A stress function for 3D frames

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:117

Article

McRobie, F. A.¹  Williams, C. J. K.² 

[1] Univ Cambridge, Engn Dept, Trumpington St, Cambridge CB2 1PZ, England

[2] Univ Bath, Dept Architecture & Civil Engn, Bath BA2 7AY, Avon, England

关键词: Maxwell stress function;    Rankine reciprocal diagrams;    Graphic statics;    Grillage analysis;    Frames;    Clifford Algebra;   

DOI  :  10.1016/j.ijsolstr.2017.03.034

来源: Elsevier

【 摘 要 】

This paper generalises Rankine diagrams for 3D trusses to be applicable to 3D frames. Rankine diagrams are a graphical representation of a state of self-stress in a 3D truss, with the area of reciprocal polygons representing the axial force in their corresponding original bars. Rankine diagrams are a polyhedral version of the continuous Maxwell-Rankine stress function. In this paper we present a new stress function. It is piecewise linear and discontinuous and it allows the analysis of 3D frames, giving all six stress resultants of axial and shear forces and bending and torsional moments in any member. A succinct statement of the stress function is given in terms of 4D Clifford Algebra. (C) 2017 Elsevier Ltd. All rights reserved.

【 授权许可】

Free