the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

an objective 3d large deformation finite element formulation for geometrically exact curved kirchhoff rods the objective of this work is the development of a new finite element formulation for beams according to the kirchhoff theory of thin rods which includes the deformation states of axial tension torsion and bending the proposed formulation accounts for large deformations in three dimensional problem settings consisting of slender prismatic beams with arbitrarily curved initial geometries and arbitrary cross section shapes like in geometrically exact reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations rotations and strains a novel orthogonal interpolation strategy is applied to the triad field representing the cross section orientation in order to fulfill the kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem the continuity requirements resulting from the corresponding weak form are fulfilled by a cubic hermite interpolation thus leading to a c1 continuous representation of the beam centerline fundamental properties such as objectivity path independence consistency and accuracy of the developed beam element are verified by means of suitable numerical examples

energy consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints the present work deals with the energy consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints the underlying differential algebraic equations daes with index three are directly discretized this approach makes possible the development of a new energy consistent time stepping scheme for general nonholonomic systems in particular both nonholonomic problems from rigid body dynamics as well as flexible multibody dynamics can be treated in a unified manner in this connection specific constrained formulations of rigid bodies and geometrically exact beams are presented moreover the newly developed discrete null space method is applied to achieve a size reduction and an improved conditioning of the discrete system the numerical examples deal with a nonholonomic rigid body system and a flexible multibody system

stress resultant geometrically nonlinear shell theory with drilling rotations part i a consistent formulation abstract in this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory the main feature of the present shell theory development which stands in contrast with the classical developments in the shell theory is the presence of a rotation component around the shell normal so called drilling rotation in the description of shell finite rotations the relationship of the proposed theory with a finite deformation theory of a three dimensional continuum with independent rotation field is clearly identified the latter is shown to be an important link which facilitates the proper choice of the shell constitutive model and a proper construction of the regularized form of the theory capable of supporting the drilling rotations the corresponding linearized form of the present shell theory is discussed in the closure

parabolic monge ampere equations on riemannian manifolds on a compact riemannian manifold m g we consider the parabolic monge ampere equation t x t logdet g x hess x t detg x x t f x x 0 phiv 0 x here is a real parameter andf 0 m r are smooth functions we show existence of for all timestindependent of if 0 then t t converges exponentially towards a solution of the stationary problem ast in the special case 0 f 0 one has 0 and we determine the convergence rate t in thel2 norm more precisely

nonlinear second order elliptic equations v the dirichlet problem for weingarten hypersurfaces on etudie le probleme de dirichlet pour une fonction u dans un domaine borne de r n a frontiere lisse strictement convexe en un point x de les courbures principales k k 1 k n du graphe x u x satisfont une relation f k 1 k n x 0 ou est une fonction positive lisse donnee sur de plus u doit satisfaire la condition aux limites de dirichlet u 0 sur sous certaines conditions on demontre qu il existe une solution u unique admissible lisse dans

existence of the global solution for the parabolic monge ampere equations on compact riemannian manifolds abstract on a compact riemannian manifold m g we consider the existence and nonexistence of global solutions for the parabolic monge ampere equation t log det g hess det g p f x x 0 0 x here p 1 and are real parameters f 0 m 0 are smooth functions on m if 0 then the solution of exists for all times t and t t converges exponentially towards a solution of its stationary equation as t in the case of 0 it does not have the global solution of thus we obtain the nonexistence of the positive solution for the stationary equation of

bifurcations and internal resonances in space curved rods abstract the paper discusses a geometrically non linear model of space curved beams the timoshenko type model is used which includes the shear effects and rotatory inertia the motion of the system is described by a non linear matrix equation which accounts for non linearities up to the second order to solve the non linear problem discretization methods based on the galerkin method are used and the resulting non linear eigenvalue problem is then solved by the continuation methods the analysis of the discretized problem allows the study of the bifurcations of solutions the post bifurcation analysis is used to explain the phenomenon of internal resonance which is of much importance in the prediction of the dynamic response of the analyzed systems the approach is illustrated by numerical examples which consider the free vibration of beams and circular arches with different boundary conditions

consistency for bi skew symmetric solutions to systems of generalized sylvester equations over a finite central algebra let be a finite dimensional central algebra with an involutorial antiautomorphism and char 2 n n be the set of all n n matrices over a aij n n is called bisymmetric if aij an i 1 n j 1 aji and biskewsymmetric if aij an i 1 n j 1 aji the following systems of generalized sylvester equations over a1x yb1 c1 i asx ybs cs a1xb1 c1xd1 e1 ii asxbs csxds es are considered necessary and sufficient conditions are given for the existence of constant solutions with bi skew symmetric constrains to i and ii as a particular case auxiliary results dealing with the system of sylvester equations are also presented

explicit isogeometric collocation for the dynamics of three dimensional beams undergoing finite motions abstract we initiate the study of three dimensional shear deformable geometrically exact beam dynamics through explicit isogeometric collocation methods the formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit geometrically consistent lie group time integrator we focus on extending the integration scheme originally proposed for rigid body dynamics to our nonlinear initial boundary value problem where special attention is required by neumann boundary conditions the overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step the capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations in this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra necessary and sufficient conditions are obtained for the matrix equation ax c and the following systemsa 1x c 1 a 1x c 1 xb 3 c 3 a 2x c 2 to have bisymmetric solutions and the systema 1x c 1 a 3xb 3 c 3 to have centrosymmetric solutions the expressions of such solutions of the matrix and the systems mentioned above are also given moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over are also mentioned

numerical integration of non linear elastic multi body systems this paper is concerned with the modelling of nonlinear elastic multi body systems discretized using the finite element method the formulation uses cartesian co ordinates to represent the position of each elastic body with respect to a single inertial frame the kinematic constraints among the various bodies of the system are enforced via the lagrange multiplier technique the resulting equations of motion are stiff non linear differential algebraic equations the integration of these equations presents a real challenge as most available techniques are either numerically unstable or present undesirable high frequency oscillations of a purely numerical origin an approach is proposed in which the equations of motion are discretized so that they imply conservation of the total energy for the elastic components of the system whereas the forces of constraint are discretized so that the work they perform vanishes exactly the combination of these two features of the discretization guarantees the stability of the numerical integration process for non linear elastic multi body systems examples of the procedure are presented

the general solution to a system of real quaternion matrix equations in this paper we consider the system of matrix equations a 1x c 1 a 2x c 2 a 3xb 3 c 3 and a 4xb 4 c 4 over the real quaternion algebra a necessary and sufficient condition for the existence and the expression of the general solution to the system are given as particular cases the corresponding results on other systems over are also obtained

global existence of solutions to parabolic monge ampere equations on riemannian manifolds abstract in this paper we study the cauchy problem of the parabolic monge ampere equation u t log g 1 det g i j i j u n log u in m n 0 u x 0 u 0 x in m n where m n is a compact complete riemannian manifold of dimension n 2 g i j denotes the metric of m n g det g i j 0 and u 0 x 1 is a smooth function we prove the global existence of solutions

existence and estimates of solutions to a singular dirichlet problem for the monge ampere equation given a strictly convex smooth and bounded domain in rn we establish the existence of a negative convex solution in c c with zero boundary value to the singular monge ampere equation det d2u p x g u an associated dirichlet problem will be employed to provide a necessary and sufficient condition for the solvability of the singular boundary value problem estimates of solutions will also be given and regularity of solutions will be deduced from the estimates

existence and non existence of solutions for a class of monge ampere equations abstract we study the boundary value problems for monge ampere equations det d 2 u e u in r n n 1 u 0 first we prove that any solution on the ball is radially symmetric by the argument of moving plane then we show there exists a critical radius such that if the radius of a ball is smaller than this critical value there exists a solution and vice versa using the comparison between domains we can prove that this phenomenon occurs for every domain finally we consider an equivalent problem with a parameter det d 2 u e t u in u 0 t 0 by using lyapunov schmidt reduction method we get the local structure of the solutions near a degenerate point by leray schauder degree theory a priori estimate and bifurcation theory we get the global structure

discrete variational lie group formulation of geometrically exact beam dynamics the goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics by using a lie group variational integrator both spatial and temporal discretization are implemented in a geometry preserving manner the resulting scheme preserves both the discrete momentum maps and symplectic structures and exhibits almost perfect energy conservation comparisons with existing numerical schemes are provided and the convergence behavior is analyzed numerically

on the mean oscillation of the hessian of solutions to the monge ampere equation we give interior a priori estimates for the mean oscillation of second derivatives of solutions to the monge ampere equation detd2u f x with zero boundary values where f x is a non dini continuous function if the modulus of continuity of f x is f r such that limr 0f r log 1 r 0 then d2uvmo

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

least squares solutions to the matrix equations ax b and xc d abstract the least squares solution and the least squares symmetric solution with the minimum norm of the matrix equations ax b and xc d are considered in this paper by the matrix differentiation and the spectral decomposition of matrices an explicit representation of such solution is given

on the symmetric solutions of linear matrix equations abstract the symmetric solutions of linear matrix equations ax c and axb c are considered the necessary and sufficient conditions for the consistency of the equations with a symmetric condition on solutions are derived using the singular value decomposition and the generalized singular value decomposition numerical algorithms for solving the equations are suggested

a representation of the general common solution to the matrix equations a1xb1 c1 and a2xb2 c2 with applications we give new necessary and sufficient conditions for the existence of a common solution to the pair of linear matrix equations a1xb1 c1 and a2xb2 c2 and derive a new representation of the general common solution to these two equations we apply this result to determine new necessary and sufficient conditions for the existence of an hermitian solution and a representation of the general hermitian solution to the matrix equation axb c

geometrically exact 3d beam theory implementation of a strain invariant finite element for statics and dynamics geometrically exact 3d beam theory has been used as a basis for development of a variety of finite element formulations it has recently become apparent that the important requirement of objectivity of adopted strain measures although provided by the theory itself does not automatically extend to a finite element formulation in this paper we present a new finite element formulation of the geometrically exact 3d beam theory specifically designed to preserve the objectivity of the adopted strain measures in order to do so the current local rotations are interpolated in a manner similar to that adopted in co rotational approaches however no approximations typical for co rotational approaches are introduced into the procedure so in contrast to co rotational formulations the present formulation fully preserves the geometric exactness of the theory a range of numerical examples serves to illustrate the problem and to assess the formulation

a kinematically exact space finite strain beam model finite element formulation by generalized virtual work principle the present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by simo and vu quoc a geometrically exact rod model incorporating shear and torsion warping deformation int j solids structures 27 3 1991 371 3931 along the lines of the work on the planar beam theory presented by saje a variational principle for finite planar deformation of straight slender elastic beams internat j solids and structures 26 1990 887 9001 we apply exact non linear kinematic relationships of the space finite strain beam theory assuming the bernoulli hypothesis and neglecting the warping deformations of the cross section finite displacements and rotations as well as finite extensional shear torsional and bending strains are accounted for in the formulation a deformed configuration of the beam is described by the displacement vector of the deformed centroid axis and an orthonormal moving frame rigidly attached to the cross section of the beam the position of the moving frame relative to a fixed reference frame is specified by an orthogonal matrix parametrized by the rotational vector which rotates the moving frame from an arbitrary position into the deformed configuration in one step also the incremental rotational vector is introduced which rotates the moving frame from the configuration obtained at the previous iteration step into the current configuration of the beam its components relative to the fixed global coordinate system are taken to be the rotational degrees of freedom at nodal points because in 3 d space both the axial and the follower moments are non conservative not the variational principle but the principle of virtual work has been introduced as a basis for the finite element discretization here we have proposed the generalized form of the principle of virtual work by including exact kinematic equations by means of a procedure similar to that of lagrangian multipliers this makes possible the elimination of the displacement vector field from the principle so that the three components of the incremental rotational vector field remain the only functions to be approximated in the finite element implementation of the principle other researchers on the other hand employ the three components of the incremental rotational vector field and the three components of the incremental displacement vector field as a result more accurate and efficient family of beam finite elements for the non linear analysis of space frames has been obtained a one field formulation results in the fact that in the present finite elements the locking never occurs any combination of deformation states is described equally precisely this is in contrast with the elements developed in literature where in order to avoid the locking a reduced numerical integration has to be applied which unfortunately diminishes the accuracy of the solution polynomials have been chosen for the approximation of the components of the rotational vector in this case the order of the numerical integration can rationally be estimated and the computer program can be coded in such a way that the degree of polynomials need not be limited to a particular value the newton method is used for the iterative solution of the non linear equilibrium equations in an non equilibrium configuration the tangent stiffness matrix obtained by the linearization of governing equations using the directional derivative is non symmetric even for conservative loadings only upon achieving an equilibrium state the tangent stiffness matrix becomes symmetric thus obtained tangent stiffness matrix can be symmetrized without affecting the rate of convergence of the newton method for non conservative loadings however the tangent stiffness matrix is always non symmetric the numerical examples demonstrate capability of the present formulation to determine accurately the non linear behaviour of space frames in numerical examples the out of plane buckling loads are determined and the whole pre and post critical load displacement paths of a cantilever and a right angle frame are traced these in the analysis of space beams standard verification example problems show excellent accuracy of the solution even when employing only one element to describe the displacements of the size of the structure itself the rotations of 2n and extensional strains much beyond the realistic values of linear elastic material

interpolation of rotational variables in nonlinear dynamics of 3d beams the formulation of dynamic procedures for three dimensional 3 d beams requires extensive use of the algebra pertaining to the non linear character of the rotation group in space the corresponding extraction procedure to obtain the rotations that span a time step has certain limitations which can have a detrimental eect on the overall stability of a time integration scheme the paper describes two algorithms for the dynamics of 3 d beams which dier in their manifestation of the above limitation the rst has already been described in the literature and involves the interpolation of iterative rotations while an alternative formulation which eliminates the above eect by design requires interpolation of incremental rotations theoretical arguments are backed by numerical results similarities between the conventional and new formulation are pointed out and are shown to be big enough to enable easy transformation of the conventional formulation into the new one 1998 john wiley sons ltd

some existence results for fully nonlinear elliptic equations of monge ampere type we study the existence and uniqueness of solutions of monge ampere type equations this type of equations has been studied extensively by caffarelli nirenberg spruck and many others see 5 through 8 and the references therein we present some existence and uniqueness results for this type of equations on compact riemannian manifolds with non negative sectional curvature we have also generalized some results in 7

objectivity of strain measures in the geometrically exact three dimensional beam theory and its finite element implementation the paper discusses the issue of discretization of the strainconfiguration relationships in the geometrically exact theory of threedimensional 3d beams which has been at the heart of most recent

symmetric and skew antisymmetric solutions to systems of real quaternion matrix equations in this paper we consider symmetric and skew antisymmetric solutions to certain matrix equations over the real quaternion algebra h first a criterion for a quaternion matrix to be symmetric and skew antisymmetric is given then necessary and sufficient conditions are obtained for the matrix equation ax c and the following system a 1x c 1xb 3 c 3 to have symmetric and skew antisymmetric solutions the expressions of such solutions of the matrix equation and the system mentioned above are also given

r s conjugate solution to a pair of linear matrix equations abstract let r and s be m m and n n nontrivial real symmetric involutions an m n complex matrix a is termed r s conjugate if a ras where a denotes the conjugate of a in this paper necessary and sufficient conditions are established for the existence of the r s conjugate solution to the system of matrix equations ax c and xb d the expression is also presented for such solution to this system in addition the explicit expression of this solution to the corresponding optimal approximation problem is obtained furthermore the least squares r s conjugate solution with least norm to this system mentioned above is considered the representation of such solution is also derived finally an algorithm and numerical examples are given

equations du type monge ampere sur les varietes riemanniennes compactes i let vn g be a c compact riemannian manifold for a suitable function on vn let us consider the change of metric g g hess and the function as a ratio of two determinants m g g 1 using the method of continuity we first solve in c the problem log m 0 c then under weak hypothesis on f we solve the general equation log m f p f in c vn using a method of iteration our study gives rise to an interesting a priori estimate on which does not occur in the complex case this estimate should enable us to solve the equation above when 0 providing we can overcome difficulties related to the invertibility of the linearised operator this open question will be treated in our next article

analogs of cramer s rule for the minimum norm least squares solutions of some matrix equations abstract the least squares solutions with the minimum norm of the matrix equations ax b xa b and axb d are considered in this paper we use the determinantal representations of the moore penrose inverse obtained earlier by the author and get analogs of the cramer rule for the minimum norm least squares solutions of these matrix equations

a consistent 3d corotational beam element for nonlinear dynamic analysis of flexible structures abstract the purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3d flexible frames the novelty of the formulation lies in the use of the corotational framework i e the decomposition into rigid body motion and pure deformation to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix as a consequence cubic interpolations are adopted to formulate both inertia and internal local terms in the derivation of the dynamic terms an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained to enhance the efficiency of the iterative procedure an approximate expression of the tangent dynamic matrix is adopted four numerical examples are considered to assess the performance of the new formulation against the one suggested by simo and vu quoc 1988 48 it was observed that the proposed formulation proves to combine accuracy with efficiency in particular the present approach achieves the same level of accuracy as the formulation of simo and vu quoc but with a significantly smaller number of elements

on the symmetric solutions of a linear matrix equation a formula for the partitioned minimum norm reflexive generalized inverse is applied to find the general symmetric solution x to the matrix equation ax b also the dimension of the space of symmetric solutions is established

on solutions of the quaternion matrix equation ax b and their applications in color image restoration by using the complex representation of quaternion matrices and the moore penrose generalized inverse we derive the expressions of the least squares solution with the least norm the least squares pure imaginary solution with the least norm and the least squares real solution with the least norm for the quaternion matrix equation ax b respectively finally we discuss their applications in color image restoration

equations du type de monge ampere sur les varietes riemanniennes compactes ii abstract let vn g be a c compact riemannian manifold without boundary given the following changes of metric g g hess l 2 g g 2 hess where a is a fixed constant we study the corresponding monge ampere equations 1 log g g 1 f p 2 log g g 1 f p we first solve eq 2 under some simple assumptions on f c then using an appropriate change of functions that enables us to take advantage of the estimates just carried out for eq 2 we extend to eq 1 all the results proved in our previous articles 5 6 for the usual monge ampere equation although equation 2 is not locally invertible and does not even admit a solution for all f 0 f c v n a similar change of functions leads to partial results about eq 1 via c2 and c3 estimates for eq 2 eventually we give some comments and errata of our previous article p delanoe j funct anal 41 1981 341 353

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

deformation modes in the finite element absolute nodal coordinate formulation abstract the objective of this study is to provide interpretation of the deformation modes in the finite element absolute nodal coordinate formulation using several strain definitions in this finite element formulation the nodal coordinates consist of absolute position coordinates and gradients that can be used to define a unique rotation and deformation fields within the element as well as at the nodal points the results obtained in this study clearly show cross section deformation modes eliminated when the number of the finite element nodal coordinates is systematically and consistently reduced using the procedure discussed in this paper one can obtain a reduced order dynamic model eliminate position vector gradients that introduce high frequencies to the solution of some problems achieve the continuity of the remaining gradients at the nodal points and obtain a formulation that automatically satisfies the principle of work and energy furthermore the resulting dynamic model unlike large rotation finite element formulations leads to a unique rotation field and as a consequence the obtained formulation does not suffer from the problem of coordinate redundancy that characterizes existing large deformation finite element formulations in order to accurately define strain components that can have easy physical interpretation a material coordinate system is introduced to define the material element rotation and deformation using the material coordinate system the timoshenko reissner and euler bernoulli beam models can be systematically obtained as special cases of the absolute nodal coordinate formulation beam models while a constraint approach is used in this study to eliminate the cross section deformation modes it is important to point out as mentioned in this paper that lower order finite elements some of which already presented in previous investigations can be efficiently used in thin and stiff structure applications

the complex monge ampere equation with infinite boundary value abstract in this article we consider the complex monge ampere equation with infinite boundary value in bounded pseudoconvex domains we prove the existence of strictly plurisubharmonic solution to the problem in convex domains under suitable growth conditions we also obtain for general pseudoconvex domains some nonexistence results which show that these growth conditions are nearly optimal

boundary regularity for the monge ampere and affine maximal surface equations in this paper we prove global second derivative estimates for solutions of the dirichlet problem for the monge ampere equation when the inhomoge neous term is only assumed to be holder continuous as a consequence of our approach we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation

on rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3d geometrically exact beam model abstract in this work we discuss the finite element implementation of the internal constraints in a three dimensional 3d geometrically exact beam model which can be formulated as holonomic constraint relationships model problems chosen for a more detailed consideration include a general joint constraint between beams and the beam connected to a rigid component appropriate modifications of the standard form of the geometrically exact beam element arrays are carried out in order to impose explicitly these kinds of constraints into time integration schemes for nonlinear dynamics consequently only the minimum number of unknowns is retained for the global set of nonlinear equations to be solved thus avoiding the use of the extra variables the lagrange multipliers and the pertinent difficulties in integrating the system of differential algebraic equations a number of numerical simulations considering dynamic analysis of multibody systems with rigid flexible components and joint constraints are presented in order to illustrate versatility of the proposed procedure

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

existence of solutions to initial value problem for a parabolic monge ampere equation and application abstract for the initial value problem of the parabolic monge ampere equation v t v xx rxv x v xx v x 2 0 x t r 0 t arising from the optimal investment of mathematical finance theory we establish the existence of solutions whose application is also given here the initial function is unbounded and a special property is required for the solution to satisfy

an iterative algorithm for solving a pair of matrix equations ayb e cyd f over generalized centro symmetric matrices a matrix email protected r n x n is said to be a symmetric orthogonal matrix if p p t p 1 a matrix email protected r n x n is said to be generalized centro symmetric generalized central anti symmetric with respect to p if a pap a pap the generalized centro symmetric matrices have wide applications in information theory linear estimate theory and numerical analysis in this paper we propose a new iterative algorithm to compute a generalized centro symmetric solution of the linear matrix equations ayb e cyd f we show when the matrix equations are consistent over generalized centro symmetric matrix y for any initial generalized centro symmetric matrix y 1 the sequence y k generated by the introduced algorithm converges to a generalized centro symmetric solution of matrix equations ayb e cyd f the least frobenius norm generalized centro symmetric solution can be derived when a special initial generalized centro symmetric matrix is chosen furthermore the optimal approximation generalized centro symmetric solution to a given generalized centro symmetric matrix can be derived several numerical examples are given to show the efficiency of the presented method

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells