Numerical Analysis Of Equilibrium Of Super-thin Elastic Rod

Super-thin elastic rod model has a extensive background, for example, cables, ropes, fiber, these can be modeled as an elastic rod model to discuss, the study of dynamics theories and numerical analysis methods has been developing rapidly in recent years. Based on Kirchhoff dynamics analogy, under the force constraint conditions, differential equations describing the static rod were derived.Firstly, this paper describes the establishment of an elastic rod Kirchhoff equation, under the given conditions of the basic assumptions, to take an elastic rod of specific length, equilibrium equation is established, which uses the Euler angle to represent this equation. When giving different initial and boundary values, MATLAB programming for Kirchhoff equation to solve and visualize is used. Because of non-linear equation, so the equation has no analytical solution, the numerical solution is obtained. Based on the numerical solution, flexible line graphics of elastic rod can be determined. There are two methods to visualize elastic rod, one is to use Marker command of MATLAB, and the second is to use coordinate transformation matrix to establish elastic rod’s shape equation. Using MATLAB software to solve the equation and keeping all other conditions remain unchanged, increasing sequence of an external force, the external force and self-contact position of elastic rod can be got, and this provides ideas for subsequent research.Secondly, in fixed-axis rotational reference of stable angular velocity, a super-thin elastic rod’s kinetic equations are established, which uses Euler angles to indicate. In ignoring the case of the flexural rigidity and torsional rigidity, elastic rod can be regarded as elastic rope to analyze, and its relative equilibrium equations can be exported, which uses the coordinate of the center line to express. Thus, Mathematica software can be used to obtain position-shaped of elastic cord which caused by initial conditions and rotation angular velocity.Finally, the prospect of this article is that the phenomenon about contact-itself under the initial condition occurs, but contact-itself under boundary condition needs further research.