Saint-Venant’s Principle in elasticity has its over 100 year’s history. Boussinesq and Love announced general statements of Saint-Venant’s Principe. The early authors made important contribution to the principle. Zanaboni “proved” a theorem ，trying to concern Saint-Venant’s Principle, but in the present paper we will prove that Zanaboni’s theorem is false.
In this article the history of development of Saint-Venant’s Principle is reviewed, referring to the most important events concerning the principle as the historical clue, and the important works and results are evaluated; the view-points that Toupin Theorem can not be considered as a mathematical expression of Saint-Venant’s Principle and that the general Saint-Venant’s Principle does not stand, but modified Saint-Venant’s principles can be proved true are published and explained; the mathematical approaches for eslablishing modified Saint-Venant’s principles are summarized; the significan
Saint-Venant's Principle is important in the theory and application of elasticity and its proof or formulation is a major attraction for authors. Among others，Toupin's Theorem plays the most influential role in the history of development concerning Saint-Venant's Principle.
The paper titled "The Study by Mr. Wu etc Concerning Saint-Venant’s Principle is Insignificant" reviewed the series of four works of “proof of Saint-Venant’s Principle” published by Wu etc .The four articles proved neither the discrete Saint-Venant type decay of section-forces of the finite elements in the chain model of discretization of the cylinder nor the discrete Saint-Venant-type decay of section-displacements, posed in their papers. Furthermore, the discrete Saint-Venant type decay of section-forces is not provable.
Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper titled "Variational Theory: Variable-independence and Consistency" . The problem of variable-independence of variational principles raised by Professor Chien Wei-zang is discussed.