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Theoretical Research on Numerical?Techniques in Stability Analysis ?? In the past few decades, with the wide use of various large-span space structural systems,significant progress has been made in area of??nonlinear??analysis techniques.??It??is??known??that??for??large-span??space structural systems, limit and bifurcation instability are two main types of instability with different characteristics. The former is a kind of geometric softening behavior under external loads with unique equilibrium path, while the latter is just a shift of equilibrium states among several possible paths. The instability modes of large-span space structures are very complex??and usually include both the limit type and the bifurcation type of instability.??In??order??to??comprehensively??know??the characteristics of the systems, tracing the complete load-deflection path is important and must be carried out. Generally,??arc-length-type and energy-type methods are two main??strategies used in??structural nonlinear tracing analysis, but the former has bean widely used due to its explicitness and clarity in conception, as well as its convenience and reliability in calculation. Unfortunately, these nonlinear analysis techniques are only usable for tracing??the??limit??type??equilibrium??path.??For the bifurcation type path, most of them do not lead to a satisfactory result.?? In Prof. Z.丫Shens Research Lab, systematic review and discussion of main arc-length type methods and the most common reasons for failures in tracing analysis have been carried out and Li??and Shen,??2004, and improvements on the arc-length type methods have been made to develop the efficiency of these methods in may circumstances, both common and special purposes. Large-displacement updating techniques Since the joint rotation displacement are not vectors as the translation displacements considering large deformation ofstructures, the linear superposition principal cannot be used to update the ro