# Jian-zhong Zhao's blog

## 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.

## 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.

## The Study by Mr. Wu etc Concerning Saint-Venant’s Principle is Insignificant

The paper titled "The Study by Mr.