POST-PEAK RESPONSE AUTOMATIC SOLUTIONS IN STRUCTURAL ENGINEERING PROBLEMS – A REVIEW

The ill-condition of stiffness matrix at the unstable region for example at the strain-softening region, the load control method will not be valid to give the solution therefore the displacement control method is essential to use. The stiffness matrix is changed at different steps by used load control and solution is found using any nonlinear solution method of Newton’s family. Therefore, Newton’s method will not give a solution to the unstable region. The iteration method and solution process may also stop when the diagonal element of the stiffness matrix becomes negative or zero if Newton's method is adopted. These difficulties need to be overcome and a non-positive definite stiffness matrix is retained and used for iteration in the arc-length method. A scientific review of literature has been made to pinpoint the difficulties faced in the prediction of complete load-displacement response of structures and techniques available to overcome the same. Displacement control methods have been reviewed with emphases on the arc length methods which can be integrated with the traditional finite element method