User login

Navigation

You are here

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. Now we review the history and the previous works, distinguishing Saint-Venant type decay from Toupin-type decay and arguing that Toupin's Theorem is not a formulation of Saint-Venant's Principle;Existence of solution of Saint-Venent type exponential decay to a boundary-value problem is not a necessary condition of existence of Toupin-type decay rate of the problem; Saint-Venant's Principle stated by Love can be disprovedmathematically  from Toupin's Theorem and  so Toupin's Theorem is mathematically inconsistent with Saint-Venant's Principle;  If  the  technical  terms are acceptable, special Saint-Venant's Principle or modified Saint-Venant's Principle or Saint-Venant's Principle with subsidiary conditions can be proved true or formulated, though Saint-Venant's
Principle in its general form stated by Boussinesq and Love is not true. This actwill encourage further research on Saint-Venant's Principle. 
KEY WORDS: Saint-Venant's Principle, Saint-Venant type decay, Toupin's theorems, Toupin-type decay,  proof,  disproof, formulationAMS Subject Classifications: 74G50

AttachmentSize
Microsoft Office document icon SV28A.doc1.3 MB
Subscribe to Comments for "Toupin-type Decay and Saint-Venant's Principle"

More comments

Syndicate

Subscribe to Syndicate