By K. Sundermeyer
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At the same time the basic equation can be verified experimentally. The derivative equation also can be tested experimentally in the interval of rapid changes and thus supported with obvious physical changes. Note that in some other cases we need to change both the independent variable and other variables in the hypothetical basic equation to satisfy the condition that the derivative correspond at any point to the tangent function value. In this way the self-proved Non-Linear Theory of Elasticity has been constructed.
2. Making a general description of the law. The effect (in this case, the deformation of a body) depends on the external force that is the cause. More correctly, it depends on the work performed by the external force. The logical relation between cause and effect exists, but it is a non-functional relation. We may call such relation an inductive relation that is validated by the inductive method of logic. We can say that the relation of the elastic phenomenon to the outside force obeys a general law that is adopted by science.
The effect of geometry of a structure as a physical whole can be presented with the new complex variable defined as geometrical stiffness, in this case R=A/L. This variable can place the equation of deformation in the domain of the tangent ftinction, in our example, e = N/ER and de/dR = -N/ER^. In order to have this derivative in the interval of rapid changes, the geometrical stiffness R is selected in the interval I