International Journal of Computational Methods

This paper deals with the interaction between a circular piezoelectric inhomogeneity (a circular piezoelectric fiber sensor) and a symmetrically branched crack. The piezoelectric inhomogeneity is embedded in a nonpiezoelectric, elastic matrix with a symmetrically branched crack near the inhomogeneity. The matrix is under a far field in-plane uniform tensile stress and an anti-plane electric field. By using the solution of a single dislocation interacting with an inhomogeneity as Green's function, the main crack and its two symmetrical branches are simulated by continuously distributed edge dislocations. The formulation results in a group of singular integral equations (SIEs). Through solving the singular integral equations numerically, the unknown distributed dislocation density functions can be obtained, and both the Mode I and Mode II stress intensity factors at the branch tips are thus evaluated. The influence of materials constants, geometrical configurations, as well as the far field electric and mechanical loading on the interaction between the branched crack and the piezoelectric inhomogeneity is discussed in detail. As the derivation procedure is very tedious, the analytical results obtained are verified by finite element computation.

This paper presents an improved version of the traction method that was proposed as a solution to shape optimization problems of domain boundaries in which boundary value problems of partial differential equations are defined. The principle of the traction method is presented based on the theory of the gradient method in Hilbert space. Based on this principle, a new method is proposed by selecting another bounded coercive bilinear form from the previous method. The proposed method obtains domain variation with a solution to a boundary value problem with the Robin condition by using the shape gradient.

Reducing the general problem of computing three-dimensional Green's function in a transversely isotropic plate to a finite summation of contributions from a series of planar problems can efficiently yield an accurate solution. Hence, solving the planar scattering problem, of the Pressure-Shear-Vertical (PSV) type or the Shear-Horizontal (SH) type, was performed by three different techniques: The boundary element method; the hybrid method; and the perfectly matched layer method. In the pursuit of these methods, the objective was to highlight their pros and cons in terms of accuracy and efficiency.

A parametric study of composite strips leads to systems of partial differential equations, coupled through interface conditions, that are naturally solved in Laplace transform space. Because of the complexity of the solutions in transform space and the potential variations due to geometry and materials, a systematic approach to inversion is necessarily numerical. The Dubner-Abate-Crump (DAC) algorithm is the standard in such problems and is implemented. The presence of discontinuous wavefronts in the problems considered leads to Gibbs phenomenon; which, in turn, overestimates the values of maximum stress. These errors are mitigated by use of Lanczos' σ-factors, which combine naturally with the DAC algorithm.

The proposed time-independent quasi-static approach for simulations of lattice structures with imperfections is based on integration of the Inverse Broyden's Method suitable for finding the equilibrium state for a large system of atoms interacting through strongly nonlinear potentials and the Recursive Inverse Matrix Algorithm (RIMA) capable of updating the inverse matrix when topological changes (broken or new bonds between the atoms) take place. In this approach, the crystal structure is treated as a truss system while the forces between the atoms situated at the nodes are defined by the inter-atomic potentials. Since both the Broyden's and the RIMA algorithms deal with the inverse matrices of the structure their coupling makes the procedure computationally efficient. In addition, the method allows analysis of lattices subjected to mixed boundary conditions. The developed code was verified by the comparison with an alternative numerical procedure based on energy minimization technique. The model and the code developed were applied to the case of a 2D hexagonal lattice with the mode I crack embedded into the structure. For the cases considered, it was observed that the crack nucleation and growth were accompanied by the dislocation emission.

The anisotropy affected fatigue cracks that propagate on the rolling direction as mixed mode I-II cracks in CCT-specimens of pure aluminum sheets were predicted using Finite Element Method. The crack growth paths were estimated based on the value of mode I, II, total stress intensity factor range, and the ratio of mode II and mode I energy release rate of the crack. The predictions of crack propagation paths in no-hole specimens and 6-type holed specimens with 0, 30, 45 and 60 degrees of rolling direction towards loading direction were performed and the results were coincided with experimental results.

The investigation of the performance of Particle Swarm Optimization (PSO) algorithm with the new variants to inertia weight in computing the optimal control of a single stage hybrid system is presented in this paper. Three new variants for inertia weight are defined and their applicability with the PSO algorithm is thoroughly explained. The results obtained through the new proposed methods are compared with the existing PSO algorithm, which has a time varying inertia weight from a higher value to a lower value. The proposed methods provide both faster convergence and optimal solution with better accuracy.

An ad hoc one-dimensional finite element formulation is developed for the eigenanalysis of inplane singular electroelastic fields at material and geometric discontinuities in piezoelectric elastic materials by using the eigenfunction expansion procedure and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics, composites or air. The order of the electroelastic singularities and the angular variation of the stress and electric displacement fields are obtained with the formulation. The influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the singular electroelastic fields and the order of their singularity are also examined. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for piezoelectric and composite multi-material wedges. The nature and speed of convergence suggests that the present eigensolution could be used in developing hybrid elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular electroelastic states.