International Journal of Computational Methods

A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It has shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.

A new method of molecular statics based on independent displacements of atoms converging to an equilibrium state is proposed. It is analogous to the molecular dynamics method and thus has similar advantages in terms of the system size which can be simulated, as well as the utilization of parallel computation. At the same time, it allows the study of fracture, crack nucleation and propagation, etc. without the computer time constraints associated with time steps in molecular dynamics. The method is demonstrated for a 2D crystal with one deficiency.

This paper presents an application of Ant Colony Optimization (ACO) algorithm to tune the parameters in the design of a novel type of nonlinear proportional-integral-differential (NLPID) controller, which is used in flight simulator. A differential tracker and a reference generator are included in the NLPID controller. The differential tracker is used to track output position and its differential, while the reference generator is used to generate reference input signals. ACO algorithm is a novel heuristic algorithm, which is based on the process of real ants in the nature searching for food. In order to tune the parameters of the NLPID controller using the new proposed grid-based ACO algorithm, an objective function based on position tracing error is constructed. The parameters tuning of NLPID can be summed up as the typical continual spatial optimization problem, grid-based searching strategy is adopted in the improved ACO algorithm, and self-adaptive control strategy for the pheromone decay parameter is also adopted. In order to enhance the searching speed, pair ants which searched from two different mesh points at the same time are used. The body structure and control system architecture of a type of flight simulator with the grid-based ACO algorithm optimized NLPID are also proposed. The simulation results demonstrate that both for the standard and random input signals, the tracking error is very small, and the whole control system with grid-based ACO algorithm optimized NLPID has quick response performance and strong robustness.

An integerization technique for creating fixed integer transforms with computationally optimal representations is presented, and the improved performance in embedded systems by employing these integerized implementations is explored. This technique uses an optimal approximation algorithm that finds the lowest-length fractional representation of the rational numbers. The integer transform approximation allows multiplication to be replaced by shift-and-add operations in hardware systems; where multiplication can take several cycles, shifts and adds take one or fewer cycles each. The multiplierless implementation furthermore benefits from employing the proposed method to represent the floating-point coefficients in very high precision requirement areas, like decimation filter design. This paper is strongly oriented around the design of coefficients with hardware constraints in mind, such as minimizing the number of required adds/subtracts and shifts required for some engineering algorithms.

This paper provides, an elastic solution for multiple curved edge cracks emanating from the boundary of the half-plane. After placing the distributed dislocations at the prospective sites of cracks in an infinite plate, the principal part of the complex potentials is obtained. By using the concept of the modified complex potentials, the complementary part of the complex potentials can be derived. The whole complex potentials satisfy the traction free condition along the boundary of half-plane automatically. This is a particular advantage of the suggested method. This concept or method of the modified complex potentials is a counterpart of the Green's function method, which is universal in mathematical physics. The direct usage of this method cannot provide a solution in detail. Comparing with the line edge crack case, the following points are significant in the presented study. The relevant kernels in the integral equation are more complicated than in the line edge crack case and the relevant integrations in the problem should be completed on curves. This paper solves a rather complicated problem, the multiple curved edge crack problem, and gives the final solution. A singular integral equation is formulated with the dislocation distribution being unknown function and the traction being the right hand term. The singular integral equation is solved by using the curve length method in conjunction with the semiopening quadrature rule. Periodic curved edge crack problem is also addressed. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

The inflatable/rigidizable tube is a basic element for inflatable space structures. It can be made of carbon fabric/epoxy prepreg which includes a rigidizable epoxy resin and woven fabric. The fabric prepreg will be kept in prepreg state while stowed and then cured post deployment to be rigid in orbit. In this paper, a simple homogenized shear model of the fabric prepreg under inner pressure action is proposed to investigate shear modulus variation with the inner pressure; the dynamic inflation and deployment process of the fabric prepreg tube is simulated by LS-DYNA with airbag and multi-cavity model, and effects on deployment properties including inflation speed, material properties, and folder geometry are investigated.

In this paper, the interval analysis method is introduced to calculate the bounds of the structural displacement responses with small uncertain levels' parameters. This method is based on the first-order Taylor expansion and finite element method. The uncertain parameters are treated as the intervals, not necessary to know their probabilistic distributions. Through dividing the intervals of the uncertain parameters into several subintervals and applying the interval analysis to each subinterval combination, a subinterval analysis method is then suggested to deal with the structures with large uncertain levels' parameters. However, the second-order truncation error of the Taylor expansion and the linear approximation of the second derivatives with respect to the uncertain parameters, two error estimation methods are given to calculate the maximum errors of the interval analysis and subinterval analysis methods, respectively. A plane truss structure is investigated to demonstrate the efficiency of the presented method.

A steady-state rolling problem with rigid-plastic, strain-rate sensitive, slightly compressible material model and nonlinear Coulomb friction law is considered. For the corresponding variational problem, existence, uniqueness and convergence results, at compressibility parameter approaching zero, are obtained. A regularized variational problem is stated and studied and its finite element approximation is analyzed. Two computational algorithms are proposed and applied to solve an illustrative example.