Limitations
Each method has noteworthy limitations. The method of mechanics of materials is limited to very simple structural elements under relatively simple loading conditions. The structural elements and loading conditions allowed, however, are sufficient to solve many useful engineering problems. The theory of elasticity allows the solution of structural elements of general geometry under general loading conditions, in principle. Analytical solution, however, is limited to relatively simple cases. The solution of elasticity problems also requires the solution of a system of partial differential equations, which is considerably more mathematically demanding than the solution of mechanics of materials problems, which require at most the solution of an ordinary differential equation. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other structural theories (such as the other two discussed here) for equations to solve. It does, however, make it generally possible to solve these equations, even with highly complex geometry and loading conditions, with the restriction that there is always some numerical error. Effective and reliable use of this method requires a solid understanding of its limitations.
Read more about this topic: Structural Analysis
Famous quotes containing the word limitations:
“That all may be so, but when I begin to exercise that power I am not conscious of the power, but only of the limitations imposed on me.”
—William Howard Taft (1857–1930)
“Much of what contrives to create critical moments in parenting stems from a fundamental misunderstanding as to what the child is capable of at any given age. If a parent misjudges a child’s limitations as well as his own abilities, the potential exists for unreasonable expectations, frustration, disappointment and an unrealistic belief that what the child really needs is to be punished.”
—Lawrence Balter (20th century)
“No man could bring himself to reveal his true character, and, above all, his true limitations as a citizen and a Christian, his true meannesses, his true imbecilities, to his friends, or even to his wife. Honest autobiography is therefore a contradiction in terms: the moment a man considers himself, even in petto, he tries to gild and fresco himself.”
—H.L. (Henry Lewis)