Further results concerning the refined theory of anisotropic laminated composite plates

A simple refined discrete-layer theory of anisotropic laminated composite plates is substantiated. The theory is based on the assumption of a piecewise linear variation of the in-plane displacement components and of the constancy of the transverse displacement throughout the thickness of the laminate. This plate model incorporates transverse shear deformation, dynamic and thermal effects as well as the geometrical non-linearities and fulfills the continuity conditions for the displacement components and transverse shear stresses at the interfaces between laminae. As it is shown in the paper, the refinement implying the fulfillment of continuity conditions is not accompanied by an increase of the number of independent unknown functions, as implied in the standard first order transverse shear deformation theory. It is also shown that the within the framework of the linearized static counterpart of the theory, several theorems analogous to the ones in the 3-D elasticity theory could be established. These concern the energetic theorems, Betti's reciprocity theorem, the uniqueness theorem for the solutions of boundary-value problems of elastic composite plates, etc. Finally, comparative remarks on the present and standard first order transverse shear deformation theories are made and pertinent conclusions about its usefulness and further developments are outlined.     

Synthesis and characterization of nanocrystalline Zn ferrites substituted with Ni

Nanocrystalline powders of nickel substituted zinc ferrite with general formula Ni_xZn_1−xFe₂O₄ (x = 0, 0.2, 0.4, 0.6, 0.8, 1) have been synthesized via sol-gel auto-combustion method using tartaric acid as combustion-complexing agent. Samples were sintered at 773 K and 973 K in static air atmosphere. The absence of the organic phase and the spinel formation were monitored by using Fourier transform infrared spectroscopy. The structure and crystallite size were analyzed from X-ray diffraction data revealing spinel mono-phase formation in the range of nanometric crystallite size confirmed also through scanning electron microscopy. Mean size of crystallites lay in the range 20-40 nm. The influence of nickel content on the microstructure was investigated considering the crystallite size, distance between adjacent crystal planes, lattice parameter and porosity. The variation of magnetic properties of the samples was studied by using vibrating samples magnetometer and discussed considering the proposed cation distribution, relative bond angles and canting angles. The highest maximum value of the magnetization (63 emu/g) was found for Ni_0.8Zn_0.2Fe₂O₄.     

Electron transport properties of some new 4-tert-butylcalix[4]arene derivatives in thin films

Temperature dependences of electric conductivity and thermoelectric power of some recently synthesized organic compounds, 4-tert-butylcalix[4]arene derivatives, are studied. Thin-film samples (d = 0.10–0.40 μm) spin-coated from chloroform solutions onto glass substrates were used. Organic films with reproducible electron transport properties can be obtained if, after deposition, they are submitted to a heat treatment within temperature range of 295–575 K.     

A meshless method for the stable solution of singular inverse problems for two-dimensional Helmholtz-type equations

We investigate a meshless method for the stable and accurate solution of inverse problems associated with two-dimensional Helmholtz-type equations in the presence of boundary singularities. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS). The existence of boundary singularities affects adversely the accuracy and convergence of standard numerical methods. Solutions to such problems and/or their corresponding derivatives may have unbounded values in the vicinity of the singularity. Moreover, when dealing with inverse problems, the stability of solutions is a key issue and this is usually taken into account by employing a regularization method. These difficulties are overcome by combining the Tikhonov regularization method (TRM) with the subtraction from the original MFS solution of the corresponding singular solutions, without an appreciable increase in the computational effort and at the same time keeping the same MFS discretization. Three examples for both the Helmholtz and the modified Helmholtz equations are carefully investigated.     

Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. The iterative MFS algorithms with relaxation are tested for over-, equally and under-determined Cauchy problems associated with the steady-state anisotropic heat conduction in various two-dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method.     

Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method

We study the stable numerical identification of an unknown portion of the boundary on which either a Dirichlet or a Robin boundary condition is provided, while additional Cauchy data are given on the remaining known part of the boundary of a two-dimensional domain, in the case of steady state anisotropic heat conduction problems. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method [53]. The optimal value for the regularization parameter is chosen according to Hansen’s L-curve criterion [17]. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples in both smooth and piecewise smooth geometries.     

The Supervised Network Self-Organizing Map for Classification of Large Data Sets

Complex application domains involve difficult pattern classification problems. The state space of these problems consists of regions that lie near class separation boundaries and require the construction of complex discriminants while for the rest regions the classification task is significantly simpler. The motivation for developing the Supervised Network Self-Organizing Map (SNet-SOM) model is to exploit this fact for designing computationally effective solutions. Specifically, the SNet-SOM utilizes unsupervised learning for classifying at the simple regions and supervised learning for the difficult ones in a two stage learning process. The unsupervised learning approach is based on the Self-Organizing Map (SOM) of Kohonen. The basic SOM is modified with a dynamic node insertion/deletion process controlled with an entropy based criterion that allows an adaptive extension of the SOM. This extension proceeds until the total number of training patterns that are mapped to neurons with high entropy (and therefore with ambiguous classification) reduces to a size manageable numerically with a capable supervised model. The second learning phase (the supervised training) has the objective of constructing better decision boundaries at the ambiguous regions. At this phase, a special supervised network is trained for the computationally reduced task of performing the classification at the ambiguous regions only. The performance of the SNet-SOM has been evaluated on both synthetic data and on an ischemia detection application with data extracted from the European ST-T database. In all cases, the utilization of SNet-SOM with supervised learning based on both Radial Basis Functions and Support Vector Machines has improved the results significantly related to those obtained with the unsupervised SOM and has enhanced the scalability of the supervised learning schemes. The highly disciplined design of the generalization performance of the Support Vector Machine allows to design the proper model for the particular training set.     

Effects of Interfacial Damage on the Global and Local Static Response of Cross-Ply Laminates

The problem of the implications of interfacial damage on the local and global static response of cross-ply laminated flat structures is addressed in this paper. As a basic prerequisite, a third-order generalized zig-zag nonlinear plate theory incorporating the effect of interfacial damage is used. The theory rests upon a representation of the displacement field which: (i) fulfills a priori the shear traction continuity conditions at each interface of the laminate and the free shear traction conditions on the top and bottom external planes of the plate, (ii) satisfies the requirement of continuous displacements at the perfectly bonded interfaces, and (iii) incorporates the interfacial tangential displacement jump condition when slip-type interlayer imperfections are present. The theory also incorporates the geometrical nonlinearities and the thermal effects. Numerical results highlighting the effect of interfacial damage on the static response of laminated composite plates in cylindrical bending are displayed and conclusions on their implications upon their load-carrying capacity are outlined. This revised version was published online in July 2006 with corrections to the Cover Date.     

Relaxation of Alternating Iterative Algorithms for the Cauchy Problem Associated with the Modified Helmholtz Equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of Kozlov, Maz'ya and Fomin(1991) applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.     

Regularized MFS-Based Boundary Identification in Two-Dimensional Helmholtz-Type Equations

We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a two-dimensional domain for problems governed by either the Helmholtz or the modified Helmholtz equation. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method. The optimal value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.