2021/04/06 by Tamás Baranyai, Baranyai, Tamás
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Classical Physics (physics.class-ph) #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Structural Analysis and Optimization #Structural Analysis of Composite Materials
paper · pdf · doi:10.48550/arxiv.2104.02313
openalex publication_date 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the most influential early works in graphic statics is one of Maxwell,\nwhere he introduced the idea of a discontinuous stress function and the use of\na 3D projective polarity for a planar problem. A recent work gave an analytical\ndescription with the goal to provide explaining power, treating planar forces\nas linear functionals (moment functionals) forming a 3D vector space, so force\nand form diagrams of planar problems can be interpreted in a 3-dimensional way.\nThe linear combination of these moment functions can naturally be used as a\ndiscontinuous stress function since the Airy stress function is known to\ncorrespond to moments of planar forces. The main contribution of this work is\nto present a dimension independent way of treating forces as functions, that\nreturns the known stress-functions of planar and spatial graphic statics. This\nis done by relying on the multi-linear function definition of\nGrassmann-algebra.\n