By L.W. Ratner
That allows you to opt for an optimum constitution between attainable comparable buildings, one must examine the elastic habit of the constructions. a brand new criterion that describes elastic habit is the speed of switch of deformation. utilizing this criterion, the secure dimensions of a constitution which are required via the strain dispensed in a constitution could be calculated. the recent non-linear thought of elasticity permits one to figure out the particular person restrict of elasticity/failure of a constitution utilizing an easy non-destructive approach to size of deformation at the version of a constitution whereas shortly it may be performed simply with a harmful try for every constitution. For development and explaining the idea, a brand new logical constitution was once brought because the foundation of the idea. one of many very important actual implications of this common sense is that it describes mathematically the common area of the potential strong actual family members.
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Extra resources for Non-Linear Theory of Elasticity and Optimal Design
Principles and Methods ofNLTE 37 because comparison of magnitudes for a physical concept is important at its own level. The other condition for the selection of a limit is that the individual limit should not exceed the limit of the material. Comparison of these two values will accomplish the selection. 7. Describing the theoretical domain of the function. The conclusion as to existence of a theoretical limit is made based on the character of the mathematical relations in the propositional function.
The notion of stiffness does exist in the Hterature. But there is no concept of geometrical stiffness as the single concept variable in the equation of deformation. This constitutes a principal difference. The derivative equation de/dR = -N/ER^ describes the rate of change of deformation due to the change of geometrical stiffness. Presented graphically the function e vs. R (Illustration 3) shows changes in the interval of slow changes of its derivative and in the interval of rapid changes. The limit of this physical function can be expected in the interval of rapid changes.
It is impossible to make a logical inference from particular to the general. The relation between general and particular is asymmetric. In NLTE, the inductive method is used for conceiving the notion 'elastic force' and for devising the equations connecting elastic force and deformation for infinitesimal element. Also, the inductive method is used for placing the fimction of deformation in the domain of the tangent fimction. The inductive conclusion then is that the derivative function should exist in the interval of rapid changes.