Teoría formal de elasticidad: método unificado para la solución de problemas de cuerpos deformables bajo la acción de cargas

Abstract

Fundamental concepts of the formal theory of elasticity as strength, deformation, Hooke law and Poisson relation are studied. It is shown that all problems of plane elasticity can be reduced to partial - differential - equation systems, where the essential equation is called biharmonic equation. The relevant principies are applied in the solution of a classic problem in material mechanics: a cantilever beam on the action of a probe charge in the free extreme. The solution are compared with the reported in the material books.

Keywords

• elasticidad
• diseño mecánico
• ley de Hooke
• relación de Poisson
• ecuaciones diferenciales
• ecuación biarmónica
• ecuación de compatibilidad
• viga en cantilever