A new algorithm for bending problems of continuous and inhomogeneous beam by the BEM

Abstract

The conventional algorithms of BEM for the bending problems of continuous beam are inefficient and have several points to be improved upon. Although such defects may not become a serious problem as far as they are put to practical use for an individual calculation, once they are applied to a kind of optimal design with a certain optimization algorithm small disadvantages in the conventional algorithm are amplified greatly and the cost of design work becomes very high. It is because a great many repetitive calculations are required in such problems. From this point of view, we intend to develop a new algorithm. Main points of this study are: (1) to improve the composition of the simultaneous equations by introducing a new formulation process; (2) to establish a scheme without any variables at intermediate points; and (3) to establish a generalized solution scheme for an inhomogeneous beam. These new algorithms will greatly reduce the size of a matrix as well as the computing time and, therefore, will bring about high efficiency on the repetitive calculations. As a result, this will give a low cost for optimal design in daily work.