2024/04/10 by Zoe Cooperband, Cooperband, Zoe, Allan McRobie +5
Engineering · #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2404.07184
openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using homological techniques we show that a pin-anchored frame that involves only moments and shears provides a conceptual bridge between the statics of moment frames and the kinematics of pin-jointed trusses. One immediate result is a long exact sequence whose alternating sum of dimensions gives a novel counting rule for self-stresses and mechanisms. This combines the Maxwell-Calladine count for pin-jointed trusses with the circuit rank (first Betti number) associated with self-stresses in moment frames. These relations apply to frames in 2, 3 or any dimensions. This work heralds a shift towards a deeper study of the relationships and dualities that exist between structural equilibria and kinematics.