By L.W. Ratner
With a purpose to decide on an optimum constitution between attainable comparable buildings, one must evaluate 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 by means of the tension dispensed in a constitution might be calculated. the recent non-linear idea of elasticity permits one to figure out the particular person restrict of elasticity/failure of a constitution utilizing an easy non-destructive approach to dimension 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 speculation. one of many vital actual implications of this good judgment is that it describes mathematically the common area of the potential sturdy actual kinfolk.
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Additional info for Non-Linear Theory of Elasticity and Optimal Design
The methods are distinct with respect to their means for reaching conclusions. (1) The deductive method in physics is based on inference with strict mathematical rules, such as from propositional function to derivative function. (2) The inductive method is used for connecting the theoretical concepts and particular laws with universal Part I. Principles and Methods ofNLTE 43 laws and definitions, and thus to justify these particulars. It is possible to make a reliable inference from general to particular.
The limit of elasticity of a structure that reveals itself in the destructive test is of a relative nature. It can be the limit of the material, or it can be the limit generated by the geometry of a structure. The actual limit of a structure is of comparatively lesser value. For practical purposes we need to know both limits. 1 Summary The linear theory of elasticity is an inadequate description of the phenomenon, for it cannot provide a description for the limit of elasticity and cannot predict the elastic behavior of a structure.
This property of the functions suggests the selection of a description of elastic relations with a non-linear function. (2) The physical function ought to be proved. For testing a function we need mathematical inference. Only a non-linear function can give a meaningful inference. (3) Verification of a description of the elastic relations can be achieved only if the basic function occupies the domain of a tangent function in the interval of rapid and slow changes. Then, the limit of elasticity can be found in the interval of rapid changes, and the behavior of any structure is defined in the full range of function of deformation.
Non-Linear Theory of Elasticity and Optimal Design by L.W. Ratner