Three-dimensional simulations of initially straight elasticas

The governing nonlinear vector differential equations for large deflections of an end-loaded, three-dimensionally deformed, initially straight, axisymmetric elastica are developed and simulated numerically without decomposition. All simulations are based on repeated applications of truncated Taylor's expansions to advance along a deformed elastica. Both initial value problems, and two-point boundary value problems with a corresponding shooting method are discussed. A number of examples are solved and compared with corresponding theoretical solutions, and with a finite element solution. An elastica solution with at least six independent equilibrium configurations satisfying a single set of boundary conditions and not heretofore treated in the literature is also presented.