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

##### Abstrakt

[...] 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.