Modern interpretation of Saint-Venant’s principle and semi-inverse method

On Saint Venant's Principle

The so-called principle of statically equivalent loads, due to Saint Venant, has been referred to for the last fifty years in almost all texts on elasticity. The statements in different books vary only slightly. Let us quote A. E. H. Love's Treatise on the mathematical theory of elasticity (4th éd., p. 132) : "According to this principle the strains that are produced in a body by the applicatio...

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...

Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

Saint-Venant’s Principle: Rationalized and Rational

This is the abstract. The problem of statement of SaintVenant’s Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of SaintVenants 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 ...

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 SaintVenant’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 ...