Undoubtedly the most important topics in this research are structural analysis, finite element methods and the basic review on Abaqus software due to the fact that this software is used as a research tool for examining the behaviour of structures. Therefore, it is essential to know about these topics and the relationships between them. An effort is made to review the important structural analysis and finite element method approaches, reports and fundamentals guiding the structural analysis of the CNC machine research in a coherent way, along with a few relevant examples from literature.
2.2 STRUCTURAL ANALYSIS
According to Mike N.Thomas, “structural analysis can be described as a physical law and mathematical calculation required for the prediction of the behaviour of any structure” (Thomas M. N., 2005). Indeed, structural analysis must put forth some other aspects that cannot be treated in a precise manner such as sound working patterns, conservation design and the concept of safety. The term structural (or structure) implies not only civil engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools (ANSYS PRODUCT). Although structural analysis uses the analytical methods for predicting the structure behaviour, regardless of those methods the formulation is based on the same fundamental relations such as equilibrium, constitutive and compatibility.
Galileo Galilei, Robert Hooke and Issac Newton were pioneers of modern structural analysis in the 17th century with their scientific works. The beginning of structural analysis was in 1638 when Galileo published “Dialogues Relating to Two New Sciences”, outlining the sciences of the strength of materials and the motion of objects (Stanford Encyclopedia of philosophy, 2005). According to Chapman Allan (2005) about 40 years later, the first statement of Hooke’s law which was produced by Robert Hooke, provides a scientific understanding of the elasticity of materials and their behaviour under load. Understanding of the fundamental laws governing structures was described by Sir Isaac Newton in 1687.
However, the physical laws which were described by these three scientists were necessary for analysing, were not sufficient for solving the problems of structural analysis. Solving these problems and equations need to have extra knowledge of mathematics.
In the 17th century, Gottfried Leibniz developed the fundamental theorem of calculus. But the further development in mathematics was in the 18th century when Leonhard Euler explained much of the mathematics and also his methods, enabling designers and engineers to model and analyse their engineering structures. The fundamental theory which is the base of most structural design is Euler-Bernoulli beam equation which was mentioned by Euler and Daniel Bernoulli in 1750....