Vulnerability Analysis Of Frame Structures Based On Flow Potential

Structural vulnerability has been a main focus in structural communityfor decades since the collapse of Ronan Point Tower in1968. Its quantitativeevaluation, however, is still a problem today. In this paper a new concept offlow potential in structures is brought forward based on which a procedure toevaluate structural vulnerability is presented. The main contents include thefollowing aspects:Firstly, energy flow field can be established by energy flow based on theresults of structural analysis, and its differential relations with flow potentialin member and2D cases is given by field thory. By discussing energy flowand flow potential in typial rectangular element, cantilever and simplysupported beam, the result of comparison shows the consistency of membersolution, elasticity solution and numerical solution.Secondly, the expression of energy flow and flow potential in planeframe member are derived in detail, and transfer rule of member end flowpotential in node of frame structure is defined. In order to find flow potentialdistribution in frame structure, an optimization model is established whichcan be solved by linear optimization analysis. And an index of structuralvulnerability is constructed with no mesh dependency by considering bothflow potential and strain energy of each member in structure. Severalexample structures are given to demonstrate the calculation of flow potentialin structures and the feasibility of the presented index of structuralvulnerability. Finally, when the presented index of structural vulnerability is applied inconceptual design, it tries to choose a reasonable structure layout scheme byavoiding those structures which easily make energy flow disturbances andsudden changes in the flow potential distribution.