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I have a question about the EQUATION constraint to apply periodical boundary conditions via Script in Abaqus. The detailes is as follows

(1) Create the node sets firstly in the PART Module;

(2) Using script to create node sets containing only one node;

(3) Using the following script to establish the EQUATION constraint

mdb.models['Job-1'].Equation(name=’Constraint-1′, terms=((1.0,

‘PART-1-1.Node-1′, 1), (1.0, ‘PART-1-1.Node-2′, 1), (-1.0, ‘RP1′, 1)))

Violating the law of energy conservation, Zanaboni Theorem is invalid

and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed.

Energy Theorem for Zanaboni Problem is suggested and proved.

Equations and conditions are established in this paper for Zanaboni Problem,

which are consistent with , equivalent or identical to each other. Zanaboni

Theorem is, for its invalidity , not a mathematical formulation or

proof of Saint-Venant's Principle.

1, Presciptive VS Performance base

node/13485#comment-21159

2, Wave and tidal energy

node/13346#comment-20356

...

The Statement of Modied Saint-Venant's Principle is suggested. The

axisymmetrical deformation of the infinite circular cylinder loaded by an

equilibrium system of forces on its near end is discussed and its formulation of Modied Saint-Venant's Principle is established. It is evident that

finding solutions of boundary-value problems is a precise and pertinent

approach to establish Saint-Venant type decay of elastic problems.               T