Tsien Hsue-Shen, an expert of mechanics, the “King of Rocketry” of China, lived in US for twenty years long. Iris Chang (by a book in 1995) and Judith R. Goodstein (by a report of a conversation with Lee Alvin DuBridge in 2003) gave accounts of Tsien’s biography.
Mathematical provability , then classi cation, of Saint-Venant's Principle are discussed. Beginning with the simplest case of Saint-Venant's Principle, four problems of elasticity are discussed mathematically. It is concluded that there exist two categories of elastic problems concerning Saint-Venant's Principle: Experimental Problems, whose Saint-Venant's Principle is established in virtue of supporting experiment, and Analytical Problems, whose Saint-Venant's decay is proved or disproved mathematically, based on fundamental equations of linear elasticity.
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 .
Zanaboni Theory is mathematically analyzed in this paper. The conclusion is that Zanaboni Theorem is invalid and not a proof of Saint-Venant's Principle; Discrete Zanaboni Theorem and Zanaboni's energy decay are inconsistent with Saint-Venant's decay; the inconsistency, discussed here, between Zanaboni Theory and Saint-Venant's Principle provides more proofs that Saint-Venant's Principle is not generally true.
Violating the law of energy conservation, Zanaboni Theorem is invalid
and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed.
Energy Theorem for Zanaboni Problem is suggested and proved.
Equations and conditions are established in this paper for Zanaboni Problem,
which are consistent with , equivalent or identical to each other. Zanaboni
Theorem is, for its invalidity , not a mathematical formulation or
proof of Saint-Venant's Principle.
The Statement of Modi ed Saint-Venant's Principle is suggested. The
axisymmetrical deformation of the infi nite circular cylinder loaded by an
equilibrium system of forces on its near end is discussed and its formulation of Modi ed Saint-Venant's Principle is established. It is evident that
fi nding solutions of boundary-value problems is a precise and pertinent
approach to establish Saint-Venant type decay of elastic problems. T
The problem of a cylinder with a small spherical cavity loaded by an
equilibrium system of forces is suggested and discussed and its formulation of Saint-Venant's Principle is established. It is evident that finding
solutions of boundary-value problems is a precise and pertinent approach
to establish Saint-Venant type decay of elastic problems.
The problem of the
infinite plate with a central hole loaded by an equilibrium system of forces is
generalized and its formulation of Special Saint-Venant's Principle is
established. It is essential to develop mathematical theories of Special
Saint-Venant's Principle one by one if Elasticity has to be constructed to be
rational, logical, rigorous and secure mechanics.
The problem of the
infinite axisymmetrical circular cylinder loaded by an equilibrium system of
forces on its near end is discussed and its formulation of Special
Saint-Venant's Principle is established. It is essential to develop
mathematical theories of Special Saint-Venant's Principle one by one if
Elasticity has to be constructed to be rational, logical，rigorous and secure mechanics.
The proof of
Saint-Venant's Principle for curved bars is discussed and the formulation of
Modified Saint-Venant's Principle of the problem is established. The study
shows that Saint-Venant's decay of stresses is valid only for the curved bars
which are “effectively infinite”. It is essential and significant to develop