Two- and three-dimensional analyses for truss structures are reviewed
with a particular focus on progressive failure. The review begins with
a general discussion of truss structures followed by a presentation o
f the geometric nonlinear formulations for these structures. Member fa
ilure models and their implementation into truss analyses are discusse
d next; first elastic postbuckling member failure then member failure
models including inelastic postbuckling response. This is followed by
an overall discussion of quasi-static constitutive models, both analyt
ical and empirical. A review of several papers on the dynamic analysis
of truss structures for defining dynamic stability and dynamic progre
ssive failure is presented next, concluding with a brief discussion on
hysteretic material behavior. A very brief discussion of some stochas
tic or probabilistic investigations into truss response and behavior i
s also included. The paper concludes with a recommended strategy for d
etermining both the static and dynamic progressive failure of truss st
ructures.