Stability boundaries of two-parameter non-linear elastic structures

The load-bearing capacity of structures can be influenced by variations in parameters, such as initial geometric defects, multi-parameter loadings, material specifications and temperature. This paper aims to introduce a new formulation to trace the stability boundaries of two-parameter elastic structures. The proposed procedure can find a set of critical points, both limit and bifurcation ones, via a modified Newton’s method. In the authors’ formulation, the residual force is set to zero, and a critically constraint is satisfied simultaneously. Numerical examples presented in this paper demonstrate the efficiency of the suggested method.