a novel isoparametric finite element displacement formulation for axisymmetric analysis of nearly incompressible materials numerical difficulties are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition in elastic plastic analysis these effects are due to a conflict between the plastic flow rule and the finite element discretization the theoretical formulation of a new six noded isoparametric displacement finite element which is well suited for elastic plastic analysis of axisymmetric constrained solids by using a rational displacement interpolation function is presented

stability and vibration of thick laminated composite sector plates this study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of shear deformable laminated sector plates made up of cylindrically orthotropic layers the non axisymmetric formulation in cylindrical coordinates is discretized in space domain in terms of two dimensional chebyshev polynomials several combinations of simply supported clamped and free edge conditions are considered convergence study has been carried out and the obtained results are compared with the results of laminated square plates and isotropic sector plates available in literature extensive results pertaining to critical buckling loads and natural frequencies are presented effects of boundary conditions number of layers moduli ratio rotary and in plane inertia plate thickness sector angle and annularity are studied

vibration of thick annular sector plates using semi analytical methods abstract this paper deals with the vibration of thick annular sector plates with simply supported straight edges the finite strip method based on the mindlin plate theory and the finite prism method based on the three dimensional elastic theory which are known as semi analytical methods are used to demonstrate the accuracy of the semi analytical methods results are compared with those obtained by other analytical and numerical methods comparison of the results of the two methods is discussed in order to analyze the thick annular plates with different thickness ratios sector angles and boundary conditions it is seen that the results of the two methods show good agreement while some discrepancies between them are shown in the cases of larger thickness ratios of higher modes and of plates with free edges

focal sets and real hypersurfaces in complex projective space let m be a real submanifold of cpm and let j denote the complex structure we begin by finding a formula for the location of the focal points of m in terms of its second fundamental form this takes a particularly tractable form when m is a complex submanifold or a real hypersurface on which ji is a principal vector for each unit normal to m the rank of the focal map onto a sheet of the focal set of m is also computed in terms of the second fundamental form in the case of a real hypersurface on which je is principal with corresponding principal curvature u if the map onto a sheet of the focal set corresponding to u has constant rank then that sheet is a complex submanifold over which m is a tube of constant radius theorem 1 the other sheets of the focal set of such a hypersurface are given a real manifold structure in theorem 2 these results are then employed as major tools in obtaining two classifications of real hypersurfaces in cpm first there are no totally umbilic real hypersurfaces in cpm but we show theorem 3 let m be a connected real hypersurface in cpm m 3 with at most two distinct principal curvatures at each point then m is an open subset of a geodesic hypersphere secondly we show that there are no einstein real hypersurfaces in cpm and characterize the geodesic hyperspheres and two other classes of hypersurfaces in terms of a slightly less stringent requirement on the ricci tensor in theorem 4 one of the first results in the geometry of submanifolds is that an umbilic hypersurface m in euclidean space must be an open subset of a hyperplane or sphere the proof goes as follows assume that the shape operator is a scalar multiple of the identity a ax and use the codazzi equation to show that x is constant then either x 0 in which case m lies on a hyperplane or the focal points fx x x l x t the unit normal all coincide and m lies on the sphere of radius 1 x centered at the unique focal point this simple idea suggests a plan of attack for classifying hypersurfaces in terms of the nature of the principal curvatures under fairly general conditions the set of focal points corresponding to a principal curvature x can be given a differentiable received by the editors december 19 1980 presented to the society at its annual meeting in san francisco january 10 1981 1980 mathematics subject classificatiom primary 53b25 53c40

totally geodesic immersions of kahler manifolds and kahler frenet curves in a given kahler manifold m j we introduce the notion of kahler frenet curves which is closely related to the complex structure j of m using the notion of such curves we characterize totally geodesic kahler immersions of m into an ambient kahler manifold open image in new window and totally geodesic immersions of m into an ambient real space form open image in new window of constant sectional curvature open image in new window

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

vibration analysis of circular mindlin plates using the differential quadrature method abstract axisymmetric free vibrations of moderately thick circular plates described by the linear shear deformation mindlin theory are analyzed by the differential quadrature dq method the first fifteen natural frequencies of vibration are calculated for uniform circular plates with free simply supported and clamped edges through these computations the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated and convergence and accuracy are thoughtfully examined the case of rigid point support at the plate centre is also considered in the present paper for which special attention is paid to the capability and convergence of the current method

influence of boundary stress singularities on the vibration of clamped and simply supported sectorial plates with arbitrary radial edge conditions abstract this paper extends previous studies made for sectorial plates having re entrant i e interior corners causing stress singularities to provide accurate frequencies when the circular edge is either clamped or simply supported an extensive review of the literature is also given herein spanning nearly the past two decades explaining the free vibration characteristics of sectorial plates in this work the classical ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements these sets include 1 mathematically complete algebraic trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained and 2 corner functions which account for the bending moment singularities at the re entrant vertex corner of the radial edges having arbitrary edge conditions extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of non dimensional frequencies for sectorial plates having either a clamped or hinged circumferential edge and various combinations of clamped hinged and free conditions on the radial edges accurate to at least four significant figure frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles 90 180 semi circular 270 300 330 350 355 360 complete circular causing a re entrant vertex corner of the radial edges for sector angles of 360 a clamped clamped clamped hinged clamped free hinged free or free free radial crack ensues one general observation is the substantial reduction in the first six frequencies as the sector angle increases for all plates except in the first two modes of plates having free free radial edges

mathematical modeling of vibration problem of nano sized annular sector plates using the nonlocal continuum theory via eight node discrete singular convolution transformation abstract in the present study free vibration analysis of nano sized annular sector plate is analyzed using the nonlocal continuum theory the method of discrete singular convolution dsc is used for numerical computations firstly equation of motion of thin plates is formulated via nonlocal elasticity then irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation the dsc procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions the effects of nonlocal parameter mode numbers sector angle and radius ratio on the vibration frequencies are investigated in detail it is seen that the size effects are significant in vibration analysis of nano scaled annular sector plates and need to be included in the mechanical model

finite element hourglassing control a new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented based on expansion of the strees in a taylor series and retention of additional terms beyond the usual constant stress term this technique has the advantage that actual rather than artificial material properties are used simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described

helical minimal immersions of compact riemannian manifolds into a unit sphere an isometric immersion of a riemannian manifold m into a riemannian manifold m is called helical if the image of each geodesic has constant curvatures which are independent of the choice of the particular geodesic suppose m is a compact riemannian manifold which admits a minimal helical immersion of order 4 into the unit sphere if the weinstein integer of m equals that of one of the projective spaces then m is isometric to that projective space with its canonical metric 0 introduction in 2 besse constructed a minimal immersion with a nice property of a strongly harmonic manifold into a sphere this nice property is that the images of geodesics of the strongly harmonic manifold are of constant curvatures as curves in the sphere and the curvatures and the osculating orders are independent of geodesics immersions with such a property are said to be helical cf 8 sakamoto 8 studied a helical immersion of a riemannian manifold m into a unit sphere the result is that if m is compact then it is a blaschke manifold and moreover if the helical immersion is minimal then m is a globally harmonic manifold it is well known that if a globally harmonic manifold is compact and simply connected then it is a strongly harmonic manifold michel s theorem cf 2 thus we can declare that the theory of helical minimal immersions of compact simply connected riemannian manifolds into a unit sphere is a submanifold version of strongly harmonic manifold theory let f m s 1 be a helical immersion of a compact riemannian manifold m into a unit sphere s 1 since m is a blaschke manifold all geodesics of m are simply closed and of the same length furthermore if we denote the cut locus of x e m by cut x then the unit tangent vectors at x of geodesics emanating from x and entering to y e cut x compose a great sphere in the unit tangent sphere at x the dimension of the great sphere is independent of x and it is equal to 0 1 3 7 or n 1 n dim m which is the index of the first conjugate point y of x cf 2 proposition 5 39 and theorem 7 23 geodesics are also helical in the euclidean received by the editors march 15 1984 and in revised form june 20 1984 1980 mathematics subject classification primary 53c40 secondary 53c42

free vibration analyses of thin sector plates by the new version of differential quadrature method abstract the new version of differential quadrature dq method is extended to analyze the free vibration of thin sector plates with various sector angles and six combinations of boundary conditions detailed formulations are given various numerical examples are studied comparisons are made with existing analytical and or numerical data numerical results indicate that convergence can be achieved with increasing in number of grid points and accurate results could be obtained with 9 9 gird or even higher grid by using the extended dq method for the cases considered

constant isotropic submanifolds with 4 planar geodesics let f be an isometric immersion of a riemannian manifold m into m we prove that if f is constant isotropic 4 planar geodesic and m is a euclidean sphere then m is isometric to one of compact symmetric spaces of rank equal to one and f is congruent to a direct sum of standard minimal immersions we also determine constant isotropic 4 planar geodesic totally real immersions into a complex projective space of constant holomorphic sectional curvature 0 introduction in 15 o neill studied isotropic immersions and showed that if the difference between the sectional curvatures of the submanifold and the ambient manifold is constant for any plane section tangent to the submanifold then the codimension must be high compared with the dimension of the submanifold unless the immersion is totally geodesic or umbilical the class of constant isotropic immersions for instance into a sphere seems to be too large to classify them for example the composition of two isotropic immersions is also isotropic and for two given isotropic immersions f1 and f2 into sp 1 and sq 1 respectively their direct sum tcosaf1 sinaf2 into sp q l 1 is also isotropic for any 0 furthermore it is well known that there are many constant isotropic immersions in equivariant isometric immersions of homogeneous spaces an isometric immersion f m m is said to be 4 planar geodesic if for each geodesic r of m the curve f oty is locally contained in a 4 dimensional totally geodesic submanifold of m the class of 4 planar geodesic immersions into a sphere is also large at least an isometric immersion of a surface into a 4dimensional riemannian manifold is always 4 planar geodesic in this paper we try to classify immersions in the intersection of these classes in particular we are able to classify constant isotropic 4 planar geodesic resp and totally real immersions of connected complete riemannian manifolds into a unit sphere resp complex projective space of constant holomorphic sectional curvature 4 in 1 we give basic equations used later and some definitions in 2 we prove that if f is a constant isotropic 4 planar geodesic resp and totally real immersion into a real space form resp cpq c then f is a helical immersion of order 4 here we recall that an isometric immersion f m m is called a helical immersion received by the editors april 3 1987 1980 mathematics subject classification 1985 revision primary 53c40

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

free vibration of annular sector plates with edges possessing different degrees of rotational restraint abstract results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented the analysis is based on a numerical method developed by the author the functions in the circumferential direction satisfying the boundary conditions along the radial edges which are required in the analysis are indicated to the best of the author s knowledge no previous results exist for such plates

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

rectangular thick plates on winkler foundation differential quadrature element solution abstract this paper deals with the static analysis of homogenous isotropic rectangular plates on winkler foundation on the basis of first order shear deformation theory an improved differential quadrature dq method called the differential quadrature element method dqem has been developed for this analysis the plates considered are subjected to a patch load or a concentrated line load which are not solvable by the global dq method the convergence and comparison studies are carried out to establish the reliability of the dqem results then the numerical results for different boundary conditions i e ssss cccc s s s s and sfsf are presented showing the parametric effects of dimensions of loading area line relative thickness ratio and elastic foundation modulus on the deflection bending and twisting moments and shear forces at selected locations most of these data are new and due to the high accuracy of the dq solution they can be useful for benchmarking future work

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

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

free vibration analysis of mindlin sector plates numerical solutions by differential quadrature method abstract in this paper the free vibration analysis of moderately thick sector plates based on mindlin s first order shear deformation theory is examined the solutions to this problem are determined using the differential quadrature dq method for numerical evaluation the dq formulations for free vibration of the mindlin sector plates in two dimensional polar co ordinate system are derived to demonstrate the accuracy of the dq method convergence and comparison studies are carried out in parametric study the first eight frequency parameters are computed for sector plates with different boundary conditions relative thickness ratios and sector angles 30 360 the effects of sector angle and relative thickness ratio on the frequency parameters are discussed

exact analytical solutions for free vibrations of thick sectorial plates with simply supported radial edges abstract the first known exact analytical solutions are derived for the free vibrations of thick mindlin sectorial plates having simply supported radial edges and arbitrary conditions along the circular edge the general solutions to the mindlin differential equations of motion contain noninteger order ordinary and modified bessel functions of the first and second kinds and six arbitrary constants of integration by exercising a careful limiting process three regularity conditions at the vertex of the radial edges are invoked to yield three equations of constraint among the six constants for sector angles exceeding 180 re entrant corners three additional linearly independent equations among the six constants are obtained by satisfying the three boundary conditions along the circular edge frequency determinant equations are derived for mindlin sectorial plates with circular boundaries which are clamped simply supported or free nondimensional frequency parameters are presented for over a wide range of salient and re entrant sector angles 30 360 and thickness to radius ratios of 0 1 0 2 and 0 4 frequency results obtained for mindlin sectorial plates are compared to those determined for classically thin sectorial plates and the results are found to be considerably different than those derived from thin plate theory particularly for the fundamental frequencies of plates having sector angles slightly greater than 180 when the circular boundary is free the frequencies for 360 sectorial plates i e circular plates having a hinged crack are compared with those for complete circular ones

real hypersurfaces and complex submanifolds in complex projective space let m be a real hypersurface in c j be the complex structure and denote a unit normal vector field on m we show that m is an open subset of a homogeneous hypersurface if and only if m has constant principal curvatures and jt is principal we also obtain a characterization of certain complex submanifolds in a complex projective space specifically c totally geodesic q pl c x p c su 5 s u 2 x 7 3 and so 10 t 5 are the only complex submani folds whose principal curvatures are constant in the sense that they depend neither on the point of the submanifold nor on the normal vector

real hypersurfaces of complex projective spaces let p denote the complex projective space with fubini study metric of constant holomorphic sectional curvature 4 and suppose m 2 it is well known that there does not exist a totally umbilical real hypersurface m of p c see tashiro and tachibana 7 moreover as a consequence of codazzi equation there does not exist a real hypersurface m of pro c with parallel second fundamental form to get this y maeda 4 estimated the norm of the derivative of the second fundamental form he showed

a non linear programming approach to kinematic shakedown analysis of composite materials using a representative volume element rve to represent the microstructure of periodic composite materials this paper develops a non linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads the shakedown analysis is performed using homogenization theory and the displacement based finite element method with the aid of homogenization theory the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites using an associated flow rule the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity by means of non linear mathematical programming techniques a finite element formulation of kinematic shakedown analysis is then developed leading to a non linear mathematical programming problem subject to only a small number of equality constraints the objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load of a composite is then obtained an effective direct iterative algorithm is proposed to solve the non linear programming problem the effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples this can serve as a useful numerical tool for developing engineering design methods involving composite materials copyright 2005 john wiley sons ltd

vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method in this paper we adopt the first order shear deformation theory in the moving least squares differential quadrature mlsdq procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates the transverse deflection and two rotations of the laminate are independently approximated with the moving least squares mls approximation the weighting coefficients used in the mlsdq approximation are obtained through the fast computation of the mls shape functions and their partial derivatives the natural frequencies of vibration are computed for various laminated plates and compared with the available published results through numerical experiments the capability and efficiency of the mlsdq method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are thoughtfully examined effects of the size of support order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

free vibration of annular sector plates by an integral equation technique abstract a numerical method is presented for the free vibration analysis of polar orthotropic clamped annular sector plates the results are compared with analytical and experimental values of other investigators a parametric study has been done by varying the sector angle and radii ratio the frequencies for isotropic and orthotropic cases are presented in the form of graphs

an analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges abstract this paper presents the first known analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges the solution is a series solution constructed using the frobenius method and exactly satisfies not only the boundary conditions along the radial and circular edges but also the regularity conditions at the vertex of the radial edges the moment and shear force singularities at the vertex are exactly considered in the solution the correctness of the proposed solution is confirmed by comparing non dimensional frequencies of isotropic plates obtained from the present solution with published data obtained from a closed form solution this paper also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fix boundary conditions along the circumferential edge a study is also carried out about the influence of elastic and shear moduli on the moment and shear force singularities at the plate origin r 0 for different vertex angles

semianalytical differential quadrature solution for free vibration analysis of rectangular plates in this paper the analysis of the titled problem is based on classical thin plate theory and its numerical solution is carried out by a semianalytical differential quadrature method the thin rectangular plates considered herein are simply supported on two opposite edges the boundary conditions at the other two edges may be quite general and between these two edges the plates may have varying thickness however the results contained in this paper are for plates that are elastically restrained against rotation at these edges and have linearly tapered thickness on the basis of comparison with the available results in the published literature it is believed that this solution method guarantees high numerical accuracy for the problem moreover the computation times involved in the evaluation of free vibration characteristics are sufficiently small indicating that the solution method may possibly be further developed for the real time analysis and design of vibrating plate systems

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed