Fixed-point iteration to nonlinear finite element analysis. Part I: Mathematical theory and background

This paper sets the stage for the implementation of the Fixed-Point Iteration (FPI) to nonlinear finite element analysis as an alternative to the existing Newton-Raphson Method (NRM) or its derivatives. The superiority of the former method over the latter one is such that it enables one to obtain nonlinear structural static or dynamic responses without inverting the structural stiffness matrix. In the first part of the paper, a new convergence correction/acceleration factor has been developed for the FPI when applied to a single nonlinear algebraic equation. This new factor causes the iteration function of the equation under consideration to rotate about an axis that passes through one of its fixed points or roots. Using this observation, the slope of the iteration function can be adjusted in the neighbourhood of a specific root to ensure the convergence of the FPI. It is found that the optimum choice of the new factor corresponds to a zero slope, evaluated at the root, of the iteration function. The rate of convergence and the error estimate of this form of the FPI is developed and compared with the NRM. The equilibrium positions of a nonlinear loaded softening spring have been obtained by both methods as an illustrative numerical example to measure the effect of the new factor on the convergence rate. The second part of the paper extends the above concept to find the solution of a linear system of algebraic equations using the FPI. This leads to a better diagonal approximate inverse for the Jacobi iteration, or method of simultaneous displacements. If the elements of the solution vector of a specific system are all equal, the new Jacobi iteration becomes an exact method and the solution is obtained in one iteration. The concept is also extended to the Gauss-Seidel iteration, or method of successive displacements. Systems involving symmetric as well as nonsymmetric coefficient matrices have been used as numerical examples and are presented. For future implementation to nonlinear finite element analysis, the active column or the skyline (or the non-zero profile) FPI algorithms are developed for programming considerations.     

Cubic isoparametric rolling/traveling finite elements

In this paper, the development and formulation of a new cubic isoparametric rolling/travelling finite element is described. The element can be used to simulate the dyanamic response of steadily rolling/traveling viscoelastic structures without the necessity of numerical time integration of the governing equations. Due to its higher order shape function, the element can more accurately simulate both the inertia and viscoelastic effects associated with rolling/traveling structures than currently available lower order moving elements. To illustrate the capabilities of the new cubic element, comparisons with exact and lower order generated results are presented.     

On the development of traveling load finite elements

Specialized finite elements are devised to handle traveling load problems in stationary and moving/rotating semi-infinite and body of revolution structures (slabs, rollers, tires, etc.). The generality of the elements is such that the full range of rectilinear/rotary loading and structural velocities can be handled. Hence, such phenomena as resonances and standing as well as traveling sub/supersonic waves can be simulated. The accuracy and capabilities of the elements is demonstrated by several numerical examples.     

Physical features and drainage priorities in Egypt

Egypt is implementing one of the largest field drainage programmes in the world. An area of 3.4 million acres had been provided with subsurface field drainage by the end of the year 1989; this acreage will increase to 5.5 million by the year 2000. The criteria for prioritising these areas are quite complex. Physical features, depth of water table and level of salinity are still the most important factors. Problem areas, such as heavy soils, unstable soils, areas under artesian pressures, Nile Valley fringe areas, areas with rice or sugar‐cane in the crop rotations, and areas with shallow barriers, require unconventional design and/or different implementation techniques. The need to replace old subsurface drainage systems is becoming an important planning factor.     

Some major implications of climatic fluctuations on water management

Climatic fluctuations affect water management in a variety of ways. Much emphasis has been placed in recent years on climatic changes that may occur in the future due to global warming resulting from increases in greenhouse gases. If and when global warming takes place, water availability and use patterns will most certainly change. At our present state of knowledge it is not possible to predict the onset of climatic changes, including their magnitude and spatial distribution, with any degree of confidence so that they can be explicitly incorporated into water management in a cost‐effective manner. The problem of climatic fluctuations appears to be more complex than the water resources profession has so far realized. Development of new methodologies to deal efficiently with climatic fluctuations is urgently needed.     

Evolution of transparent manufacturing: An architecture for a Java-based controller of a CIM cell

Because of recent advances in the area of networking and information systems, today's manufacturing systems face an increasing demand for easy access, and easy integration. This demand has driven the area of factory automation towards a more transparent structure, especially at the shop-floor control level. In this light, the cell level controller must not only allow consistent operation within the cell, but also provide networking facilities to the applications in the higher tier. In this paper, a Java-based architecture for such a controller is proposed, and pertinent design issues discussed. An implementation of this architecture is also investigated for feasibility in a multi-platform environment. Case studies and evaluation of the controller are presented.     

Effect of gamma irradiation on ethylene propylene diene terpolymer rubber composites

Composites of ethylene propylene dine terpolymer rubber (EPDM), high density polyethylene (HDPE) and ground tire rubber powder (GTR) at different ratios were subjected to gamma irradiation at various doses up to 250 kGy. The physical, mechanical and thermal properties were investigated as a function of irradiation dose and blend composition. Gamma irradiation led to a significant improvement in the properties for all blend compositions. The results indicate that the improvement in properties is inversely proportional to the substituted ratio of GTR, attributed to the development of an interfacial adhesion between GTR and blend components. The results were confirmed by examining the fracture surfaces by scanning electron microscopy.     

Carbonyl and thiocarbonyl compounds. XII. Synthetic Experiments with Diazoxanthenes

9-Diazothioxanthene reacts with phenanthraquinone as well as with 3,4-dichloro-1,2-naphthoquinone giving the cyclic ethers 4 and 5 , respectively. The action of hydrochloric acid on the products is stressed. The cyclic ethers 7a and 7b are obtained from the reaction between 9-diazo-1,2-benzoxanthene and tetrachloro- or tetrabromo-o-benzoquinone. Authentic sample of 7b could be obtained by the reaction of 9,9-dichloro-1,2-benzoxanthene with tetrabromocatechol. 9-Diazoxanthene reacts with 1,4-benzo- and -naphthoquinone to give the pyrazolines 8a and 9a respectively, which readily give diacetyl derivatives upon acetylation.