Search results

This paper describes a parallel algorithm for the dynamic relaxation (DR) method. The basic theory of the dynamic relaxation is briefly reviewed to prepare the reader for the parallel implementation of the algorithm. Some fundamental parallel processing schemes have been explored for the implementation of the algorithm. Geometric Parallelism was found suitable for the DR method when using transputer‐based systems. The evolution of the parallel algorithm is given by identifying the steps which may be executed in parallel. The structure of the parallel code is discussed and then described algorithmically. Two geometrically non‐linear parallel finite element analyses have been performed using different mesh densities. The number of processors was varied to investigate algorithm efficiency and speed ups. Using the results obtained it is shown that the computational efficiency increases when the computational load per processor is increased.

The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms.

Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures.

To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments.

To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate.

Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures.

It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.

This paper is concerned with a new proposal regarding the analysis of visco‐elastoplasticity and fatigue and is based on rheological‐dynamical theory. Due to the analogy between rheological model and dynamical model with viscous damping, it becomes obvious that inelastic response of members is essentially a dynamical problem. An analytical rheological‐dynamical viscoelasto‐ plastic solution of one‐dimensional longitudinal continuous vibration under loading and solution for the stress relaxation as unloading have been developed and used to obtain the fatigue limit of thin long bars. Rheologic behavior of the bar can be characterized by one parameter, like in a single‐degree‐of‐freedom spring mass system. In all inelastic strains time rate effects are always present to some degree. Whether or not their exclusion has a significant influence on the prediction of the material fatigue behavior depends upon several factors like: maximum absolute stress in the cycle, coefficient of asymmetry of cycle, creep coefficient, slope of the strain hardening portion of the stress‐strain curve, relative frequency and uniaxial yield stress. This paper provides description of dynamic magnification factor, relaxation of stress, stress concentration and the fatigue limit of thin long symmetrical bars.

Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy.

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration.

The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths.

Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells.

Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures.

Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

This paper presents a routing method for two dimensional transputer arrays particularly designed for parallel non‐linear and dynamic finite element analysis. Some general routing strategies with their strengths and weaknesses are discussed. The need for problem specific routing algorithms in transputer systems is considered and the communication requirements for parallel finite element analysis described. From the communication requirements the design parameters for the routing method are specified and the architectural design of the Router presented. An example of the use of the Router in the parallel non‐linear finite element analysis is given and the robustness of the routing methodology is illustrated by using arbitrary mappings of finite element subdomains distributed over a transputer array.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

A unified approach is presented for the pseudo‐transient (static) linear and geometrically non‐linear analyses of composite laminates. A finite element idealization with a four‐noded linear and a nine‐noded quadrilateral isoparametric elements, both belonging to the Lagrangian family are used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The accuracy of the formulation is then established by comparing the presnt pseudo‐transient analysis results with the present static Newton‐Raphson method results and other available analytical closed‐form two dimensional and finite element solutions. The usefulness and effectiveness of this approach is established by comparing computational time required by this approach and Newton‐Raphson's approach.

A hydrodynamic semiconductor device simulator, DYNA, is introduced. A new relaxation time evaluation scheme for two‐valley semiconductors is proposed to account for the dependence of the electron mobility on the impurity scattering. Some robust solution methods are used in the simulator for treating the highly nonlinear system of equations. The simulation results for a nonuniformly‐doped GaAs MESFET are also shown.

The purpose of this paper is to propose multigrid methods in conjunction with explicit approximate inverses with various cycles strategies and comparison with the other smoothers.

The main motive for the derivation of the various multigrid schemes lies in the efficiency of the multigrid methods as well as the explicit approximate inverses. The combination of the various multigrid cycles with the explicit approximate inverses as smoothers in conjunction with the dynamic over/under relaxation (DOUR) algorithm results in efficient schemes for solving large sparse linear systems derived from the discretization of partial differential equations (PDE).

Application of the proposed multigrid methods on two-dimensional boundary value problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than the V-cycle multigrid schemes presented in a recent report (Filelis-Papadopoulos and Gravvanis).

The limitations of the proposed scheme lie in the fact that the explicit finite difference approximate inverse matrix used as smoother in the multigrid method is a preconditioner for specific sparsity pattern. Further research is carried out in order to derive a generic explicit approximate inverse for any type of sparsity pattern.

A novel smoother for the geometric multigrid method is proposed, based on optimized banded approximate inverse matrix preconditioner, the Richardson method in conjunction with the DOUR scheme, for solving large sparse linear systems derived from finite difference discretization of PDEs. Moreover, the applicability and convergence behavior of the proposed scheme is examined based on various cycles and comparative results are given against the damped Jacobi smoother.

The present experiments are intended to help characterize defects in very thin MOS oxide and at its Si/SiO₂ interface using a temperature‐dependent electrical characterization method, high low temperature capacitance voltage method and, especially, to investigate high temperature range. Oxide‐fixed traps are differentiated from slow‐state traps and from fast‐state traps by evaluating their electrical behaviour at different temperatures. The analysis points out the excess current after Fowler Nordheim electron injection based on hole generation, trapping, and hopping transport at high temperatures. The defect relaxation property versus temperature is investigated and defect relaxation activation energies are calculated. Creation mechanisms of interface states are especially identified by injection at different temperatures and these are compared with the other two kinds of defects. Fast‐state traps and all defect cross‐sections are calculated along and their creation activation energies are determined from Arrhenius plots.