Conference publications

Abstracts

XXI conference

Shape memory for rigid plasic solids with internal degrees of freedom

Najshtut Yu.S.

Samara State Architectural and Building Academy 194 Molodogvardeyskaya St., Samara, 443001, Russia Phone: (846) 336-87-78, E-mail: neustadt99@mail.ru

Rigid plastic solids can be identified with a differential manifold in three-dimensional space [1]

, , k  6 (1)

The differential forms of coordinate variables depend on the functions , defined by the properties of the solids. The variables are internal degrees of freedom that need to meet six equations of structure resulting from equalities that provide for existence of the system solutions.

Let the volume load be applied to the internal points of the manifolds. The generalized forces are linked to the internal degrees of freedom in such a way that the principle of virtual powers is satisfied

= 0

In the specified formula the letter D designates the domain of coordinate variation , while dV is an element of volume.

There are generalized forces in the rigid plastic shape memory solid for the set load so that the following inequalities are satisfied

(2)

The coefficients are such that the quadratic form in the middle of the inequality is elliptical and .

Ultimate load theorems [2] are true “both ways”. The shape memory provides for the inequality on the left: there is a number n

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