2016 Volume 72 Issue 2 Pages I_303-I_312
In a previous paper, we have proposed a novel reduction method for the treatment of the continua. Here I provide several lines of evidence showing that the reduction method can be regarded as a generalized force method. In the reduction method, the simultaneous equation is constructed with both equilibrium and compatibility conditions using the stiffness matrices of each individual finite element. Therefore, the reduction method includes both deformation method and force method. When the compatibility condition rows are satisfied at first, then equilibrium condition rows should be solved separately. However, it is important to notice that the remaining rows can be regarded as deformation method matrix because the unknowns of simultaneous equation are represented by a parameter vector contracting the plural parameter vectors of the individual element. If a scheme for the statically determinate main system is successfully established by eliminating extra parameters, then only the force method matrix remains. In this context, the reduction method should be regarded as a generalized force method, which I call GFM, rather than classical two-step-type force method, which at first looks for the statically determinate main system and then solves the force method matrix. Although we previously expected that the iteration method would be adaptively improved for solving the simultaneous equation of GFM, I found in this study that neither the explicit methods such as the improved SOR method nor the implicit methods such as the Krylov's space method cannot be useful. Hence, I propose an alternative scheme based on Guassian elimination method, modified with skyline method that memorize nonzero elements only and sweep-out method that eliminates extra parameters by using absolute max. pivot.
