On the variational derivation of boundary value problems in the dynamics of structural elements

Ricardo Oscar Grossi

Ricardo Oscar Grossi 1.Research Member of CONICET. - Facultad de Ingeniería - Universidad Nacional de Salta

Keywords: Variational calculus, rigorous formalism, functional, admissible directions

Abstract

The calculus of variations is an old branch of mathematical analysis concerned with the problem of extremizing functionals, a generalization of the problem of finding extremes of functions of several variables. This discipline has a long history of interaction with other fields of mathematics and physics, particularly with mechanics. Engineers and applied mathematicians have increasingly used the techniques of calculus of variations to solve a large number of problems. Nevertheless, in this discipline the «operator»

d has been assigned special properties and handled using heuristic procedures. A mechanical « d -method»

has been developed and extensively used, as can be observed in the current engineering literature.

The objective of this paper is to present a rigorous formalism for the determination of boundary value problems which describe the static or dynamic behavior of structural elements. A discussion about the shortcomings of the use of the vague mechanical d -method is presented.

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Author Biography

Ricardo Oscar Grossi, 1.Research Member of CONICET. - Facultad de Ingeniería - Universidad Nacional de Salta

Doctor en Ingeniería. Se desempeña como Profesor Regular Titular Plenario en la Facultad de Ingeniería de la Universidad Nacional de Salta. Especialista en Matemática Aplicada en Ingeniería. Investigador del CONICET. Categoría I en el Programa de Incentivos. Director del Programa de Matemática Aplicada de <Salta.