Pseudolinear and Equivalent Systems for Large Deflections of Members

The research in this paper consists of an analytical study of the computation of large deflections of uniform and variable stiffness members by using pseudolinear or nonlinear equivalent systems of constant stiffhess. By using the second‐order nonlinear differential equation of the elastic curve, a mathematical proof was first obtained, in order to establish the existence of exact pseudolinear or nonlinear equivalent systems of constant stiffness EI that can replace the initial nonlinear system whose moment of inertia I, or stiffness EI, is either uniform or variable. Once the equivalent system of constant stiffness is obtained, linear or nonlinear analysis can be applied to this equivalent system in order to determine displacement requirements of the initial nonlinear system. The equivalent system will always be of constant stiffness, and its deflection curve will be identical to that of the initial nonlinear system. The use of equivalent pseudolinear or nonlinear systems simplifies a great deal the mathematical complexity of the nonlinear problem, particularly when the initial problem has continuously varying stiffness EI along its length. For convenience, a very accurate approximate method is also introduced.