New tangent stiffness matrix for geometrically nonlinear analysis of space frames

A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.

Numerical evaluation of buckling behavior in space structure considering geometrical parameters with joint rigidity

The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.

Indexing the bit-code and distance for fast KNN search in high-dimensional spaces

Various index structures have recently been proposed to facilitate high-dimensional KNN queries, among which the techniques of approximate vector presentation and one-dimensional (1D) transformation can break the curse of dimensionality. Based on the two techniques above, a novel high-dimensional index is proposed, called Bit-code and Distance based index (BD). BD is based on a special partitioning strategy which is optimized for high-dimensional data. By the definitions of bit code and transformation function, a high-dimensional vector can be first approximately represented and then transformed into a 1D vector, the key managed by a B+-tree. A new KNN search algorithm is also proposed that exploits the bit code and distance to prune the search space more effectively. Results of extensive experiments using both synthetic and real data demonstrated that BD out- performs the existing index structures for KNN search in high-dimensional spaces.

Global Attractor for High-dimensional Spacially Discrete FitzHugh-Nagumo System in Weighted Space

In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ^2×lσ^2.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.

Hierarchic Computations in Geometric Space—Showing Sharp Diffraction in Quasicrystals

A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edge-sharing unit cells that are pentagonally close packed in hierarchic structures having a geometric reciprocal lattice. The hierarchic symmetry replaces translational symmetry in crystal diffraction. Details in the calculation show how the symmetry is simulated in diffraction.

A three-dimensional numerical study on the effect of geometric asymmetry on arcjet thruster performance

In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.

An Initial Research on the Geometric Theory of Quasicrystal Structures

The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .

Some Geometric Inequalities on the Radii of Inscrib ed Sphere of a Simplex and Its Subsimplex

In this paper, we obtain some geometric inequalities on the radii of inscribed sphere of a simplex and its subsimplex, as particular case of this paper, we obtain some main results of [1].

On a Pair of Geometric Parameters of Orlicz Norm

For the geometric parameters Q and q of Orlicz norm, we prove where This result improves the traditional estimations of Chen S. T., Rao, M. M. and Wu C.X.

Geometric Analogy and Products of Vectors in <i>n</i>Dimensions

The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of determinants. Such a structure allows extending, for analogy, the ideas of the cross product for a type of the product of vectors in higher dimensions, through the systematic increase of the number of rows and columns in determinants that constitute the equations. So, in a n-dimensional space with Euclidean norm, we can associate n – 1 vectors and to obtain an n-th vector, with the same geometric characteristics of the product in three dimensions. This kind of operation is also a geometric interpretation of the product defined by Eckman [1]. The same analogies are also useful in the verification of algebraic properties of such products, based?on known properties of determinants.

Geometric Morphometrics Applied to Cartography

The morphological differences between two geographical maps can be highlighted by a polycentric distance cartogram resulting from a bidimensional regression.Beyond the communicational interest of the transformations thus produced,the method makes it possible to reveal the differences in structure and therefore constitutes a real research tool.However,bidimensional regression can only compare the shape of two maps.Since the 1990s,geometric morphometrics has revolutionized the morphological analysis of natural structures(and others).It has since been applied in many fields of research but not in cartography.This article describes the theoretical and methodological bases of a method combining bidimensional regression with a geometric morphometrics approach to compare the shape of several geographical maps.Geometric morphometrics and bidimensional regression indeed share common approaches of the statistical shape analysis like homologous landmarks and interpolation grids.However,there is no software in geometric morphometrics capable of directly reading geographical data,which would facilitate the work of cartographers accustomed to GIS software.That is why we present MapMorphy,a tool specifically developed for this task.An example on ancient maps illustrates the method.

Geometrical Meaning of Time and the Theory of Relativity

New geometrical model of time is suggested where time of body’s motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to definite length of four-dimension trajectories that is clocks appear to be standards for measurements of length in four-dimension space analogously as hard sticks are standards for measurements of length in three-dimension space. This means that space and time are entities of the same geometrical nature. A suggested interpretation of time leads to necessity of changes in general theory of relativity. These changes are unessential for body’s motion in weak gravitational field.

Completing Einstein’s Spacetime

The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.

Generalized elastic curves in the Lorentz flat space L^4

In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.

Lattices Associated with a Finite Vector Space

Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.

Fuzzy optimization of space frame

Fuzzy concepts are introduced into structural optimization to solve fuzzyoptimization problems with a crisp objective function and fuzzy constraints, also a non-membershipfunction is used to convert fuzzy constrains into crisp constrains. Two models are discussed wherethe objective function considered is the volume of space frame and the fuzzy constrains are designlimits by the axial strength, slenderness, deflection, thickness and diameter of space frame member.

Quasi-static Deployment Simulation for Deployable Space Truss Structures

A new method was proposed for quasi-static deployment analysis of deployable space truss structures. The structure is assumed a rigid assembly, whose constraints are classified as three categories:rigid member constraint, joint-attached kinematic constraint and boundary constraint. And their geometric constraint equations and derivative matrices are formulated. The basis of the null space and M-P inverse of the geometric constraint matrix are employed to determine the solution for quasi-static deployment analysis. The influence introduced by higher terms of constraints is evaluated subsequently. The numerical tests show that the new method is efficient.

3D Braided Material Based on Space Group <i>R</i>3 Symmetry

A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.

Means of Choice for Interactive Management of Dynamic Geometry Problems Based on Instrumented Behaviour

Our paper presents a project that involves two research questions: does the choice of a related problem by the tutorial system allow the problem solving process which is blocked for the student to be restarted? What information about learning do related problems returned by the system provide us? We answer the first question according to the didactic engineering, whose mode of validation is internal and based on the confrontation between an a priori analysis and an a posteriori analysis that relies on data from experiments in schools. We consider the student as a subject whose adaptation processes are conditioned by the problem and the possible interactions with the computer environment, and also by his knowledge, usually implicit, of the institutional norms that condition his relationship with geometry. Choosing a set of good problems within the system is therefore an essential element of the learning model. Since the source of a problem depends on the student’s actions with the computer tool, it is necessary to wait and see what are the related to problems that are returned to him before being able to identify patterns and assess the learning. With the simultaneity of collecting and analysing interactions in each class, we answer the second question according to a grounded theory analysis. By approaching the problems posed by the system and the designs in play at learning blockages, our analysis links the characteristics of problems to the design components in order to theorize on the decisional, epistemological, representational, didactic and instrumental aspects of the subject-milieu system in interaction.

建筑表皮的美学特征对面料创新设计的启示与实践

为了探讨面料创新设计的多元化,分析了建筑表皮的风格、肌理透叠美学以及参数化几何图案设计对面料创新的启示。首先介绍了建筑表皮设计在面料创新中的关键作用,强调了建筑表皮设计与时尚前沿的密切联系,以及其对不同生活方式群体的需求满足;然后,详细探讨了建筑表皮肌理透叠美学的意境美和微空间美,以及其在面料结构创新中的应用。通过分析建筑表皮肌理的“透”和“叠”,阐述了其在面料设计中的独特价值,以及透叠设计带来的意境感和微空间效果;最后讨论了建筑表皮参数化几何图案设计对面料创新的启示。通过介绍参数化设计的原理和实践案例,阐明了参数化几何图案设计对面料创新的重要意义,以及其为面料设计带来的新可能性和视野;主张在面料创新设计中充分借鉴建筑表皮设计的思维和技术,促进面料设计发展更加多元化、艺术化和科技化。