singular basis functions and curvilinear triangles in the solution of the electric field integral equation basis functions are formulated that account for singularities in the charge density near an edge on a conducting body the formulation is general and the basis functions are valid for planar as well curvilinear geometries in principle singularities of any order can be treated but best results are obtained for so called knife edge singularities results are compared with exact solutions or measurements where available for some simple problems

singular higher order divergence conforming bases of additive kind and moments method applications to 3d sharp wedge structures we present new subsectional singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges the bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood singular bases of this kind complete to arbitrarily high order are described in a unified and consistent manner for curved quadrilateral and triangular elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components adequate modelling of the divergence and removal of spurious solutions these singular high order bases provide more accurate and efficient numerical solutions of surface integral problems several test case problems are considered in the paper thereby obtaining highly accurate numerical results for the current and charge density induced on 3d sharp wedge structures the results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problems

a high order laminated plate theory with improved in plane responses in order to improve the accuracy of the in plane responses of the shear deformable laminated composite plate theories a new high order laminated plate theory was developed based upon reissner s new mixed variational principle int j num meth eng 20 1366 1984 to this end a zig zag shaped c0 function and legendre polynomials were introduced into the approximate in plane displacement distributions across the plate thickness the accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by pagano j comp mat 3 398 1969 a comparison with the exact solutions obtained for several symmetric and asymmetric cross ply laminates indicates that the present theory accurately estimates in plane responses even for small span to thickness ratios

field singularities at metal dielectric wedges the wedges discussed are the dielectric wedge the metallic 90 deg corner on a dielectric plane and the adjacent 90 deg metallic and dielectric corners the field components perpendicular to the edge may become infinite according to a law 1 r n numerical data are given for n and plots of lines of force of bar e or bar h are shown

oscillation and comparison results for delay difference equations abstract we establish a necessary and sufficient condition for the existence of positive solutions and obtain sturm type comparison theorem for the difference equation x n 1 x n i 1 m pi n x n ki o n 0 we also obtain the following comparison result equation oscillates if and only if x n 1 x n i 1 m qi n x n ki o n 0 oscillates provided n lim pi n qi i 1 2 m

curl conforming hierarchical vector bases for triangles and tetrahedra a new family of hierarchical vector bases is proposed for triangles and tetrahedra these functions span the curl conforming reduced gradient spaces of nedelec the bases are constructed from orthogonal scalar polynomials to enhance their linear independence which is a simpler process than an orthogonalization applied to the final vector functions specific functions are tabulated to order 6 5 preliminary results confirm that the new bases produce reasonably well conditioned matrices

singular hierarchical scalar basis functions for triangular cells a new family of hierarchical basis functions is proposed for triangular cells these functions incorporate singular behavior to model fields with corner singularities the functions are of the additive kind and combine a traditional polynomial complete representation on triangles with additional singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest the condition numbers arising from the use of these functions is investigated

rational transverse shear deformation higher order theory of anisotropic laminated plates and shells abstract a rational transverse shear deformation higher order theory of multilayered anisotropic plates and shallow shells is developed for the solution of statical problems for two possible cases cross ply and angle ply laminates the theory developed differs from existing ones by three features firstly it is based on the hypotheses which are fully tied to the physical and mechanical characteristics of the anisotropic layers secondly the theory is built on a rational level of difficulty i e it does not add complexity in comparison with other known theories developed for more simple laminated structure thirdly the hypotheses take directly into account the influence of external subject to both normal and tangential loads relying on the specific approach for the derivation of hypotheses all the relations of the stress strain state of anisotropic laminated shells are obtained using the variational approach the system of governing differential equations and corresponding boundary conditions are derived the analytical solution for this system is given and both special cases are stated namely cross ply and angle ply laminates for which such solution exists the results of the calculations are given and compared with exact three dimensional and some approximate solutions available in the literature the influence of the laminated structure upon the exactness of results and the characteristics of stress strain state is studied and discussed

least squares strain smoothing for the eight node serendipity plane stress element least square strain smoothing is applied to the popular eight node serendipity quadrilateral plane stress element substitute shape functions derived from the least squares principle are provided explicitly for smoothing the strain matrix it is found that the spurious shear straining modes appearing in the unsmoothed formulation are now completely eliminated the nodal stress values can thus be computed directly without any smoothed extrapolation from the gauss point stresses

hierarchical finite element bases for triangular and tetrahedral elements we describe a hierarchical basis for the p version of the finite element method in two and three dimensions the corresponding stiffness matrices are shown to have good sparsity properties and better conditioning than those generated from existing hierarchical bases

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

oscillation of nonlinear delay difference equations abstract in this paper two interesting oscillation criteria are obtained for all solutions of the nonlinear delay difference equations of the form yn 1 yn pnf yn k 0 n 0 1 2 some applications are given to demonstrate the advantage of results obtained in this paper our results also improve the existing results in the literature even when applying them to the linear delay difference equation

an improved discrete kirchhoff quadrilateral element based on third order zigzag theory for static analysis of composite and sandwich plates a new improved discrete kirchhoff quadrilateral element based on the third order zigzag theory is developed for the static analysis of composite and sandwich plates the element has seven degrees of freedom per node namely the three displacements two rotations and two transverse shear strain components at the mid surface the usual requirement of c1 continuity of interpolation functions of the deflection in the third order zigzag theory is circumvented by employing the improved discrete kirchhoff constraint technique the element is free from the shear locking the finite element formulation and the computer program are validated by comparing the results for simply supported plate with the analytical navier solution of the zigzag theory comparison of the present results with those using other available elements based on zigzag theories for composite and sandwich plates establishes the superiority of the present element in respect of simplicity accuracy and computational efficiency the accuracy of the zigzag theory is assessed by comparing the finite element results of the square all round clamped composite plates with the converged three dimensional finite element solution obtained using abaqus the comparisons also establish the superiority of the zigzag theory over the smeared third order theory having the same number of degrees of freedom copyright 2006 john wiley sons ltd

dynamic analysis of composite plate with multiple delaminations based on higher order zigzag theory in a recent paper cho and kim journal of applied mechanics proposed a higher order cubic zigzag theory of laminated composites with multiple delaminations the proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces in this work we investigate the dynamic behavior of laminated composite plates with multiple delaminations a four node finite element based on the efficient higher order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies mode shape and time response through the dynamic version of the variational approach the dynamic equilibrium equations and variationally consistent boundary conditions are obtained natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method to prevent penetration violation at the delamination interfaces unilateral contact constraints by lagrange multiplier method are applied in the time response analysis the present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations

oscillation of delay difference equation we introduce some new techniques to analyze generalized characteristic equations to obtain several infinite sum sharp conditions for oscillation of the following delay difference equation xn 1 xn i 1mpi n xn ki 0 n 0 1 2 where pi n 0 and ki are positive integers

an improved discrete kirchhoff quadrilateral thin plate bending element by combining discrete kirchhoff theory with least squares smoothed shape functions an improved quadrilateral thin plate bending element is derived this element exhibits improved performance over an earlier dkq element in predicting both displacements and stresses numerical examples are presented comparing the element with many other quadrilateral elements for standard test problems

moment method calculations on apertures using basis singular functions the transmission properties of perforated perfectly conducting screens are of practical interest the treatment of nonperiodical structures by numerical techniques such as the method of moments is very computer intensive in this paper it is shown that using basis functions that incorporate the edge as well as the corner singularities the number of unknowns can be drastically reduced the advantages and limitations of the method are discussed numerical results are presented illustrating the transmission properties of arrays of square and rectangular apertures

new oscillation criteria for first order delay difference equations in this paper some new oscillation criteria are obtained for the first order delay difference equation x n 1 x n k k k 1 k 1x n k f n x n l 1 x n l s 0 n 0 1 2 where k l 1 l 2 l s are positive integer numbers f is a function our results improve the known results in the literature and some examples are given to demonstrate the advantage of our results

singular higher order complete vector bases for finite methods this paper presents new singular curl and divergence conforming vector bases that incorporate the edge conditions singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements the higher order basis functions are obtained as the product of lowest order functions and silvester lagrange interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties are discussed and these bases are proved to be fully compatible with the standard high order regular vector bases used in adjacent elements the curl divergence conforming singular bases guarantee tangential normal continuity along the edges of the elements allowing for the discontinuity of normal tangential components adequate modeling of the curl divergence and removal of spurious modes solutions these singular high order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems sample numerical results confirm the faster convergence of these bases on wedge problems

singular hierarchical curl conforming vector bases for triangular cells a new family of hierarchical vector basis functions is proposed that accurately models fields near corners these are additive functions that combine singular bases incorporating general exponents with a full set of existing hierarchical polynomial basis functions to form the representation the functions are described for triangular cells and several results are provided to illustrate the improvement in accuracy resulting from their use a simple method for numerically constructing the singular basis functions on the fly is also provided the numerical construction of these singular basis functions facilitates their use for modeling fields near corners made of penetrable material

bending vibration and buckling of simply supported thick multilayered orthotropic plates an evaluation of a new displacement model abstract based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously the non linear in the von karman sense equations of motion for thick multilayered orthotropic plates are developed successively the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates in order to assess the accuracy of the proposed theory the sample problem of the bending free undamped vibration and buckling of a three layered symmetric cross ply square plate simply supported on all edges is investigated for purposes of comparison numerical results from the exact elasticity theory the classical lamination kirchhoff theory and the shear deformation theory timoshenko and mindlin with three different values of the shear correction factor are also presented it is found that the proposed approach is very efficient in predicting the global responses deflection natural frequencies and buckling loads of thick multilayered plates and models effects such as the distortion of the deformed normals not attainable from the classical lamination theory as well as the shear deformation theory