Abstract A system is robust if it can withstand arbitrary damage. There are many practical ways to design in robustness but there is yet no accepted theory of robustness. One insight into the lack of robustness is gained if it were possible to identify how a system is vulnerable. This insight is in the form of ‘a theory of structural vulnerability’ developed at the University of Bristol for 2-dimensional structures [Lu Z, Yu Y, Woodman NJ, Blockley DI. A theory of structural vulnerability. The structural engineer 1999:77(18):17–24]. It is a theory of form and connectivity the purpose of which is to identify weak links within a structure. In this paper further development of the theory and its application to 3-dimensional structures is presented. Algorithms for implementing the theory are described and illustrated through three examples.
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