martes, 31 de enero de 2012

A brief summary on the stiffness method for structural engineering

Well, another year has gone by, and it has been a while since the last post. Life in Barcelona is being quite busy, so I am not dealing very well with my updates...This doesn't mean I am not researching, but apparently the topics I am getting to are deeper and deeper, so conclusions are getting harder to write...

The following is a summary of what I found here:

It is authored by the famous Zienkiewicz, so it must be a warranty of rigor. Out of it I have written my own summary, on pure chronological order, that goes as follows:

  • 1862: Glebsch, Alfred wrote an algorithm for 3D trusses where no moments were involved. The models one would get out of it is as putting lots of springs connected by pins.
  • 1883: Saint Venant, Andre wrote an article with comments on Glebsch's methodology.
  • 1880: Manderla, Heinrich proposed an iterative method for the solution of the set of equations involved in pin-jointed trusses
  • 1892: Mohr, Otto introduced the notion of "secondary stresses". He was referring to the moments. They were called secondary then as in steel and iron trusses the main ones were axial.
  • 1910: Richardson provided the study of the stresses in a dam by means onf the Airy stress function.
  • 1914: Bendixsen, Axel published a method similar to the slope deflection for structures with internal hyperstaticity.
  • 1915: Wilson&Money proposed the slope deflection method, apparently unaware of Bendixsen's.
  • 1922: Ĉaliŝev gave an iterative solution of successive approximations for frames without side-sway.
  • 1930: Cross, Hardy published his famous method for redistributing unbalanced moments according to the internal stiffnesses of the composing bars. This provided the engineer with the necessary joint rotations.
  • 1932: Grinter wrote a method for multi-story frames with side-sway called "method of successive corrections"
  • 1935: Southwell tackled the problem of the constraints in a similar manner giving his famous method of "systematic relaxation of constraints", commonly known as dynamic relaxation.
  • 1941: Courant, Richard explained his "variational methods for the solution of problems of equilibrium and vibrations". As he was a mathematician, the practical application of his work results still of some difficulty.
  • 1943: McHenry in U.S. and Hrenikoff in Canada proposed a lattice analogy for the solution of stress problems so that continuum could be represented as a set of beams.
  • 1944: Kron, Gabriel provided a complete algorithm in matrix form for 3D frames. In the 1930s it became fashionable to show the whole process of solving the linear equations in this systematic manner.
  • 1954: Argyris wrote his "Energy theorems ans structural analysis", a comprehensive presentation of both the force and the displacement method for complicated airplane structures.
  • 1967: Zienkiewicz presented his summary of the "Finite Element Method in structural Mechanics".