COMMON ENERGY DECAY INDICES OF SAINT-VENANT’S PRINCIPLE

Several common energy indices of Saint-Venant’s Principle are put forward by means of the chain model and energy principles. The chain model is to set a series of sections in an elastic body, to cut the body into a series of substructures or links, which connect with the others one by one to form a link chain. Thusly, it is named as “chain model”. Some integral forms of energy indices are defined on the sections so that the mean “nearer” or “farther” can be expressed by the number of the sections. Saint-Venant’s Principle expects the energy indices are monotone decreasing with the number of the sections. Since the shape of the body and the substructures (links) and the sections are arbitrary, the energy indices must be deduced by means of energy principles. Then they are indeed deduced out. These energy indices are all defined on the sections of the body, all positive, all monotone decreasing with distance from the forced domain to the section (or with the number of the section), all approach to zero when the stress and strain on the section approaching to zero. It must be noticed that these energy indices are valid in case of arbitrary shape of elastic body. Saint-Venant’s Principle may get its mathematical form by these indices, if the decay of the energy indices is proved fast enough.