A Caution on the Use of Generalized Differential Equations

Sometimes in numerical studies it is tempting to attempt to understand how a particular boundary value problem might be affected by the order of the differential equation representing the relationship between stress and strain. For example, the general equation. 

This equation, is in fact the same as the equation for the three-parameter solid and may be written as. 

Obviously, in this case the coefficients of the differential equation cannot be selected arbitrarily and must satisfy the above inequality in order to be physically meaningful. 

Refer to Flugge (1974) for additional discussion on this subject and other inequalities. 

Description of Parameters for Various Elementary Mechanical Models 

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