vibration analysis of shear deformable circular arches by the differential quadrature method the differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in plane and out of plane vibration of circular arches based on the bresse timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped clamped end conditions and the results are compared with numerical solutions by another method the present method gives good accuracy with only a limited number of grid points

influence of centerline extensibility on the in plane free vibrations of loaded circular arches free vibrations of circular arches about a prestressed static equilibrium state are investigated the equations of motion for the small amplitude free vibrations about the initial equilibrium state attained under distributed tangential and normal loading derived in a previous paper and specialized to constant curvature are used particular attention is given to the influence of centerline stretching during the vibratory motion the vanishing of the loaded free vibration frequencies signals static buckling and the load intensities at which the frequencies go to zero correspond to the static buckling loads free vibrations with no initial loading is treated as a special case of the problem considered it is shown that exact numerical values for the frequencies can be obtained in this case in general the presence of distributed initial loading precludes the possibility of obtaining closed form analytical solutions barring a few simple loading situations such as uniform constant directional pressure as the governing differential equations have variable coefficients in the present work numerical results are obtained for uniform arches subjected to gravity loading the galerkin method with polynomial trial functions that satisfy the geometric boundary conditions is employed in obtaining accurate values of free vibration frequencies convergence of the method with increasing number of terms in the assumed expansion representing the true solution is demonstrated arches with pinned and clamped end support conditions are considered considerably different frequencies are found depending upon whether one includes or ignores the influence of centerline stretching during the vibratory motion

in plane vibration of circular arches with variable cross sections abstract free and forced in plane vibrations of circular arches with variable cross sections are investigated using the kirchhoff assumptions for thin beams and taking the neutral axis as inextensible a closed form solution is obtained for circular arches of uniform cross section this exact solution is used for circular arches with stepped cross sections and is applied to obtain an approximate solution for arches with non uniform cross sections for free vibration an analytic form of frequency equation is obtained by using the general solution expressed in terms of some initial parameters at one end of the arch while for forced vibration the system s response is obtained analytically by solving a set of algebraic equations with only three unknowns several examples are presented to illustrate the validity and accuracy of the method

the curved beam deep arch finite ring element revisited an attempt is made to understand the errors arising in curved finite elements which undergo both flexural and membrane deformation it is shown that with elements of finite size i e a practical level of discretization at which reasonably accurate results can be expected there can be errors of a special nature that arise because the membrane strain fields are not consistently interpolated with terms from the two independent field functions that characterize such a problem these lead to errors described here as of the second kind and a physical phenomenon called membrane locking it seems possible to determine optimal integration rules that will allow the extensional deformation of a curved beam deep arch finite ring element to be modelled by independently chosen low order polynomial functions and which will recover the inextensional case in the penalty limit of extreme thinness without spurious locking constraints what is emphasized is that the choice of shape functions or subsequent operations to determine the discretized functionals must consistently model the physical requirements the problem imposes on the field variables

efficient 2 dimensional approximate matching of half rectangular figures efficient algorithms exist for the approximate two dimensional matching problem for rectangles this is the problem of finding all occurrences of an m m pattern in an n n text with no more than k mismatch insertion and deletion errors in computer vision it is important to generalize this problem to non rectangular figures we make progress towards this goal by defining half rectangular figures of height m and area a the approximate two dimensional matching problem for half rectangular patterns can be solved using a dynamic programming approach in time o an2 we show an o kn2formula formula k2n2 algorithm which combines convolutions with dynamic programming note that our algorithm is superior to previous known solutions for k m13 at the heart of the algorithm are the smaller matching problem and the k aligned ones with location problem these are interesting problems in their own right efficient algorithms to solve both these problems are presented

exact solution of in plane vibrations of circular arches with account taken of axial extension transverse shear and rotatory inertia effects exact solution of free in plane vibrations of circular arches of uniform cross section is given by considering axial extension transverse shear and rotatory inertia effects in contrast with kirchhoff s beam theory the restrictions of perpendicular cross section and inextensible arc length are removed the principal axes of the cross section are assumed to coincide with the principal normal and binormal vectors of the centerline of the beam a solution procedure is applied to obtain the fundamental matrix for various end conditions natural frequencies and mode shapes are given in figures and tables

two genetic algorithms for solving the uncapacitated single allocation p hub median problem this paper deals with the uncapacitated single allocation p hub median problem usaphmp two genetic algorithm ga approaches are proposed for solving this np hard problem new encoding schemes are implemented with appropriate objective functions both approaches keep the feasibility of individuals by using specific representation and modified genetic operators the numerical experiments were carried out on the standard orlib hub data set both methods proved to be robust and efficient in solving usaphmp with up to 200 nodes and 20 hubs the second ga approach achieves all previously known optimal solutions and achieves the best known solutions on large scale instances

on the construction of classes of suffix trees for square matrices we provide a uniform framework for the study of index data structures for a two dimensional matrixtext1 n 1 n whose entries are drawn from an ordered alphabet an index fortextcan be informally seen as the two dimensional analog of the suffix tree for a string it allows on line searches and statistics to be performed ontextby representing compactly the n3 square submatrices oftextin optimalo n2 space we identify 4n 1families of indices fortext each containing ni 1 2i 1 isomorphic data structures we also develop techniques leading to a single algorithm that efficiently builds any index in any family ino n2logn time ando n2 space such an algorithm improves in various respects the algorithms for the construction of the pat tree and the lsuffix tree the framework and the algorithm easily generalize tod 2 dimensions moreover as part of our algorithm we provide new algorithmic tools that yield a space efficient implementation of the naming scheme of r karpet al in proceedings fourth symposium on theory of computing pp 125 136 for strings and matrices

exact two dimensional solutions for in plane natural frequencies of laminated circular arches exact analysis on the in plane free vibration of simply supported laminated circular arches is carried out based on the two dimensional theory of elasticity the method of separation of variables is employed to expand all the variables into fourier series about the longitudinal coordinate so that the system of partial differential equations is reduced to the ordinary one about the radial coordinate the state space method is used to derive a series of simultaneous first order differential equations due to the variable coefficients posed by the radial coordinate analytical solutions are rather unpractical and hence the approximate laminate model is adopted to translate the state equation into the one with constant coefficients the relation between the state vector at the inner and outer surface of the arch is finally obtained according to the continuity conditions at interfaces and the traction free conditions at the two lateral surfaces the formulation is validated by comparing the present results to those available in literature effects of geometric parameters and stacking sequences on the natural frequencies of circular arches are investigated and discussed numerical results presented in this paper provide benchmarks for future analysis of circular arches

elasticity solution for vibration of 2 d curved beams with variable curvatures using a spectral sampling surface method summary an accurate spectral sampling surface method for the vibration analysis of 2 d curved beams with variable curvatures and general boundary conditions is presented the method combines the advantages of the sampling surface method and spectral method the formulation is based on the 2 d elasticity theory which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced specifically a set of non equally spaced sampling surfaces parallel to the beam s middle surface are primarily collocated along the thickness direction and the displacements of these surfaces are chosen as fundamental beam unknowns this fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces each of the fundamental beam unknowns is then invariantly expanded as chebyshev polynomials of the first kind and the problems are stated in variational form with the aid of the penalty technique and lagrange multipliers which provide complete flexibility to describe any arbitrary boundary conditions finally the desired solutions are obtained by the variational operation copyright 2016 john wiley sons ltd

in plane free vibration analysis of circular arches with varying cross sections using differential quadrature method abstract a differential quadrature dq methodology recently developed by the authors is used to obtain a general and a computationally efficient and accurate dq solution for free vibration of variable cross section circular thin arches as an improvement to the classical theory and in order to evaluate the higher order natural frequencies more accurately the commonly used hypothesis of the inextensibility of the central axis is removed this enables one to study the effects of slenderness ratio on the natural frequencies especially at higher order modes rotary inertia is included in the formulation and its influence on natural frequencies is studied arches with different types of boundary conditions including those with elastic constraint against rotation at their ends are considered for the cases where a change in the cross sectional or material properties of the arch occurs a numerical domain decomposition technique in conjunction with dq methodology is developed and incorporated to verify the accuracy of the methodology the results are compared with those of exact solutions and or other approaches such as finite elements rayleigh ritz galerkin cell discretization methods and other dq methodologies in particular excellent solution agreements are achieved with those of exact solutions the generalized differential quadrature rule and the optimized rayleigh ritz method solutions

a black box for online approximate pattern matching we present a deterministic black box solution for online approximate matching given a pattern of length m and a streaming text of length n that arrives one character at a time the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives our solution requires o s j 1 l o g 2 mt n 2 j 1 n time for each input character where t n m is the total running time of the best offline algorithm the types of approximation that are supported include exact matching with wildcards matching under the hamming norm approximating the hamming norm k mismatch and numerical measures such as the l 2 and l 1 norms for these examples the resulting online algorithms take o log 2m o mlogm o log 2m e 2 o klogklogm o log 2m and o mlogm time per character respectively the space overhead is linear in the pattern size which we show is optimal for any deterministic algorithm

genetic algorithms for solving the discrete ordered median problem in this paper we present two new heuristic approaches to solve the discrete ordered median problem domp described heuristic methods named hga1 and hga2 are based on a hybrid of genetic algorithms ga and a generalization of the well known fast interchange heuristic gfi in order to investigate the effect of encoding on ga performance two different encoding schemes are implemented binary encoding in hga1 and integer representation in hga2 if binary encoding is used hga1 new genetic operators that keep the feasibility of individuals are proposed integer representation keeps the individuals feasible by default so hga2 uses slightly modified standard genetic operators in both methods caching ga technique was integrated with the gfi heuristic to improve computational performance the algorithms are tested on standard orlib p median instances with up to 900 nodes the obtained results are also compared with the results of existing methods for solving domp in order to assess their merits

closed form solutions of a multi cracked circular arch under static loads abstract generalised functions have been widely adopted in structural mechanics to treat singularities of beam like structures however due to the curved geometry that couples axial and transversal displacements their use has never been explored for curved beams in this paper the capability of distributions of leading to closed form exact solutions for multi cracked circular arch is shown the exact closed form solution of a circular euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained damage under the form of concentrated cracks has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of dirac s delta functions the resulting nontrivial generalised six order differential equations have been derived and solved in closed form independently of the number of along arch concentrated cracks the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression this latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem the results have been validated through some comparisons with finite element numerical simulations examples referred to multi cracked euler arches with different boundary conditions damage and load scenarios are presented

efficient two dimensional pattern matching in the presence of errors abstract we give an algorithm for two dimensional pattern matching in the presence of errors we find that the complexity of our algorithm is o kn 1 n 2 log n 2 n 1 2 n 2 kn 1 m 1 m 2 where the pattern is an n 1 n 2 array the text is an m 1 m 2 array and k is the number of mismatches allowed

quality of trial functions in quadratic isoparametric representation of an arc an examination is made of displacement trial functions found in the quadratic isoparametric representation of an arc special attention is given to the quality of curvature change description and to effective manipulation of the trial functions various interpolation formulae are derived which have relevance to curved shell finite element design under love kirchhoff assumptions

generalized string matching given a pattern string of length n and an object string of length m the string matching problem asks for the positions of all occurrences of the pattern in the object string this paper investigates a generalization of string matching in which the pattern is a sequence of pattern elements each compatible with a set of symbols the alphabet of symbols is infinite with its members encoded in a finite alphabet in contrast to standard string matching which can be solved in simultaneous linear time and constant space it is shown that generalized string matching requires a time space product of omega n 2 log n on a powerful model of computation when the alphabet is restricted to n symbols our proof uses a method of borodin the obvious algorithm for generalized string matching requires time o nm where n is the length of the encoding of the pattern and m is that of the object string we describe an algorithm which solves generalized string matching in time o n m mn 1 2 o

order preserving matching we introduce a new string matching problem called order preserving matching on numeric strings where a pattern matches a text if the text contains a substring of values whose relative orders coincide with those of the pattern order preserving matching is applicable to many scenarios such as stock price analysis and musical melody matching in which the order relations should be matched instead of the strings themselves solving order preserving matching is closely related to the representation of order relations of a numeric string we define the prefix representation and the nearest neighbor representation of the pattern both of which lead to efficient algorithms for order preserving matching we present efficient algorithms for single and multiple pattern cases for the single pattern case we give an o nlogm time algorithm and optimize it further to obtain o n mlogm time for the multiple pattern case we give an o nlogm time algorithm

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

the submatrices character count problem an efficient solution using separable values the subsequence character count problem has as its input an array s s 1 s n of symbols over alphabet and a natural number m its output is for every i i 1 n m 1 the number of different alphabet symbols occurring in the subsequence s i s i 1 s i m 1 the subsequence character count problem is a natural problem that has many uses it can be solved in linear time for finite alphabets and in time o n log m for infinite alphabets when the character count problem is generalized to two dimensions it becomes the submatrix character count problem its input is an n n matrix t over alphabet and a natural number m its output is for every i j i j 1 n m 1 the number of different alphabet symbols occurring in the submatrix t i k j l k 0 m 1 l 0 m 1 the straightforward one dimensional solution slides a window along the text adding an element and deleting an element at every step the problem with two dimensions is that at every move of the window there are m elements added and m deleted in this paper we present an alternate one dimensional solution that generalizes to two dimensions we achieve a o n2 time solution to the submatrix character count problem over a finite alphabet and a o n2 log m solution over an infinite alphabet

a generalized differential quadrature element method abstract the generalized differential quadrature element method gdqem has been proposed the element weighting coefficients are generated by a generic differential quadrature gdq with which the element weighting coefficients for elements having arbitrary configurations can be straightly generated by using this gdq technique the governing differential or partial differential equations defined on all elements the transition conditions on the inter element boundary of two adjacent elements and the boundary conditions can be discretized a global algebraic equation system can be obtained by assembling all of the discretized equations this method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm without adopting the mapping technique

free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four parameter power law distribution based on the first order shear deformation theory fsdt this paper focuses on the dynamic behavior of moderately thick functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal these constituents are graded through the thickness from one surface of the shell to the other a generalization of the power law distribution presented in literature is proposed two different four parameter power law distributions are considered for the ceramic volume fraction some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power law distributions for the first power law distribution the bottom surface of the structure is ceramic rich whereas the top surface can be metal rich ceramic rich or made of a mixture of the two constituents and on the contrary for the second one symmetric and asymmetric volume fraction profiles are presented in this paper the homogeneous isotropic material can be inferred as a special case of functionally graded materials fgm the governing equations of motion are expressed as functions of five kinematic parameters by using the constitutive and kinematic relationships the solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell the discretization of the system equations by means of the generalized differential quadrature gdq method leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology numerical results concerning six types of shell structures illustrate the influence of the power law exponent of the power law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered

nonconservative stability problems via generalized differential quadrature method abstract in this paper the generalized differential quadrature gdq method is applied to solve classical and nonclassical nonconservative stability problems various cantilever beams subjected to slope dependent forces are considered first the governing differential equation for a nonuniform column subjected to an arbitrary distribution of compressive subtangential follower forces is obtained the effect of the variability of the mechanical properties along the beam length is also considered then the application of the gdq procedure leads to a discrete system of algebraic equations from which the system critical loads can be obtained by solving an associated eigenvalue problem a parametrical study for different levels of nonconservativeness of the applied load is carried out for some classical benchmark cases such as beck s leipholz s and hauger s column problems finally applications to geometrically and mechanically tapered beams subjected to nonpotential subtangential follower forces are investigated as nonclassical cases it has been proved that the method can efficiently solve structural nonconservative elastic problems and more in general problems governed by a nonsymmetric system of algebraic equations

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

the uniqueness characteristics of mixed finite element methods in linear elasticity having established the non uniqueness in general of quadratic linear functionals in elasticity the investigative work on this topic is reviewed whence it is noted that there is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination a comparison of the weighted averages obtained from the single field and reissner s principles is then used to identify a higher order uniqueness criterion for the latter a detailed consideration of the application of the new condition to the arch equations demonstrates how and why singular solutions can be obtained and thence how suitable forms of remedial action can often be identified finally several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed methods

an alphabet independent approach to two dimensional pattern matching there are many solutions to the string matching problem that are strictly linear in the input size and independent of alphabet size furthermore the model of computation for these algorithms is very weak they allow only simple arithmetic and comparisons of equality between characters of the input in contrast algorithms for two dimensional matching have needed stronger models of computation most notably assuming a totally ordered alphabet the fastest algorithms for two dimensional matching have therefore had a logarithmic dependence on the alphabet size in the worst case this gives an algorithm that runs in o n 2 log m with o m 2 log m preprocessing the authors show an algorithm for two dimensional matching with an o n 2 text scanning phase furthermore the text scan requires no special assumptions about the alphabet i e it runs on the same model as the standard linear time string matching algorithm the pattern preprocessing requires an ordered alphabet and runs with the same alphabet dependency as the previously known algorithms

differential quadrature for multi dimensional problems the technique of differential quadrature for the solution of partial differential equations introduced by bellman et al is extended and generalized to encompass partial differential equations involving multiple space variables approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented application of these formulae is demonstrated on the solution of the convection diffusion equation for the two and three dimensional space dependent cases and for both the transient and steady state dispersion of inert neutrally buoyant pollutants from continuous sources into an unbounded atmosphere

2 d differential quadrature solution for vibration analysis of functionally graded conical cylindrical shell and annular plate structures this paper focuses on the dynamic behavior of functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the first order shear deformation theory fsdt is used to analyze the above moderately thick structural elements the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal that are graded through the thickness from one surface of the shell to the other two different power law distributions are considered for the ceramic volume fraction the homogeneous isotropic material is inferred as a special case of functionally graded materials fgm the governing equations of motion expressed as functions of five kinematic parameters are discretized by means of the generalized differential quadrature gdq method the discretization of the system leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology for the homogeneous isotropic special case numerical solutions are compared with the ones obtained using commercial programs such as abaqus ansys nastran straus pro mechanica very good agreement is observed furthermore the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good different typologies of non uniform grid point distributions are considered finally for the functionally graded material case numerical results illustrate the influence of the power law exponent and of the power law distribution choice on the mechanical behavior of shell structures

general anisotropic doubly curved shell theory a differential quadrature solution for free vibrations of shells and panels of revolution with a free form meridian abstract the generalized differential quadrature gdq method is applied to study the dynamic behavior of anisotropic doubly curved shells and panels of revolution with a free form meridian the first order shear deformation theory fsdt is used to analyze the above mentioned moderately thick structural elements in order to include the effect of the initial curvature in the evaluation of the stress resultants three different approaches specifically qatu approach toorani lakis approach and reissner mindlin approach are considered and compared an improvement of the classical reissner mindlin theory crmt using a different kinematical model is considered by so doing a generalization of the theory of anisotropic doubly curved shells and panels of revolution is proposed four different anisotropic shell theories namely general first order shear deformation theory by qatu gfsdtq general first order shear deformation theory by toorani lakis gfsdttl general first order shear deformation theory by reissner mindlin gfsdtrm and classical reissner mindlin theory crmt are compared in order to show the differences and the accuracy of these theories the solution is given in terms of generalized displacement components of points lying on the middle surface of the shell simple rational bezier curves are used to define the meridian curve of the revolution structures results are obtained taking the meridian and circumferential coordinates into account without using the fourier modal expansion methodology furthermore gdq results are compared with those obtained by using commercial programs such as abaqus ansys nastran straus and pro mechanica very good agreement is observed

analytical and differential quadrature results for vibration analysis of damaged circular arches the present paper focuses on in plane linear free vibrations of circular arches in undamaged and damaged configurations for the model herein utilized the equations of motion in terms of displacements and rotation take into account shearing and axial deformations and rotary inertia the cracked section of the arch is modeled with an elastic spring an exact analytical method of solution and an approximate numerical one are presented the first method solves the fundamental system in closed form by means of a characteristic polynomial the second one is based on a simple and efficient differential quadrature and domain decomposition technique natural frequencies and mode shapes are computed for some significant cases showing very good agreement between the two approaches

deterministic sampling a new technique for fast pattern matching consider the following three stage strategy for recognizing patterns in larger scenes mimic randomization deterministically sample several positions of the pattern search for sample find all occurrences of the sample in the scene verify for each occurrence of the sample verify occurrence of the full pattern this strategy has led to the core of the new idea given in this paper consider the string matching problem given the pattern a sample of its positions is carefully selected whose size is at most logarithmic the deterministic sample then the sample is searched for for nonperiodic patterns the sample has the following perhaps surprising property it is possible to disqualify all occurrences of the sample positions but one within each neighborhood of locations in the text without any further comparisons of characters this provides sparse verification this approach enables the text analysis stages search for sample and verify to be performed in o log n time and optimal spe

application of the generalized differential quadrature rule to initial boundary value problems partial differential equations pdes for the forced vibration of structural beams are solved in this paper using the recently proposed generalized differential quadrature rule gdqr the gdqr techniques are first applied to both spatial and time dimensions simultaneously as a whole no other classical methods are needed in the time dimension the objective of this paper is to formularize the gdqr expressions and corresponding explicit weighting coefficients while the derivation of explicit weighting coefficients is one of the most important aspects in the differential quadrature methods it should be emphasized that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems and they are distinctly different for pdes of different orders an euler beam and a timoshenko beam are employed as examples accurate results are obtained the proposed procedures can be applied to problems in other disciplines of sciences and technology where the problems may be governed by other pdes with different orders in the time or spatial dimension

stability and accuracy of three fourier expansion based strong form finite elements for the free vibration analysis of laminated composite plates summary in the present paper strong form finite elements are employed for the free vibration study of laminated arbitrarily shaped plates in particular the stability and accuracy of three different fourier expansion based differential quadrature techniques are shown these techniques are used to solve the partial differential system of equations inside each computational element the three approaches are called harmonic differential quadrature fourier differential quadrature and improved fourier expansion based differential quadrature methods the improved fourier expansion based differential quadrature method implements auxiliary functions in order to approximate functional derivatives up to the fourth order with respect to the fourier differential quadrature method that has a basis made of sines and cosines all the present applications are related to literature comparisons and the presentation of new results for further investigation within the same topic a study of such kind has never been proposed in the literature and it could be useful as a reference for future investigation in this matter copyright 2016 john wiley sons ltd

exact and approximate dynamic analysis of circular arches using dqm abstract a modified version of the differential quadrature method is applied to two versions of the sixth order differential equation of motion governing free in plane inextensional vibrations of circular arches see henrych 1981 all the boundary conditions can be imposed exactly without introducing points see e g bert and malik 1996 consequently the results are calculated with high precision and a comparison between exact and approximate frequencies becomes possible the convergence rate of the discretization method is shown to be very fast even for the higher eigenvalues so that a small number of lagrangian coordinates permits a good approximation to the true results it is shown that the approximate formulation leads to noticeable errors for the first frequencies of deep arches whereas shallow arches and higher order frequencies can be safely calculated with the simplified approach the paper ends with some tables in which the first ten free vibrations frequencies for clamped arches two hinged arches and cantilever arches are compared with some known results from the literature

an ilp formulation and genetic algorithm for the maximum degree bounded connected subgraph problem a general instance of a degree constrained subgraph problem may be found in an edge weighted or vertex weighted graph g whereas the objective is to find an optimal weighted subgraph subject to certain degree constraints on the vertices of the subgraph this class of combinatorial problems has been extensively studied due to its numerous applications in network design if the input graph is bipartite these problems are equivalent to classical transportation and assignment problems in operational research this paper is an illustration of a research of the np hard maximum degree bounded connected subgraph problem mdbcs it is a classical np complete problem moreover this paper offers a first integer linear programming formulation of the mdbcs and a formal proof that it is correct a genetic algorithm for obtaining the optimal solution of mdbcs has also been provided the proposed solution comprises a genetic algorithm ga that uses binary representation fine grained tournament selection one point crossover simple mutation with frozen genes and caching technique