Discussion of paper by Suryanarayan Patnaik and Pasala Dayaratnam

✍ Scribed by John Robinson

• Publisher: John Wiley and Sons
• Year: 1971
• Tongue: English
• Weight: 112 KB
• Volume: 3
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620030312

✦ Synopsis

In the basic force method, the element force variables are given by {f} = [01u {a> = (Pol -P11 ([&IT [GI [B11)-' mIT [GI [BOD) {PI (1) (2) and in the displacement method by {f) = [.ID {a> = [TI [Kl-l {PI In these two equations, {a} is a vector of element areas and [aIu is a diagonal matrix of compatible stresses. The element areas are also contained in matrices [GI and [K]. These equations are therefore non-linear in the areas.

The authors have developed a 'new' force method formulation which gives linear equations in the areas. In this method the nodal equilibrium equations,

PI {f} = {PI

and the continuity equations,

(3) are combined into one system, that is,

The [B,] matrix contains the redundant systems which can be automatically generated from the [B] matrix by applying 'The Rank Technique' (see Reference 1, chapter 7). The authors have referenced this work but it should be pointed out that their 'new' force method formulation (equation 5) is not new but was also developed in Reference 1, chapter 8, and in two earlier paper^.^.^ However, their application and investigation of this formulation for optimized design is stimulating.

* Suryanarayan Patnaik and Pasala Dayaratnam, 'Behaviour and design of pin connected structures', Int. J.