sensitivity analysis of nonlinear material and its application to shape optimization a direct sensitivity analysis technique for the path dependent nonlinear problem based on the updated lagrangian formulation is suggested in which the elastoplastic material of bilinear constitutive law is assumed for such a material property the design sensitivities are discontinuous at the material transition points the incremental equilibirum equation is differentiated with respect to the design variables to derive the sensitivity equations which ar solved during the newton raphson iterative scheme of response analysis

optimization of mechanical systems on strategy of non linear first order approximation the paper presents an extended approach to non linear first order approximation of non linear programming problems and it explains how to transform an approximate problem into a strictly convex one the essence of the proposed approximation technique is to rewrite each given function hj as a composite gjo j the function j has to be chosen the paper explains how to do this while gj is linear approximated with gj the approximation of hj is then obtained as gjo j this approach enables one to obtain approximate functions with variable conservativeness which implies an adjustable approximate problem a solution procedure which replaces the original problem with a sequence of approximate problems can therefore adjust each succeeding approximate problem to improve the convergence properties the theory is illustrated with a three parameters controlled approximation this technique represents together with an optimality criteria based solution procedure a powerful and economic tool for solving nonlinear programming problems the three parameters which influence to a great extent the conservativeness of the approximate functions are under full control of the optimizer they are varied automatically during the process of optimization to speed up the convergence or to prevent oscillations the benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system

characterizing isochronous points and computing isochronous sections abstract we consider two dimensional autonomous systems of differential equations x y x p x y y x y q x y where is a real constant and p and q are smooth functions of order greater than or equal to two these systems so called centre focus type systems have either a centre or a focus at the origin we characterize the systems with a weak isochronous focus at the origin by means of their radial and azimuthal coefficients we prove in this case the existence of a normalized vector field and an isochronous section which arrives at the origin with defined direction we also provide algorithms that compute the radial and azimuthal coefficients terms of normalized vector field and of isochronous section of a system as applications we analyze the weak isochronous foci for quadratic systems and for systems with cubic non linearities and we give a three parameter family of rayleigh equations with four local critical periods

moment method analysis of large axially symmetric reflector antennas using entire domain functions the moment method technique utilizing entire domain basis functions is applied to the analysis of large axially symmetric reflector antennas the electric surface current is modeled as a finite series of sinusoids whose domain consists of the entire generating curve this expansion results in a matrix size of less than 5 of that produced with subdomain basis functions only a slight increase in the cpu requirements occurs from this analysis the results from this technique show good agreement when compared to both physical optics and a subdomain based moment method formulation on small axially fed paraboloidal and hyperboloidal reflector antennas extension to a large 100 lambda paraboloidal reflector with f d 0 4 produces results comparable to that obtained using physical optics convergence is obtained with as few as two expansion terms per wavelength discretization of the generating curve with four points per wavelength leads to results which agree within 0 5 db over data from a more densely defined curve

a higher order parallelized multilevel fast multipole algorithm for 3 d scattering a higher order multilevel fast multipole algorithm mlfma is presented for solving integral equations of electromagnetic wave scattering by three dimensional 3 d conducting objects this method employs higher order parametric elements to provide accurate modeling of the scatterer s geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer s surface this higher order scheme leads to a significant reduction in the mesh density thus the number of unknowns without compromising the accuracy of geometry modeling it is applied to the electric field integral equation efie the magnetic field integral equation mfie and the combined field integral equation cfie using galerkin s testing approach the resultant numerical system of equations is then solved using the mlfma appropriate preconditioning techniques are employed to speedup the mlfma solution the proposed method is further implemented on distributed memory parallel computers to harness the maximum power from presently available machines numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme

spectral elements for the integral equations of time harmonic maxwell problems we present a novel high order method of moments mom with interpolatory vector functions on quadrilateral patches the main advantage of this method is that the hdiv conforming property is enforced and at the same time it can be interpreted as a point based scheme we apply this method to field integral equations fies to solve time harmonic electromagnetic scattering problems our approach is applied to the first and second nedelec families of hdiv conforming elements it consists in a specific choice of the degrees of freedom dof made in order to allow a fast integral evaluation in this paper we describe these two sets of dof and their corresponding quadrature rules sample numerical results on fie confirm the good properties of our schemes faster convergence rate and cheap matrix calculation we also present observations on the choice of the discretization method depending on the fie selected

guaranteed convergence method of analysis of the scattering by an arbitrarily oriented zero thickness pec disk buried in a lossy half space in this paper a guaranteed convergence method for the accurate and efficient analysis of the electromagnetic scattering by an arbitrarily oriented zero thickness perfectly electrically conducting pec disk buried in a lossy half space is presented an electric field integral equation efie in the vector hankel transform domain is obtained by expanding the unknown surface current density in cylindrical harmonics a convergence of exponential type is achieved by means of galerkin s method with expansion functions reconstructing the expected physical behavior of the bm n th harmonic at the center and the edge of the disk the obtained coefficient matrix can be quickly computed since its elements can be reviewed as the sum of single integrals efficiently evaluable by means of an analytical acceleration technique and double integrals of exponentially decaying functions

an approach to optimal design of structures with non linear response a commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems where each of these is obtained as an approximation of the original problem considering structures with linear response this procedure works very well and can be implemented quite straightforwardly however considering structures with non linear response the situation is more sophisticated since structural stability properties have to be taken into account the paper presents an approach to optimal design of statically loaded structures with non linear response it is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained these similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level which is lower or at most equal to the critical load level by this approach the structural stability requirements are taken into account in an effective manner the efficiency is illustrated with several examples involving kinematic as well as material non linear effects

on deriving a locally corrected nystrom scheme from a quadrature sampled moment method a novel high order method of moment procedure with quadrature point based discretization is presented the scheme is equivalent to a moment method employing smooth basis and testing functions applying a fixed point numerical quadrature approximation for the outer integral mapping the current to the quadrature points then leads to a formulation that is equivalent to that derived via the locally corrected nystrom method the convergence properties of the current density and rcs for smooth and singular geometries in two and three dimensions are also studied

limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers let p be a uniform isochronous cubic polynomial center we study the maximum number of small or medium limit cycles that bifurcate from p or from the periodic solutions surrounding p respectively when they are perturbed either inside the class of all continuous cubic polynomial differential systems or inside the class of all discontinuous differential systems formed by two cubic differential systems separated by the straight line y 0 in the case of continuous perturbations using the averaging theory of order 6 we show that the maximum number of small limit cycles that can appear in a hopf bifurcation at p is 3 and this number can be reached for a subfamily of these systems using the averaging theory of first order we prove that at most 3 medium limit cycles can bifurcate from the periodic solutions surrounding p and this number can be reached in the case of discontinuous perturbations using the averaging theory of order 6 we prove that the maximum number of small limit cycles that can appear in a hopf bifurcation at p is 5 and this number can be reached for a subfamily of these systems using the averaging method of first order we show that the maximum number of medium limit cycles that can bifurcate from the periodic solutions surrounding p is 7 and this number can be reached we also provide all the first integrals and the phase portraits in the poincare disc for the uniform isochronous cubic centers

gauss jacobi quadratures for weakly strongly hyper and nearly singular integrals in boundary integral equation methods for domains with sharp edges and corners abstract we present gauss jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular strongly singular hypersingular and nearly singular integrals that arise in integral equation formulations of potential problems for domains with sharp edges and corners the rules are tailored to weight functions with algebraic endpoint singularities of a fairly general form thus allowing one to easily incorporate a wide class of domains into the analysis numerical examples illustrate the accuracy and stability of the proposed algorithms it is shown that the same level of high accuracy can be achieved for any choice of the external variable the usefulness of the method is exemplified by application to the solution of a singular integral equation that arises in time harmonic electromagnetic scattering by either closed or open perfectly conducting cylindrical objects with edges and corners such as polygon cylinders and bent strips some practical aspects concerning the role of nearby singularities in achieving a highly accurate solution of singular integral equations are also discussed

nystrom type method in three dimensional electromagnetic diffraction by a finite pec rotationally symmetric surface time harmonic electromagnetic wave diffraction by a perfectly electrically conducting pec finite rotationally symmetric surface located in free space is investigated the problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations ies for the surface current components these ies are discretized by the nystrom type method of discrete singularities using the interpolation type quadrature formulas from the solutions of corresponding matrix equations the near and the far field patterns are obtained the presented method has guaranteed convergence for arbitrary not axially symmetric primary field

integral equation analysis of radiating structures of revolution a methods for solving radiation problems involving structures of revolution is presented that is based on the direct solutions of one dimensional integral equations for the currents the kernels of these equations are derived explicitly and their singularities are studied efficient methods for their computation are presented the numerical solution is obtained by a method of moments technique using sinusoidal basis functions applications include the determination of the current densities reflection coefficient and far field patterns for several waveguide fed structures numerical checks and comparisons with experiment demonstrate the accuracy of the method

a novel grid robust higher order vector basis function for the method of moments a set of novel grid robust higher order vector basis functions is proposed for the method of moments mom solution of integral equations for three dimensional 3 d electromagnetic em problems these basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the lagrange interpolation polynomials the highlight of these basis functions is that the lagrange interpolation points are chosen to be the same as the nodes of the well developed gaussian quadratures as a result the evaluation of the integrals in the mom is greatly simplified additionally the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch which is a very stringent requirement for traditional vector basis functions the proposed basis functions are implemented with point matching for the mom solution of the electric field integral equation the magnetic field integral equation and the combined field integral equation numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions

a general procedure for the direct computation of turning and bifurcation points we address the formulation and numerical implementation of general purpose algorithme suitable for the direct computation of stability points in non linear solid mechanics the effectiveness of the resulting algorithm is illustrated by numerical simulation that include bifurcation and loss of stability in elastoplasticity non linear rods and non linear three dimensional shells

full wave analysis and optimization of a tara like shield assisted paraboloidal reflector antenna using a nystrom type method using the recently developed method based on the rigorous theory of singular and hypersingular integral equations ies and nystrom type discretization a paraboloidal reflector assisted with a conical shield is investigated to decrease the computation time we propose a new method of calculation of the modal green s functions in the quasi optical range the far and near fields of the studied reflector are analyzed in the transmission and reception cases and reveal fine features that escape asymptotic analysis elementary numerical optimization of the shield assisted paraboloidal antenna is performed

minimum weight design of non linear elastic structures with multimodal buckling constraints it well known that multimodal instability is an event particularly relevant in structural optimization here in the context of non linear stability theory an exact method is developed for minimum weight design of elastic structures with multimodal buckling constraints given an initial design the method generates a sequence of improved designs by determining a sequence of critical equilibrium points related to decreasing values of the structural weight multimodal buckling constraints are imposed without repeatedly solving an eigenvalue problem and the difficulties related to the non differentiability in the common sense of state variables in multimodal critical states are overcome by means of the lagrange multiplier method further constraints impose that only the first critical equilibrium states local maxima or bifurcation points on the initial equilibrium path of the actual designs are taken into account copyright 2002 john wiley sons ltd

phase portraits of uniform isochronous quartic centers in this paper we classify the global phase portraits in the poincare disc of all quartic polynomial differential systems with a uniform isochronous center at the origin such that their nonlinear part is not homogeneous

minimum weight design of truss structures with geometric nonlinear behavior the paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior the nonlinear critical load is determined by finding the load level at which the hessian of the potential energy ceases to be positive definite a recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables number of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements element stresses system stability etc 1 2 the optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables the optimality criterion was derived by differentiating the lagrangian with respect to the design variables the displacements were assumed to be small and in the finite element analysis linear equilibrium equations were solved to determine the response of the structure to the ap plied loads in the case of system stability the constraints were defined see refs 3 6 by the associated linear eigenvalue problem this definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections the correct procedure for these structures would be to analyze the structure by using nonlinear equilibrium equations this will be particularly true for large space structures lss in this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior in the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode this design tends to become im perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub stantially the imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal see ref 7 a real structure has geometric im perfections and these structures tend to have nonlinear

method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas abstract this work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin dielectric circular disk on substrate antennas to simulate resistive and thin dielectric disk features we use two side generalized boundary conditions gbc the analysis is based on the singular integral equations ies and the method of analytical regularization mar exploiting a galerkin method gm with judicious basis functions which convert ies into the fredholm second kind infinite matrix equations unlike previously known numerical techniques this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency

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

a higher order multilevel fast multipole algorithm for scattering from mixed conducting dielectric bodies a higher order multilevel fast multipole algorithm mlfma is presented for computing electromagnetic scattering from three dimensional bodies comprising both conducting and dielectric objects the problem is formulated using the poggio miller chang harrington wu tsai 1973 1977 approach for multiple homogeneous dielectric objects and the combined field approach for conducting objects the resultant integral equations are discretized by the method of moments mom in which the conducting and dielectric surfaces interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling an implicit matrix filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions the resultant numerical system is then solved by mlfma which is tailored to accommodate the material properties of dielectric scatterers and the solution is accelerated using an incomplete lu decomposition preconditioner numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems

a recursive quadratic programming method with active set strategy for optimal design recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics there are two recursive quadratic programming methods that have been published in the literature one is by han and the other is by pshenichny published in 1977 and 1970 respectively the algorithm of pshenichny had been undiscovered until now and is examined here for the first time it is found that the proof of global convergence by han requires computing sensitivity coefficients derivatives of all constraint functions of the problem at every iteration this is prohibitively expensive for large scale applications in optimal design in contrast pshenichny has proved global convergence of his algorithm using only an active set strategy this is clearly preferable for large scale applications the method of pshenichny has been coded into a fortran program applications of this method to four example problems are presented the method is found to be very reliable however the method is found to be very sensitive to local minima i e it converges to a local minimum nearest to the starting design thus for optimal design problems which usually possess multiple local minima it is suggested that pshenichny s method be used as part of a hybrid method

on new triangle quadrature rules for the locally corrected nystrom method formulated on nurbs generated bezier surfaces in 3 d nonuniform rational b splines nurbs are the most widely used technique in today s geometric computer aided design systems for modeling surfaces combining the locally corrected nystrom lcn method with nurbs requires formulating lcn on both quadrilateral and triangular bezier surfaces as a typical nurbs generated bezier mesh includes elements of both the types while on quadrilateral elements the product of 1 d gaussian quadrature rules can be applied to lcn effectively gaussian integration rules available for triangles cannot efficiently be applied to lcn for two reasons first they do not possess the same number of quadrature points as the number of functions in a complete set of polynomial basis at an arbitrary order second they exacerbate the condition number of the resulting matrix equation at higher orders due to an increasing density of quadrature points near the edges and corners of triangles in this paper we construct a new set of quadrature rules for bezier triangles i e degenerate quadrilaterals based on the newton cotes equidistant quadrature rules and apply these rules to the lcn solution of the electric magnetic and combined field integral equations results show that the new family of quadrature rules overcomes both the aforementioned issues and can be applied to lcn effectively for orders from 0 to 9 inclusively

study of mixed order basis functions for the locally corrected nystro spl uml m method a high order locally corrected nystro spl uml m lcn method employing the mixed order basis functions proposed by c 80al spl iota s 80kan and peterson is presented for the electromagnetic scattering by targets composed of both dielectric and conducting bodies an integral operator based on a combined field formulation for conducting surfaces and a mu spl uml ller formulation for dielectric surfaces is used it is found that for general scattering objects mixed order basis functions accelerate the convergence of the lcn solution can eliminate spurious charges and can significantly reduce the condition number of the impedance matrix

shape optimal design of elastic space frames with non linear response this paper describes an approach to shape optimal design of elastic planar frames with non linear response the foundation of the proposed approach forms an appropriate strategy of shape representation of the structure based on the design element technique a frame structure is treated as to be assembled from several frame design elements which in turn may consist of several appropriately joined beam finite elements the shape of each frame design element is defined by convenient functions involving bezier blending polynomials the original formulation of the beam finite element proposed by saje is modified in order to fit nicely into the context of the frame design element technique the formulation of the shape optimal design problem in a form of a problem of non linear mathematical programming and its solution by employing gradient based methods of mathematical programming are discussed briefly the theory is illustrated with two numerical examples

design sensitivity analysis and optimization of nonlinear structuralresponse using incremental procedure this paper describes procedures for design sensitivity analysis of nonlinear structural response using the incremental solution scheme the total and updated lagrangian approaches are discussed sensitivity analyses for the stress strain and displacement constraints are developed in the optimization process the buckling load constraint is also imposed numerical aspects of design sensitivity analysis are discussed three numerical examples are solved to illustrate the design sensitivity analysis and optimization process the numerical procedures are stable and work well they can be applied to more complex structures to optimize them

numerical solution of the helmholtz equation in 2d and 3d using a high order nystrom discretization we show how to solve time harmonic scattering problems by means of a high order nystrom discretization of the boundary integral equations of wave scattering in 2d and 3d the novel aspect of our new method is its use of local corrections to the discretized kernel in the vicinity of the kernel singularity enhanced by local corrections the new algorithm has the simplicity and speed advantages of the traditional nystrom method but also enjoys the advantages of high order convergence for controlling solution error we explain the practical details of implementing a scattering code based on a high order nystrom discretization and demonstrate by numerical example that a scattering code based on this algorithm can achieve high order convergence to the correct answer we also demonstrate its performance advantages over a high order galerkin code

fast solution methods in electromagnetics various methods for efficiently solving electromagnetic problems are presented electromagnetic scattering problems can be roughly classified into surface and volume problems while fast methods are either differential or integral equation based the resultant systems of linear equations are either solved directly or iteratively a review of various differential equation solvers their complexities and memory requirements is given the issues of grid dispersion and hybridization with integral equation solvers are discussed several fast integral equation solvers for surface and volume scatterers are presented these solvers have reduced computational complexities and memory requirements

locally corrected multidimensional quadrature rules for singular functions accurate numerical integration of singular functions usually requires either adaptivity or product integration both interfere with fast summation techniques and thus hamper large scale computations this paper presents a method for computing highly accurate quadrature formulas for singular functions which combine well with fast summation methods given the singularity and the n nodes we first construct weights which integrate smooth functions with order k accuracy then we locally correct a small number of weights near the singularity to achieve order k accuracy on singular functions as well the method is highly efficient and runs in o nk 2d n log 2 n time and o k 2d n space we derive precise error bounds and time estimates and confirm them with numerical results which demonstrate the accuracy and efficiency of the method in large scale computations as part of our implementation we also construct a new adaptive multidimensional product gauss quadrature routine with an effective error

a sparse factorization for fast computation of localizing modes localizing modes provide an effective basis for developing efficient error controlled factorizations of the dense matrices encountered in integral equation formulations of wave phenomena at low to moderate frequencies an essential component of these factorization algorithms is the numerical determination of the underlying localizing modes this communication describes the details of an efficient procedure for computing the so called non overlapping localizing modes the principle component of the procedure is a qr like factorization of the sparse multilevel data structure used to compress discrete integral operators numerical examples demonstrate the performance of the algorithm

efficient handling of stability problems in shell optimization by asymmetric worst case shape imperfection the paper presents an approach to shape optimization of proportionally loaded elastic shell structures under stability constraints to reduce the stability related problems a special technique is utilized by which the response analysis is always terminated before the first critical point is reached in this way the optimization is always related to a precritical structural state the necessary load carrying capability of the optimal structure is assured by extending the usual formulation of the optimization problem by a constraint on an estimated critical load factor since limit points are easier to handle the possible presence of bifurcation points is avoided by introducing imperfection parameters they are related to an asymmetric shape perturbation of the structure during the optimization the imperfection parameters are updated to get automatically the worst case pattern and amplitude of the imperfection both the imperfection parameters and the design variables are related to the structural shape via the design element technique a gradient based optimizer is employed to solve the optimization problem three examples illustrate the proposed approach copyright 2007 john wiley sons ltd

exponentially converging nystrom methods in scattering from infinite curved smooth strips part 1 tm case low order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required high order modeling on the other hand can fill the need for enhanced accuracy but at the expense of greater implementation cost to supplement such methods this paper presents nystrom techniques both easily implemented and highly accurate relevant to te scattering by arbitrarily shaped smooth infinite curved strips the analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges as a result the proposed solutions are exponentially converging in addition by eliminating inner product integrals closed form analytical expressions are obtained for all matrix elements thus our algorithms have very low implementation and computational cost detailed numerical examples and case studies amply demonstrate the efficiency stability and extremely high accuracy of the algorithms these algorithms apply uniformly from electrically small to electrically large conducting screens with only slight modifications the present analysis can be also used to obtain exponentially converging galerkin solutions

uniform isochronous cubic and quartic centers revisited abstract in this paper we completed the classification of the phase portraits in the poincare disc of uniform isochronous cubic and quartic centers previously studied by several authors there are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively