Nonlinear analysis of a twisted axially loaded elastic rod

Abstract

Abstract.A slender, inextensible elastic rod is acted upon by a twisting couple and an axial load. The position of the rod's centerline is determined by two fourth-order, coupled, nonlinear boundary value problems, each of which contains two eigenparameters. These equilibrium equations admit the trivial solution for all values of the eigenparameters, i.e., for any axial load and any twisting couple. The linearized equilibrium equations have a countable number of eigencurves. Through using the implicit function theorem for Banach spaces it is shown that from each of the eigencurves of the linear problem there bifurcates a two-parameter sheet of nontrivial solutions of the nonlinear equilibrium equations.

Magnetic tweezers measurements of the nanomechanical properties of DNA in the presence of drugs

“…It should be noted that the naive mechanical model predicts a specific power law dependence of n b and Δz as a function of the applied force ( n b ∝ F 1/2 ; Δ z ∝ F -1/2 ), see Equation. ( 4 )&( 5 ) This prediction is not confirmed by the data, as previously reported in the literature ( 2 , 55–58 ). This discrepancy is not really surprising, considering the reasonable possibility that B increases with the imposed overtwist.…”

“…We point out that there are more rigorous mechanical models of the buckling and post-buckling behavior of chains under torsion ( 55–58 ). However, we think that the naive model is still valuable given our goal of obtaining a qualitative discrimination between different molecular interaction.…”

Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables

“…As the ends slowly approach, the rod initially buckles in its fundamental buckling mode as expected. The end tension and torque required to initiate buckling (of a twisted clamped rod) is derived in [32] as the buckling condition cos p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi…”

“…7(a). Starting from d = 0, the rod first buckles as per (14) in its fundamental mode which resembles a helix with small helical diameter [32]. The helical diameter increases with d and the spatial equilibrium ultimately becomes planar with an interior loop at the bifurcation point (denoted by the triangle).…”

Helicoidal buckling of an elastic rod

“…(17) 9 (19) show that the twisting moment M 3 differs from C O and C 3, except at bifurcation loading. Extension of this equality to the non-linear analysis, as stated in [5 ] is not justified.…”