free vibration analysis of functionally graded plates using the element free kp ritz method a free vibration analysis of metal and ceramic functionally graded plates that uses the element free kp ritz method is presented the material properties of the plates are assumed to vary continuously through their thickness according to a power law distribution of the volume fractions of the plate constituents the first order shear deformation plate theory is employed to account for the transverse shear strain and rotary inertia and mesh free kernel particle functions are used to approximate the two dimensional displacement fields the eigen equation is obtained by applying the ritz procedure to the energy functional of the system convergence studies are performed to examine the stability of the proposed method and comparisons of the solutions derived with those reported in the literature are provided to verify its accuracy four types of functionally graded rectangular and skew plates al al2o3 al zro2 ti 6al 4v aluminum oxide and sus304 si3n4 are included in the study and the effects of the volume fraction boundary conditions and length to thickness ratio on their frequency characteristics are discussed in detail

mathematical analysis of giving up smoking model via harmonic mean type incidence rate abstract this article deals with qualitative analysis of a smoking model and provides parametric conditions for controlling diseases under the influence of smoking the model is obtained by taking into account a novel uptake function which relates the incidence of potential smoker with occasional smoker of harmonic mean type for the potential and occasional smokers introducing a new type of incidence rate the local as well as global stabilities for the proposed model are discussed at its steady states minimizing the number of individuals involved in a substance abuse in any community is very difficult task therefore we have introduced four control variables in the controlled system pontrygin s maximum principal is used to derive optimality system finally the obtained results are illustrated numerically and graphically

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

analytic solutions of a nonlinear convective equation in population dynamics analytic solutions are presented for a simple nonlinear convective equation of use in population dynamics in spite of its simplicity the equation predicts rich behavior including a velocity inversion transition stability considerations are also presented

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

geometrically nonlinear analysis of functionally graded plates using the element free kp ritz method abstract the nonlinear response of functionally graded ceramic metal plates fgps under mechanical and thermal loads is investigated using the mesh free kp ritz method the nonlinear formulation is based on the first order shear deformation plate theory and the von karman strains which deal with small strains and moderate rotations the material properties of fgps are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents the approximation of the displacement field is expressed in terms of a set of mesh free kernel particle functions the bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking the nonlinear behavior of the deflection and axial stress is studied for fgps under thermal and mechanical loading and the influences of the volume fraction exponent boundary condition and material properties on the nonlinear response of fgps are examined

a numeric analytic method for approximating a giving up smoking model containing fractional derivatives smoking is one of the main causes of health problems and continues to be one of the world s most significant health challenges in this paper the dynamics of a giving up smoking model containing fractional derivatives is studied numerically the multistep generalized differential transform method for short msgdtm is employed to compute accurate approximate solutions to a giving up smoking model of fractional order the unique positive solution for the fractional order model is presented a comparative study between the new algorithm and the classical runge kutta method is presented in the case of integer order derivatives the solutions obtained are also presented graphically

postbuckling analysis of laminated composite plates using the mesh free kp ritz method abstract a ritz method based on kernel particle approximation for the field variables is proposed for the postbuckling analysis of laminated composite plates the first order shear deformation plate theory fsdt is employed to model the plate flexure the ritz method is used to obtain the discretized non linear equations a geometrically non linear analysis is used to trace the postbuckling paths of the plate typical numerical examples including isotropic plates and cross ply and angle ply laminated composite plates have been solved using the proposed method the results are in close agreement with the series solution as well as previous finite element results available in the literature

numerical solution of transient heat conduction problems using improved meshless local petrov galerkin method an improved meshless local petrov galerkin mlpg method is presented and applied to calculate the two dimensional unsteady state heat conduction problems in this method the moving kriging interpolation is employed instead of the traditional mls approximation to construct the mlpg shape functions which possess kronecker delta function property and thus make it easy to implement essential boundary conditions and then the heaviside step function is used as the test function over a local sub domain since no mesh is needed either for integration of the local weak form or for construction of the shape functions the presently developed mlpg method is a truly meshless method several examples are performed to illustrate the accuracy and efficiency of the present method a good agreement can be found among the proposed analytical and finite element methods

radial basis function networks in the numerical solution of linear integro differential equations the purpose of this paper is to present a new method to solve the linear integro differential equations using radial basis function rbf networks the approximate solution is represented by means of rbfs whose coefficients are computed by training a rbf network and is written as a sum of two parts the first part employs a growing rbf network whose parameters are adjusted to minimize an appropriate error function and are constructed so as not to effect the supplementary conditions of the equations the second part only satisfies the supplementary conditions numerical examples are given to demonstrate the proposed idea and method

nonlinear analysis of laminated composite plates using the mesh free kp ritz method based on fsdt a mesh free kp ritz method of solution based on the kernel particle approximation for the field variables is proposed for the large deflection flexural analysis of laminated composite plates the first order shear deformation theory fsdt is used for modeling the flexure the nonlinear solution algorithm is based on the total lagrangian formulation with green s strain measures and von karman assumptions the incremental form of nonlinear equations is obtained by taylor series expansion and newton s method is used to solve these equations test problems involving square and rectangular composite plates with ssss and cccc boundary conditions are solved to assess the efficacy of the proposed method the results are in excellent agreement with the series solution as well as the finite element solution already reported in the literature

a meshless local moving kriging method for two dimensional solids abstract an improved meshless local petrov galerkin method mlpg for stress analysis of two dimensional solids is presented in this paper the mlpg method based on the moving least squares approximation is one of the recent meshless approaches however accurate imposition of essential boundary conditions in the mlpg method often presents difficulties because the mlpg shape functions does not possess the kronecker delta property in order to eliminate this shortcoming this approach uses the moving kriging interpolation instead of the traditional moving least square approximation to construct the mlpg shape functions and then the heaviside step function is used as the test function over a local sub domain in this method the essential boundary conditions can be enforced as the fem no domain integration is needed and only regular boundary integration is involved in addition the sensitivity of several important parameters of the present method is mainly studied and discussed comparing with the original meshless local petrov galerkin method the present method has simpler numerical procedures and lower computation cost the effectiveness of the present method for two dimensional solids problem is investigated by numerical examples in this paper

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

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

global regularity of solution for general degenerate parabolic equations in 1 d abstract this paper considers the cauchy problem for the general degenerate parabolic equations 1 1 with initial data 1 2 in the critical condition meas u g u 0 0 we obtain the regular estimate g u c 1 where g u u 0 g s ds a new maximum principle is introduced to obtain the estimate and is applied to some special equations such as prous media equation an infiltration equation to obtain the optimal estimate u m 1 x m finally an interesting equation related to the broadwell model where g u has two zero points is studied and a uniquely regular solution u c 1 is obtained moreover the estimates u x f u u 2 g u and inf x 0 x 1 4 t inf x 0 x are proved for the solution of the navier stokes equations corresponding to the broadwell model

improved bounds for reduction to depth 4 and depth 3 koiran showed that if an n variate polynomial f n of degree d with d n o 1 is computed by a circuit of size s then it is also computed by a homogeneous circuit of depth four and of size 2 o d log n log s using this result gupta kamath kayal and saptharishi found an upper bound for the size of a depth three circuit computing f n we improve here koiran s bound indeed we transform an arithmetic circuit into a depth four circuit of size 2 o d log d s log n then mimicking the proof in 2 it also implies a 2 o d log d s log n upper bound for depth three circuits this new bound is almost optimal since a 2 d lower bound is known for the size of homogeneous depth four circuits such that gates at the bottom have fan in at most d finally we show that this last lower bound also holds if the fan in is at least d

non commutative arithmetic circuits depth reduction and size lower bounds abstract we investigate the phenomenon of depth reduction in commutative and non commutative arithmetic circuits we prove that in the commutative setting uniform semi unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree and unrestricted depth earlier proofs did not work in the uniform setting this also provides a unified proof of the circuit characterizations of the class logcfl and its counting variant logcfl we show that ac1 has no more power than arithmetic circuits of polynomial size and degree no log log n improving the trivial bound of no log n connections are drawn between tc1 and arithmetic circuits of polynomial size and degree then we consider non commutative computation we show that over the algebra max concat arithmetic circuits of polynomial size and polynomial degree can be reduced to o log2 n depth and even to o log n depth if unbounded fanin gates are allowed this establishes that optlogcfl is in ac1 this is the first depth reduction result for arithmetic circuits over a non commutative semiring and it complements the lower bounds of kosaraju and nisan showing that depth reduction cannot be done in the general non commutative setting we define new notions called short left paths and short right paths and we show that these notions provide a characterization of the classes of arithmetic circuits for which optimal depth reduction is possible this class also can be characterized using the auxpda model finally we characterize the languages generated by efficient circuits over the semiring 2 union concat in terms of simple one way machines and we investigate and extend earlier lower bounds on non commutative circuits

a mathematical model approach for tobacco control in china as a tobacco victimized country in the world china is being burdened by smoking related illnesses this paper concentrates on the problem of controlling smoking in china we propose a mathematical model described by ordinary differential equations with a saturated incidence rate to explore the effect of controlling smoking by setting up designed smoking areas and raising the price of cigarettes the sufficient criteria for the local and global stabilities of the equilibria are obtained furthermore a sensitivity analysis is performed to gain insight into which factors are the most important in controlling smoking lastly we carry out numerical simulations to illustrate and verify the analytic conclusions and provide a control measure

dulac criteria for autonomous systems having an invariant affine manifold abstract for a class of higher dimensional autonomous systems that have an invariant affine manifold conditions are derived to preclude the existence of periodic solutions on the invariant manifold it is established that these conditions are robust under certain types of local perturbations of the vector field as a consequence each bounded semitrajectory on the invariant manifold is shown to converge to a single equilibrium using a c 1 closing lemma for this class applications to autonomous systems that are homogeneous of degree 1 are also considered

a pb 2 ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform abstract this paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free simply supported and clamped boundaries the pb 2 ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies the ritz approach along with the in plane and transverse displacements assumed in the form of orthogonal polynomials is used to formulate the problems numerical results for the vibration frequencies for wide ranges of aspect ratio shallowness ratio and thickness ratio are presented several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented as usual the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature

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

numerical solution of nonlinear volterra fredholm hammerstein integral equations via collocation method based on radial basis functions abstract a numerical technique based on the spectral method is presented for the solution of nonlinear volterra fredholm hammerstein integral equations this method is a combination of collocation method and radial basis functions rbfs with the differentiation process drbf using zeros of the shifted legendre polynomial as the collocation points different applications of rbfs are used for this purpose the integral involved in the formulation of the problems are approximated based on legendre gauss lobatto integration rule the results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme

numerical solution of the second kind integral equations using radial basis function networks in this paper a new method using radial basis function rbf networks is presented for solving the linear second kind integral equations of fredholm and volterra types this method employs a growing neural network as the approximate solution of the integral equations whose the activation functions are rbfs the parameters weights centers and widths of the approximate solution are adjusted by using an unconstrained optimization problem numerical results show that our method has the potentiality to become an efficient approach for solving integral equations

the meshless method for a two dimensional parabolic problem with a source parameter in this paper the reproducing kernel particle method rkpm is used for finding the solution of a two dimensional parabolic inverse problem with a source control parameter and the corresponding discrete equations are obtained comparing with the numerical methods based on mesh the reproducing kernel particle method only needs the scattered nodes instead of meshing the domain of the problem the reproducing kernel particle method is an efficient mesh free technique for the numerical solution of partial differential equations the result of numerical example is presented

free vibration analysis of conical shells via the element free kp ritz method in this paper we consider the free vibration analysis of thin conical shells under different boundary conditions the analysis is carried out using the element free kp ritz method the present study is based on the classical thin shell theory the kernel particle kp functions are employed in hybridized form with harmonic functions to approximate the two dimensional displacement field in order to examine the numerical stability of the present approach convergence studies are performed based on the influences of the support size and the number of nodes to verify the accuracy of this method comparisons of the present results are made with results available in the open literature this study also examines in detail the effects of semi vertex angles and boundary conditions on the frequency characteristics of the conical shells

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

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

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

arithmetic circuits the chasm at depth four gets wider in their paper on the chasm at depth four agrawal and vinay have shown that polynomials in m variables of degree o m which admit arithmetic circuits of size 2 o m also admit arithmetic circuits of depth four and size 2 o m this theorem shows that for problems such as arithmetic circuit lower bounds or black box derandomization of identity testing the case of depth four circuits is in a certain sense the general case in this paper we show that smaller depth four circuits can be obtained if we start from polynomial size arithmetic circuits for instance we show that if the permanent of nxn matrices has circuits of size polynomial in n then it also has depth 4 circuits of size n o n l o g n if the original circuit uses only integer constants of polynomial size then the same is true for the resulting depth four circuit these results have potential applications to lower bounds and deterministic identity testing in particular for sums of products of sparse univariate polynomials we also use our techniques to reprove two results on the existence of nontrivial boolean circuits of constant depth for languages in logcfl reduction to polylogarithmic depth for arithmetic circuits of polynomial size and polynomially bounded degree

fast parallel computation of polynomials using few processors it is shown that any multivariate polynomial of degree d that can be computed sequentially in c steps can be computed in parallel in o log d log c log d steps using only cd o 1 processors

interpolating element free galerkin method for the regularized long wave equation and its error analysis abstract combining the simplified interpolating moving least squares imls method with the galerkin weak form an interpolating element free galerkin iefg method is presented for the numerical study of the regularized long wave rlw equation the trial function in the imls method has one less unknown coefficient than in the traditional mls approximation and the shape functions satisfy the interpolating property at nodes then the iefg method can apply the essential boundary conditions naturally and directly and has high computational accuracy and then this paper studies the error estimates of the iefg method for rlw equation the error estimate of the semi discrete iefg method for the rlw equation on the influence domain radius is first studied and then the convergence rate of the full discrete scheme of the method on the influence domain radius and time step is studied the theoretical results show that the iefg method for rlw equation has good convergence rate for the purpose of demonstration three selected numerical examples are given to demonstrate the method and the mathematical theory of this paper