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Inconsistency of Biography of Tsien Hsue-Shen

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.

Saint-Venant's Principle: Experimental and Analytical

Mathematical provability , then classication, 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.

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 .

Zanaboni Theory and Saint-Venant's Principle: Updated

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.

Zanaboni Theorem and Saint-Venant's Principle

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.

Saint-Venant's Principe of the Problem of the Cylinder: Modified

The Statement of Modied Saint-Venant's Principle is suggested. The
axisymmetrical deformation of the infinite circular cylinder loaded by an
equilibrium system of forces on its near end is discussed and its formulation of Modied 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.               T

Saint-Venant's Principe of the " Cavity in Cylinder " Problem

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.

Special Saint-Venant's Principe of the “ Hole in Plate” Problem


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.


Modified Saint-Venant's Principe of the Problem of Curved Bars


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

Zanaboni Theorem Is Invalid:Re-review

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.

Saint-Venant’s Principle and Its Proof : History and Review

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

Zanaboni Theorem Is Not True

Zanaboni  Theorem  Is  Not  True

Toupin-type Decay and Saint-Venant's Principle

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.

Variational Theory: Variable-independence and Consistency

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.

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