Analytical Approach for Stability of Variable Cross-section Compression Bars

摘要

Variable cross-section compression bar is an important structural member in engineering structure. When the compression of the bar reaches its critical load, the whole structure will lost the stability. Thus it is studied that analytical approach for stability of variable cross-section compression bars with perturbation method. First, the perturbation method which is of particular importance in solving linear homogeneous differential equation of second order with variable coefficients is derived in detail. Then the analytical solution of the bending differential equation of variable cross-section compression bar is constructed by using perturbation method. And the critical load of variable cross-section compression bar with the boundary constraints is obtained. Finally, as the numerical examples, the critical loads of variable cross-section compression bar are calculated, and the calculation result agreed well with the result recorded in other literatures. It is shown by several numerical examples that this method is simple and practicable, and owns good precision.