What is the best method to calculate the first buckling critical load for column of a non-uniform cross sectional area or a variable modulus of elasticity?
Do you suggest finite element method or finite difference method to solve such problem.
You could work out an estimated value by using an average second moment of area (depending on the shape of your column). Alternatively, the finite element method will give you a more accurate solution.
Various methods can be used to solve the problem. Whichever method is chosen, however, the result should be same. The finite element and finite difference methods are OK, but you need a computer and appropriate software at hand. For quick analysis, one can apply a simpler approach based on the Ritz or Galerkin procedures.