The following is a summary of what I found here: www.civil.iitb.ac.in/~sghosh/CE317/history-stiffness-method.pdf
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".