Abstract
The dynamic in-plane instability process of extreme point type for pin-ended arches when a central radial load applied suddenly with infinite duration is analyzed with finite element method in this study. The state of arch can be determined by the crown’s vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation. When the arch structure reaches the dynamically stable critical state, the kinetic energy of the structure is very small or even zero. The dynamic critical load of elastic arch calculated with the theoretical analysis method which is based on energy principle is proved accuracy enough by comparing with the finite element calculation results and the percentage of the differences between them are no more than 4.5 %. The maximal elastic strain energy is certain for the elastic-plastic arch in certain geometry under both a sudden load and static load. The maximal elastic strain energy in static calculation can be used in determining the state of the elastic-plastic arch under dynamic sudden loads applied and this method is more accurate which errors won’t exceed 3.5 %. The accuracy of dynamic critical load calculation method for elastic arch is verified by numerical calculation in this study, and based on the characteristic of elastic strain energy in critical state, a method for determining the stability of elastic-plastic arch is presented.
Highlights
When an in-plane load is applied suddenly to a shallow circular arch that is fully braced laterally, the load will impart kinetic energy to the arch and will cause the arch to oscillate about an equilibrium position
Considering the above analysis, in finite element analysis, the state of arch can be determined by the vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation
Reasonable guess is made which is that the maximal elastic strain energies of an elastic-plastic arch under a central radial load is certain in both static load and sudden load
Summary
When an in-plane load is applied suddenly to a shallow circular arch that is fully braced laterally, the load will impart kinetic energy to the arch and will cause the arch to oscillate about an equilibrium position. There are three main methods used in dynamic researches on arches, including: Solving the dynamic equation to obtain the dynamic response and critical buckling load of arches, numerical method and test method. Previous investigations on the dynamic buckling of arches are carried out with a rigid-plastic material model assumption and the structural deformation become relatively simple for analysis [1,2,3] This method is applicable for the dynamic mechanical calculation when the structure undergoes small deformation. In Han Qiang’s study [8], snap-through buckling of an elastic shallow arch underground impact is investigated through energy balance equation with Hamiltonian principle and the stability critical state and dynamic response of the structure are given. Considering the advantages of numerical simulation in structural dynamic analysis, researches are carried out with finite element method on dynamic stability critical state of pin-ended arches under a sudden central concentrated load. The dynamic stability analysis of arch is given from energy point of view
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