Large Finite Systems Research Articles

On the convergence rate of iterative methods for the solution of positive definite linear equations

The convergence rates of the point-Jacobi method and of the successive overrelaxation (including the Gauss-Seidel) method for symmetric positive definite linear equations are determined as functions of the spectrum of the matrix which is scaled to ones on the principal diagonal. It is seen that the convergence rate is strongly dependent upon the magnitude of the smallest eigenvalue and that for even mildly ill-conditioned matrices the convergence is very slow. It is also shown that the finite difference representation of the three-dimensional Laplace operator leads to remarkably well-conditioned matrices even when the number of equations is very large. Numerical experiments were performed supporting the analysis. It is concluded that the methods studied are virtually limited to large finite difference systems, but that they are very well adapted to such systems.

Rate-type creep law of aging concrete based on maxwell chain

It is shown that the linear creep law of concrete can be characterized, with any desired accuracy, by a rate-type creep law that can be interpreted by a Maxwell chain model of time-variable viscosities and spring moduli. Identification of these parameters from the test data is accomplished by expanding into Direchlet series the relaxation curves, which in turn are computed from the measured creep curves. The identification has a unique solution if a certain smoothing condition is imposed upon the relaxation spectra. The formulation is useful for the step-by-step time integration of large finite element systems because it makes the storage of stress history unnecessary. For this purpose a new, unconditionally stable numerical algorithm is presented, allowing an arbitrary increase of the time step as the creep rate decays. The rate-type formulation permits establishing a correlation with the rate processes in the microstructure and thus opens the way toward rational generations to variable tempeature and water content. The previously developed Kelvin-type chain also permits such a correlation, but its identification from test data is more complicated.

The design, development, documentation and support of a major finite element system

The paper discusses various aspects of large general purpose finite element systems which may be of interest both to prospective developers and practising engineers. Although many of the points discussed apply to any field in which the method has been used, attention is concentrated on the static stress analysis problem. The paper considers in detail the initial design decisions concerning program structure, language, usage of available core storage, and methods of accessing backing store. The various facilities which may be of use in such a general system are listed and discussed. The problems which may arise as the development of a system proceeds are considered in three phases; specification, programming and testing. The types of documentation relevant to large engineering systems are described and the importance of an efficient and well organised client support and updating procedure is stressed.