buckling of arbitrary quadrilateral anisotropic plates the problem of buckling of arbitrary quadrilateral anisotropic plates with different boundary conditions under combined in plane loading is considered a rayleigh ritz method combined with a variational formulation and a first order transverse shear deformation theory is used the ritz functions consist of polynomials which include circulation functions that impose various boundary conditions numerical results are obtained for isotropic orthotropic and anisotropic plates with skewed geometries and are compared with existing results that use series solutions and with results generated from finite element simulations

eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

prebuckling and buckling of unsymmetrically laminated composite panels with stringer run outs a meshless approach is developed and used to predict buckling loads of discretely assembled composite panels made from skin and stiffeners particular emphasis is given to stringer run outs within a stiffened panel where abrupt eccentricity can trigger very large transverse displacements of the skin in front of the run out tip and perturb the internal in plane loads distribution the effect of load eccentricity is included in the formulation the final set of nonlinear equations is obtained by combining von karman s formulation for moderately large deflections in plates with an extended timoshenko approach for small initial perturbations solutions are calculated by means of a rayleigh ritzmethod in conjunctionwith agalerkin technique orthogonal eigenfunctions are employed to expand the variables of interest in generalized fourier series an iterative algorithm is proposed to calculate buckling loads limits of applicability convergence of results and further potential exploitations are discussed numerical results are compared with those from finite element analysis and other numerical approaches

static and stability analyses of arbitrary straight sided quadrilateral thin plates by dqm abstract a differential quadrature dq methodology is employed for the static and stability analysis of irregular quadrilateral straight sided thin plates a four noded super element is used to map the irregular physical domain into a square computational domain second order transformation schemes with relative ease and low computational effort are employed to transform the fourth order governing equations of thin plates between the domains within the domain the displacements are the only degrees of freedom whereas along the boundaries the displacements as well as the second order derivatives of the displacements with respect to the associated normal coordinate variables in the computational domain are the two sets of degrees of freedom the implementation procedures for different boundary conditions including free edge boundaries are formulated to demonstrate the accuracy convergency and stability of the methodology detailed studies of skewed and trapezoidal plates for different geometries under different boundary and loading conditions are made good agreement is achieved between the results of the present methodology and those of other dq methodologies or other comparable numerical algorithms

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

buckling of arbitrary quadrilateral plates with intermediate supports using the galerkin method abstract a numerical method is developed for the stability analysis of arbitrary quadrilateral shaped elastic plates with internal supports the procedure uses the galerkin method in conjunction with the natural coordinates of the plate as a basis for the analysis of general plates the method is programmed and several numerical exaples are presented to illustrate the scope and efficacy of the procedure local plate buckling loads of skew rhombic trapezoidal and rectangular plates with intermediate line supports are obtained and where possible the results are compared with known solutions in the literature

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

approximate nonlinear analysis method for debonding of skin stringer composite assemblies doi 10 2514 1 31914 a nonlinear approach is developed and used to predict crack initiation in discretely assembled composite panels made from skin and stringers particular emphasis is given to stringer run outs within a stiffened panel for the optimization of novel composite wing configurations the nonlinear structural behavior is obtained by means of the von karman formulation for moderately large deflections in plates three dimensional assemblies are schematized and the effect of eccentricity is included in the simulation solutions are calculated by means of a rayleigh ritz approach based on galerkin s orthogonal eigenfunctions and a linear elastic fracture mechanics based model is used to simulate the crack initiation in the critical regions numerical results obtained by means of the present method are validated against tests reported in the literature and compared with advanced nonlinear finite element analysis limits of applicability and further potential exploitations are discussed a validation study showed fairly good correlation with reported experimental data

static and dynamic analysis of arbitrary quadrilateral flexural plates by b3 spline functions abstract this paper presents static and free vibration analysis of arbitrary quadrilateral flexural plates by b3 spline functions an actual arbitrary quadrilateral thin flat plate is mapped onto a square basic plate and a superelement is constructed for the whole plate the present numerical analysis is based on a spline net with finite spline points on the square basic plate combination of b3 spline functions gives an easy way to satisfy various boundary conditions the displacement function constructed by b3 spline functions in two directions has been formed to possess more flexibility to model the deflection shape efficiently the main features of the present method are minimal input preparation easier programming and higher accuracy achieved by a system with fewer degrees of freedom compared with analytical solutions and other numerical methods the method proposed yields excellent results for the test cases considered

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

computability of probability measures and martin lof randomness over metric spaces in this paper we investigate algorithmic randomness on more general spaces than the cantor space namely computable metric spaces to do this we first develop a unified framework allowing computations with probability measures we show that any computable metric space with a computable probability measure is isomorphic to the cantor space in a computable and measure theoretic sense we show that any computable metric space admits a universal uniform randomness test without further assumption

stability and vibration of shear deformable plates first order and higher order analyses abstract this work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions the reissener mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of reddy have been applied to the plate s analysis the governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy the solution is obtained by the extended kantorovich method this approach is combined with the exact element method for the vibration and stability analysis of compressed members which provides for the derivation of the exact dynamic stiffness matrix including the effect of in plane and inertia forces the large number of numerical examples demonstrates the applicability and versatility of the present method the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate s theory and with published results many new results are given too

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

rapid analysis of variable stiffness beams and plates legendre polynomial triple product formulation copyright 2017 john wiley sons ltd numerical integration techniques are commonly employed to formulate the system matrices encountered in the analysis of variable stiffness beams and plates using a ritz based approach computing these integrals accurately is often computationally costly herein a novel alternative is presented the recursive analytical polynomial integral definition rapid formulation the rapid formulation offers a significant improvement in the speed of analysis achieved by reducing the number of numerical integrations that are performed by an order of magnitude a common legendre polynomial basis is employed for both trial functions and stiffness load variations leading to a common form for the integrals encountered the legendre polynomial basis possesses algebraic recursion relations that allow these integrals to be reformulated as triple products with known analytical solutions defined compactly using the wigner 3j coefficient the satisfaction of boundary conditions calculation of derivatives and transformation to other bases is achieved through combinations of matrix multiplication with each matrix representing a unique boundary condition or physical effect therefore permitting application of the rapid approach to a variety of problems indicative performance studies demonstrate the advantage of the rapid formulation when compared to direct analysis using matlab s integral and integral2 copyright 2017 john wiley sons ltd

further characterizations of design optimality and admissibility for partial parameter estimation in linear regression the paper gives a contribution to the problem of finding optimal linear regression designs when only s out of k regression parameters are to be estimated also a treatment of design admissibility for the parameters of interest is included previous results of kiefer and wolfowitz 1959 karlin and studden 1966 and atwood 1969 are generalized in particular a connection to tchebycheff type approximation of ri valued functions is found which has been known in case s 1 strengthened versions of the results are obtained for invariant designs in situations when invariance properties of the regression setup are available applications are given to multiple quadratic regression and to one dimensional polynomial regression 1 introduction consider a linear regression y x a f x x e with an unknown coefficient vector a e r k and a known r valued function f on the experimental region y the range f y is assumed to be compact as usual observations y1 yn on the dependent variable y taken at points xl xn e e x respectively are assumed to have expectations y x 1 0 and to be pairwise uncorrelated suppose that the experiment aims at estimating ka where k is a given s x k matrix of rank s for example when the first s components of a are to be estimated one has k is 0 where it denotes the unit matrix of order s we will study design optimality and admissibility for estimating ka within the approximate design theory an approximate design is a probability measure on x with finite support the infornation matrix per observation and unit of variance of f is m t ff x f x dd x e f x f x ox f x supp

buckling analysis of general triangular anisotropic plates using polynomials the problem of buckling of general triangular anisotropic plates with different boundary conditions subjected to combined in plane loads is considered solutions for plate buckling are obtained by using a rayleigh ritz method combined with a variational formulation the ritz functions consist of polynomials that include circulation functions that are used to impose various boundary conditions both classical laminated plate theory and first order shear deformation theory are used numerical buckling results obtained for isotropic and anisotropic triangular plates are compared with results from existing series solutions

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

random elements in effective topological spaces with measure following a suggestion of zvonkin and levin we generalize martin lof s definition of infinite random sequences over a finite alphabet via randomness tests to effective topological spaces with a measure we show that under weak computability conditions there is a universal randomness test we prove a theorem on randomness preserving functions which corrects and extends a result by schnorr and apply it to a number of examples in particular we show that a real number is random if and only if it has a random b ary representation for any b 2 we show that many computable continuously differentiable real functions preserve randomness especially all computable analytic functions which are not constant on any open subset of their domain preserve randomness finally we introduce a new randomness concept for subsets of natural numbers which we characterize in terms of random sequences surprisingly it turns out that there are infinite co r e random sets

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

probabilistic computability and choice we study the computational power of randomized computations on infinite objects such as real numbers in particular we introduce the concept of a las vegas computable multi valued function which is a function that can be computed on a probabilistic turing machine that receives a random binary sequence as auxiliary input the machine can take advantage of this random sequence but it always has to produce a correct result or to stop the computation after finite time if the random advice is not successful with positive probability the random advice has to be successful we characterize the class of las vegas computable functions in the weihrauch lattice with the help of probabilistic choice principles and weak weak k nig s lemma among other things we prove an independent choice theorem that implies that las vegas computable functions are closed under composition in a case study we show that nash equilibria are las vegas computable while zeros of continuous functions with sign changes cannot be computed on las vegas machines however we show that the latter problem admits randomized algorithms with weaker failure recognition mechanisms the last mentioned results can be interpreted such that the intermediate value theorem is reducible to the jump of weak weak k nig s lemma but not to weak weak k nig s lemma itself these examples also demonstrate that las vegas computable functions form a proper superclass of the class of computable functions and a proper subclass of the class of non deterministically computable functions we also study the impact of specific lower bounds on the success probabilities which leads to a strict hierarchy of classes in particular the classical technique of probability amplification fails for computations on infinite objects we also investigate the dependency on the underlying probability space besides cantor space we study the natural numbers the euclidean space and baire space

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

uniform test of algorithmic randomness over a general space the algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution these restrictions seem artificial some progress has been made to extend the theory to arbitrary bernoulli distributions by martin lof and to arbitrary distributions by levin we recall the main ideas and problems of levin s theory and report further progress in the same framework the issues are the following allow non compact spaces like the space of continuous functions underlying the brownian motion the uniform test deficiency of randomness dp x depending both on the outcome x and the measure p should be defined in a general and natural way see which of the old results survive existence of universal tests conservation of randomness expression of tests in terms of description complexity existence of a universal measure expression of mutual information as deficiency of independence the negative of the new randomness test is shown to be a generalization of complexity in continuous spaces we show that the addition theorem survives the paper s main contribution is introducing an appropriate framework for studying these questions and related ones like statistics for a general family of distributions

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

approximation of the buckling problem for reissner mindlin plates this paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the reissner mindlin equations these coefficients are the reciprocals of the eigenvalues of a noncompact operator we give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues then we consider the numerical computation of these coefficients and their corresponding modes for the finite element approximation of reissner mindlin equations it is well known that some kind of reduced integration or mixed interpolation has to be used to avoid locking in particular we consider duran liberman elements which have been already proved to be locking free for load and vibration problems we adapt the classical approximation theory for noncompact operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues these estimates are valid with constants independent of the plate thickness we report some numerical experiments confirming the theoretical results finally we refine the analysis in the case of a uniformly compressed plate

mind change complexity of inferring unbounded unions of restricted pattern languages from positive data this paper shows that the mind change complexity of inferring from positive data the class of unbounded unions of languages of regular patterns with constant segment length bound is of the form w w a b assuming that the patterns are defined over a finite alphabet containing at least two elements here a and b are natural numbers and we give tight bounds on their values based on the length of the constant segments and the size of the alphabet of the pattern languages this is to the authors knowledge the first time a natural class of languages has been shown to be inferable with mind change complexity above w w the proof uses the notion of closure operators on a class of languages and also uses the order type of well partial orderings to obtain a mind change bound the inference algorithm presented can be easily applied to a wide range of classes of languages finally we show an interesting connection between proof theory and mind change complexity

buckling of rectangular mindlin plates with internal line supports this paper considers the elastic buckling of rectangular mindlin plates under normal inplane forces the plates may have any number of internal line straight or curved supports that span between any two edges based on the energy functional derived from the incremental total potential energy approach the newly developed pb 2 rayleigh ritz method is applied for solution the special feature of this method is the pb 2 ritz function which consists of the product of 1 a two dimensional polynomial function and 2 a basic function formed from taking the product of the equations of the boundaries and internal line supports with each equation raised to appropriate powers as shown herein the method is convenient for analysts since no discretization is required and very accurate results can be obtained buckling load intensity factors for rectangular plates with various boundary conditions and various thickness and aspect ratios are tabulated for designers these may also serve as benchmark values for the testing of other numerical methods

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

analyzing two dimensional sine gordon equation with the mesh free reproducing kernel particle ritz method abstract we consider an analysis of the non linear two dimensional sine gordon sg equation the analysis is performed using the mesh free reproducing kernel particle ritz method kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

the generalized differential quadrature rule for fourth order differential equations the generalized differential quadrature rule gdqr proposed here is aimed at solving high order differential equations the improved approach is completely exempted from the use of the existing point technique by applying multiple conditions in a rigorous manner the gdqr is used here to static and dynamic analyses of bernoulli euler beams and classical rectangular plates numerical error analysis caused by the method itself is carried out in the beam analysis independent variables for the plate are first defined the explicit weighting coefficients are derived for a fourth order differential equation with two conditions at two different points it is quite evident that the gdqr expressions and weighting coefficients for two dimensional problems are not a direct application of those for one dimensional problems the gdqr are implemented through a number of examples good results are obtained in this work copyright 2001 john wiley sons ltd

computability on subsets of metric spaces the notions recursively enumerable and recursive are the basic notions of effectivity in classical recursion theory in computable analysis these notions are generalized to closed subsets of euclidean space using their metric distance functions we study a further generalization of these concepts to subsets of computable metric spaces it appears that different characterizations which coincide in case of euclidean space lead to different notions in the general case however under certain additional conditions such as completeness and effective local compactness the situation is similar to the euclidean case we present all results in the framework of type 2 theory of effectivity which allows to express effectivity properties in a very uniform way instead of comparing properties of single subsets we compare corresponding representations of the hyperspace of closed subsets such representations do not only induce a concept of computability for single subsets but they even yield a concept of computability for operations on hyperspaces such as union intersection etc we complete our investigation by studying the special situation of compact subsets

on the duality between locally optimal tests and optimal experimental designs abstract locally unbiased tests with maximal power curvature are determined as the solutions of an optimization problem which turns out to be of dual type as compared to the optimal design problem in both cases the proper optimization problem is concerned with matrices only and the transition from the matrix problem to the original variables is a separate second step this approach provides a novel statistical interpretation of the dual problem that arises with the optimal design problem

on uniform relationships between combinatorial problems the enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic with one of the most common frameworks for doing so being reverse mathematics in this setting one investigates which theorems provably imply which others in a weak formal theory roughly corresponding to computable mathematics since the proofs of such implications take place in classical logic they may in principle involve appeals to multiple applications of a particular theorem or to non uniform decisions about how to proceed in a given construction in practice however if a theorem q implies a theorem p it is usually because there is a direct uniform translation of the problems represented by p into the problems represented by q in a precise sense formalized by weihrauch reducibility we study this notion of uniform reducibility in the context of several natural combinatorial problems and compare and contrast it with the traditional notion of implication in reverse mathematics we show for instance that for all n j k 1 if j k then ramsey s theorem for n tuples and k many colors is not uniformly or weihrauch reducible to ramsey s theorem for n tuples and j many colors the two theorems are classically equivalent so our analysis gives a genuinely finer metric by which to gauge the relative strength of mathematical propositions we also study weak konig s lemma the thin set theorem and the rainbow ramsey s theorem along with a number of their variants investigated in the literature weihrauch reducibility turns out to be connected with sequential forms of mathematical principles where one wishes to solve infinitely many instances of a particular problem simultaneously we exploit this connection to uncover new points of difference between combinatorial problems previously thought to be more closely related

buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp cloud method abstract this paper presents the simple hp cloud meshless method for the stability analysis of moderately thick plates with various shapes subjected to uniaxial and biaxial in plane compressive and pure shear loads to allow the effect of transverse shear deformation on the critical buckling load of the plate the mindlin s plate theory is employed simple hp cloud method is applied for constructing the cloud shape functions and for discretization of the domain shepard functions are also used for the partition of unity and complete polynomials are utilized for the enrichment functions part the simple hp cloud method has kronecker delta property so contrary to most of meshless methods the essential boundary conditions can be imposed directly constructing the stiffness and geometry matrices leads to an eigenvalue problem that should be solved to determine the critical buckling load of the plate numerical results are verified against the results reported elsewhere to illustrate the accuracy and effectiveness of the present method to show the applications of simple hp cloud method in the buckling analysis of moderately thick plates local buckling coefficients of various shapes of plates rectangular skew trapezoidal triangular circular semi circular hexagonal and general shape with different boundary conditions are determined also local buckling coefficients of plates with point supports and intermediate support are calculated