Saint-Venant’s Principle: Rationalized and Rational

This is the abstract. The problem of statement of SaintVenant’s Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of SaintVenants 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 boundaryvalue 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.