| The thin elastic rod model is widely used in many fields such as life,engineering,and biology.Due to the geometric similarity,the elastic thin rod can be used as mechanical model from the cable-stayed bridge cables,submarine cables,ropeways to rod-shaped bacteria,DNA and other biological tissues.In recent years,elastic thin rod models have attracted attention in simulating the mechanical behavior of DNA and active tissue growth.External constraints and growth ha ve equally important effects on the deformation or buckling behavior of thin elastic rods.In this paper,the deformation behavior of elastic thin rods constrained by one side and the instability of elastic thin rods caused by growth are studied.The specific content mainly includes the following two aspects.1.The deformation behavior of a thin elastic rod with one side restrained under torsion is studied.The elastic thin rod studied in this paper is constrained in the cylindrical surface,and the end is located on the cylindrical surface.O ne end is fixed and the other end can rotate and slide axially.Based on the K irchhoff elastic thin rod model,the differential equation of the elastic thin rod under unilateral constraints is established.The idea and calculation steps for solving the equations by shooting method are given.Numerically solve and draw the image of the corresponding elastic thin rod.2.The buckling behavior of elastic thin rods in viscous media induced by growth factors was studied.Based on the elastic morphology rod theory,the equilibrium equation of the elastic growth rod in the viscous medium is derived.Using perturbation expansion,a set of differential equations for determining the instability threshold of elastically growing thin rods in viscous media is given.The results were applied to analyze the stability of the DNA growth loop,and its buckling criterion was obtained.The influence of the modal selection and viscosity resistance of the DNA growth loop on the instability of the DNA growth loop was discussed. |
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