A hybrid,finite element—finite difference approach to simplified large deflection analysis of structures

A new and considerably simplified solution technique for geometrically nonlinear problems is introduced. In contrast to the existing numerical methods, the present approach obtains an approximate large deflection pattern from the linear displacement vector by successively employing updated correction factors. Conservation of energy principle yields a general expression for these subsequent corrections. While the linear portion of the strain energy can be computed using finite element approach, evaluations of its nonlinear counterparts often require mathematical discretization techniques. The simple, self-correcting iterative procedure is unconditionally stable and its fast oscillatory convergence offers further computational efficiency. To illustrate the application of the proposed method and to assess its accuracy, moderately large deflections of beam, plate and flexible cable structures have been computed and compared with known analytical solutions. If required, the obtained results—which are acceptable for most design purposes—can be further improved.