Saint-Venant's Principle: Rationalized and Rational

The problem of statement of Saint-Venant's Principle is concerned.  Statement of Boussinesq or Love  is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of Saint-Venant’s Principle of elasticity  is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant's Principle is suggested to fit and guide  applications of the principle  to  fields of continuum physics and cover the analogical case as well as the non-analogical case discovered and discussed in this paper . `` Constraint-free " problems  are suggested and `` Constraint-free "  Rational Saint-Venant's Principle or Rational Saint-Venant's Principle with Relaxed Boundary Condition is developed to generalize the principle and  promote   its applications   to  fields of continuum  physics . Applications of Analogical Rational Saint-Venant's Principle and `` Constraint-free " Rational Saint-Venant's Principle are exemplified, emphasizing `` properness " of the boundary-value problems.  Three kinds of properly posed boundary-value problems, i.e., the boundary-value problem with the undetermined boundary function, the boundary-value problem with the implicit  boundary condition and the boundary-value problem with the explicit  boundary condition, are suggested for both `` constrained " and `` constraint-free " problems.