Study On Buckling Of Bar Caused By Axial Stress Wave Through Energy Method

As one of the most common structural elements,the bar has been widely used in aerospace,atomic energy,chemical industry,vessel,architecture and machinery and many other fields.The bar buckling has always been a very classic research topic in solid mechanics.In this paper,based on the energy method,the dynamic buckling of bar under axial impact is studied.The specific contents are as follows:(1)Considering the elastic stress waves,the Lagrangian function is established based on the energy method,and then the trial function and the Lagrangian function that meet the boundary conditions are substituted into the second Lagrange equation,obtaining an analytical expression of the critical impact velocity.The analytical expression showed that the critical buckling velocity is related to the impact mass,the critical length,and the radius of inertia.(2)Considering the elasto-plastic stress wave,the critical buckling conditions of elasto-plastic bar under an impact by rigid are derived based on the energy method and Lagrange function.Furthermore,the analytical expression of the critical velocity is given.The analytical expression showed that the critical elasto-plastic buckling impact velocity is related to the impact mass,the critical length,the inertia radius,and the yield limit.(3)Considering the elastic stress waves,the buckling caused by the time and space coupling stress wave is studied.The critical condition of buckling caused by stress wave which formed like ?(t)f(x),?(t)+f(x)and ?(xt)are derived through the stability of the solution.Analytical expressions of critical buckling stress(impact velocity)under time-varying stress wave and exponential decay stress wave are derived.The analytical expression showed that critical buckling stress(impact velocity)is related to the critical length and the radius of inertia.(4)Example analysis showed that:The larger critical length and the smaller critical impact velocity of buckling indicates that the stress wave effect has a significant influence on buckling.Higher-order modes of buckling is excited easily by the high-speed impact.The larger inertial radius,the greater critical velocity,and it indicated demonstrate that the improving of inertia radius can effectively increase the resistance to impact buckling.From strong to weak,the buckling resistance is the clamped-clamped constrained bar,pinned-clamped constrained bar,and the free-clamped constrained bar,respectively.The stress wave form has a significant effect on dynamic buckling.For the impact buckling of rigid masses,the larger the impact mass is,the smaller the critical impact velocity of buckling is,indicating that the initial kinetic energy of the impact has an important effect on buckling.The larger the yield limit is,the smaller the critical impact velocity of buckling is,showing that elasto-plastic buckling is affected by the yield limit of bar material.For the impact buckling under time-varying stress wave,the critical buckling stress(impact velocity)will decrease as the wavelength of the stress wave increases.