miércoles, 11 de enero de 2012

S.E.C.S.: Short history of research in structural optimization

S.E.C.S. New Structural Efficiency Clasification System

Short history of research in structural optimization

For a long time humans have wondered about the possibility of doing things more efficiently.

  • In the field of thermodynamics, the First and Second Law and Carnot's Principle (1824), marked the starting point for energy efficiency.
  • In the structural field, the Rule of Galileo (1638), marks the origin of research in structural efficiency, complete with Maxwell's Theorem (1890) and Michell's Theorem (1904).

Galileo developed a size limit in terms of material (A = reach), while Mitchell studied the limits of optimization in several structural problems, through a geometrical methodology that allows the development of others.
There have been made many researchs since then, particularly since 1960's and especially in the last decade, probably because of the importance of energy and material savings in the historical moment of our consumer society.
These investigations have been developed, as we see, around three main ways:
  • Criticism Michell geometric system of new generation systems, research schemes applicable to other structural problems.
  • Combination of the Rule of Galileo with Maxwell and Michell Theorems.
  • Development of new parameters + methods in Structural Design.
Research around Michell Theorem
While Michell theorem is mathematically irreproachable, there are doubts about the geometric procedures developed for their structural schemes.
Michell offers different ways of describing space, ever provided by orthogonal but sometimes curved coordinates, even changing their curvature. This produces singularities at certain points, usually where concentrated loads are applied, which creates discussion about its feasibility and its treatment.
Moreover, Mitchell published within his theorem several examples of space descriptive schemes that solve specific structural problems:
Plane descriptions:
  • Cantilever with concentrated load;
  • Priority centered point load perpendicular to the axis (with / without space restrictions);
  • Three concurrent point charges;
Spatial descriptions:
  • Torsion due to concentrated moments applied on the same axis.

Since then (1904) other structural schemes have been raised (centered point load axis parallel to the axis, e.g.) but still missing distributed loads model definition, especially the uniform orthogonal spread load on an axis.

Also several methods have been applied different to purely geometric calculation Michell structures, such as genetic algorithms, simulated annealing, auto-organised chaos, or ground structure method.

Michell Theorem and self-weight.
In the structural schemes raised by Michell is not considered the weight of the structure. It's as if they were not dependent structures of a gravitational field so that the only existing forces were initially defined in the problem.
On practice is not very useful since the normal structures are subject to Earth's gravitational field or inertia forces with mass distribution law, so Michell schemes, according to the rule of Galileo has been called infinitesimalsize (L->0) or density = 0.

One of the keys to ‘materialize’ Michell's Theorem is the development of Michell scheme for spread loads, mainly the uniform spread load bending.


Ricardo Aroca and his four structural design variables
One of the new avenues opened in the design and structural optimization poses four independent factors that allow the design and comparative analysis of structures:
  • The Galilean size, meaning the relationship between structure size and material reach.
  •  Structural scheme, related to the Michell optimum structures.
  • Slenderness, or proportions of the structure.
  • Thickness, or cross section of each element of the structure.

Each of these parameters can be analyzed individually and is plenty useful from the design phase of the structure.

Our first objective.
Once the study of all existing documentation, we would like to make a personal approach to the Michell scheme for spread load, through a study of properties derived from the main theorem. Today we have several ideas about this, but they have to be compared with existing researchs.

Next week, More!

Quisco Mena

GALILEO, (1638) Discorsi e Dimostrazioni Matematiche.
SADI CARNOT, N.L. (1824) Réflexions sur la puissance motrice du feu et sur les machines propres à déveloper cette puissance. Ed. Bachelier, París.
MAXWELL, J.C. (1890) Scientific Papers. Tomo II. Camb. Univ. Press.
MICHELL, A.G.M. (1904) ‘‘The Limits of Economy of Material in Frame-structures’’, Philosophical Magazine, S.6, v. 8, n47, pp. 589–597.
CROSS, H. (1936) The relation of analysis to structural design. Trans Am. Soc. Civil Eng. 62:1363-1408
HEMP, W. (1958) Theory of structural design. Report 214, N.A.T.O. Advisory for Aeronautical R&D, Palais de Chaillot, Paris.
DE MIGUEL, J.L. (1974) Trabajo estructural: un nuevo escalar de las estructuras. Tesis doctoral, Escuela Técnica Superior de Arquitectura de la Universidad Politécnica de Madrid.
Jaenicke, I (1984) Estructuras y Modulación. Tesis doctoral, Escuela Técnica Superior de Arquitectura de la Universidad Politécnica de Madrid.
VÁZQUEZ, M. (1995) Un nuevo algoritmo para la optimación de estructuras: el recocido simulado. Informes de la Construcción, v. 46, no 436, pp. 49-69.
VÁZQUEZ, M. y otros (2011) Notas sobre el Teorema de Michell. Universidad Politécnica de Madrid, Departamento de Estructuras de Edificación.
CERVERA, J.; VÁZQUEZ, M. (2011) Galileo, Maxwell, Michell, Aroca: Midiendo el rendimiento estructural. Universidad Politécnica de Madrid, Departamento de Estructuras de Edificación.

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