations for the general case of elastic anisotropic materials. The first part provides also a reader with a knowledge of yield criteria of not only ductile , isotropic material but also of modern orthotropic materials. The first part concludes with the energy methods in mechanics of materials. Although this part is devoted to advanced topics of mechanics of materials it contains as well some very basic problems (like the concept of equivalent stress for combined load) since they are not included into the syllabus of prerequisite subjects of Basic Mechanical Engineering I and II delivered to the students of Mechanical Engineering and Applied Computer Science (IFE), to whom the book is devoted mainly. The second part contains the theoretical foundations of the Finite Element Method, preceded with the description of the general concept of FEM and the short review of matrix algebra. Afterwards, the basic types of finite elements are discussed and their stiffness matrices are derived. The last part is devoted to selected advanced problems of mechanics of materials, including bending of thin plates, axi-symmetrical problems of the theory of elasticity and very basic introduction to the analyses of buckling of structural members. Each problem is discussed on the basis of analytical methods and simultaneously examples of numerical FE solutions are presented. In the section dealing with bending of rectangular plates the finite difference method is presented as an example of another, alternative numerical method that can be used in mechanics of materials. The third part concludes with the short chapter introducing a reader the problems of fatigue of structures. Some of the discussed topics are illustrated using exemplary problems with detailed solutions. However, the authors assume that a reader can find more of such problems in special text-books containing collections of problems of mechanics of materials to be solved.