Compatibility conditions for discrete elastic structures
In: Rendiconti del Seminario Matematico Università e Politecnico Torino, Jg. 58 (2000) ; Nr. 1, S. 37-48
Zeitschriftenaufsatz / Fach: Maschinenbau
The theory of plane, elastic trusses is reconsidered from the viewpoint of the continuum theory of elastic media. A main difference between continuum and discrete theories is the following: In the continuous case all quantities are declared throughout the whole body, whereas in the discrete case each quantity has its own "carrier". In a truss, for instance, displacements and applied forces are declared in the nodes while strain and stress live in the members of the truss. The paper deals with the proper formulation of compatibility conditions for a truss. They are derived along the same lines as St.-Venant's compatibility conditions of plane elasticity, i.e., by stipulating that Cesàro's integrals are path independent. Compatibility conditions can be formulated at each inner node of a truss, and they relate the strains of all members which constitute the rosette surrounding the inner node.