Newton-Raphson Techniques in Finite Element Methods for Non-Linear Structural Problems

Mathematical procedures of Newton-Raphson techniques in finite element methods for non-linear structural problems are summarized These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results are used to study the convergency performances of these techniques for material non-linearity problems and deformation non-linearity problems, separately. Converged finite element results are used to study various non-linear structural problems having plastic failure, non-linear fracture or non-linear buckling mechanics behaviours.