Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix(MRRM), a reverberation matrix for planar framed structures composed of anisotropic Timoshenko(T) beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method(FEM) results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli(EB) beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.     

greetings to our Readers

The word PARTICUOLOGY was coined to parallel the Chinese title for the science and technology of particles,颗粒学(ke-li-xue), by combining the Latin prefix particula for particles and the Greek suffix logia denoting subject of study.Although particuology was practiced for many years in China, as described by Song Ying-Xing in his medieval writing,Tien Kung Kai Wu (开工开物, ca. 1637), such as the winnowing of grain and the panning of iron sand, particuology wasrecognized only in the relatively recent past as a cross-, inter- and multi-disciplinary subject, absorbing the knowledge of     

Various Reciprocal Theorems and Variational Principles in the Theories of Nonlocal Micropolar Linear Elastic Mediums

In the first part of our paper,we have extended the concepts of the classical convolution and the“convolution scalar product”given by I.Hlavácěk and presented the concepts of the“convolution vector”and the“convolution vector scalar product”,which enable us to extend the initial value as well as the initial-boundary value problems for the equation with the operator coefficients to those for the system of equations with the operator coefficients.In the second part of this paper,based on the concepts of the convolution vector and the con-volution vector scalar product,two fundamental types of reciprocal theorems of the non-local micro-polar linear elastodynamics for inhomogeneous and anisotropic solids are derived.In the third part of this paper,based on the concepts and results in the first and second parts as well as the Lagrange multiplies method which is presented by W.Z.Chien,four main types of variational principles are given for the nonlocal micropolar linear elastodynamics for inhomogeneous     

THE SCHRDINGER EQUATION OF THIN SHELL THEORIES

This work is the continuation of the discussions of[50]and[51].In this paper:(A)The Love-Kirchhoff equation of small deflection problem for elastic thin shellwith constant curvature are classified as the same several solutions of Schr(?)dingerequation,and we show clearly that its form in axisymmetric problem;(B)For example for the small deflection problem,we extract the general solution ofthe vibration problem of thin spherical shell with equal thickness by the force in centralsurface and axisymmetric external field,that this is distinct from ref.[50]in variable.Today the variable is a space-place,and is not time;(C)The von Kármán-Vlasov equation of large deflection problem for shallow shellare classified as the solutions of AKNS equations and in it the one-dimensional problem isclassified as the solution of simple Schr(?)dinger equation for eigenvalues problem,and wetransform the large deflection of shallow shell from nonlinear problem into soluble linearproblem.     

DEGREE THEORY FOR MULTIVALUED (S) TYPE MAPPINGS AND FIXED POINT THEOREMS

The main purpose of this paper is devoted to generalizing the results of Browder.This paper consists of four parts.In the first part,we introduce the concepts ofmultivalued(S)and(S)_ ,type mappings and the concepts of the limits of multivalued(S)and(S)_ type mappings.These kinds of mappings contain many monotone type mappings,such as maximal monotone mapping,bounded pseudo-monotone mapping and boundedgeneralized pseudo-monotone mapping,as its special cases.In the second part we define thepseudo-degree for(S)type mapping and the degree for(S)_ type mapping.These twokinds of degrees are all the generalizations of the degree defined by Browder.Asapplications,we utilize the degree theory presented in part 2 to study the existence ofsolutions for the multivalued operator equations(see part3)and to obtain some new fixedpoint theorems in part4.     

Analysis and handling of bio-nanoparticles and environmental nanoparticles using electrostatic aerosol mobility

The successful application of differential mobility analysis for the characterization and manipulation of nanoparticles at atmospheric pressure has given rise to further development of this technique.The parallel differential mobility analyzer provides the possibility to simultaneously measure a size spectrum of nanoparticles and select a particular set of nanoparticles with a defined size for collection(as well as enrichment) and further orthogonal analysis(as for example electron microscopy,atomic force microscopy or mass spectrometry).Performing a high resolution measurement of electrical mobility diameters allows molecular weight determination of species with ultrahigh molecular masses in the mega Dalton range(e.g.protein complexes).The precise size measurement of the human rhinovirus has confirmed the potential of this technique to analyze even intact infectious human-pathogenic viruses. Moreover,the real-time measurement of nanoparticle occurrence in an urban environment confirms the versatility of the method presented here and its applicability also in other areas of importance.     

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomials,termed as HWENO schemes,is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids.The developed HWENO methodology utilizes high-order derivative information to keep WENO reconstruction stencils in the von Neumann neighborhood.A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils,making higher-order scheme stable and simplifying the reconstruction process at the same time.The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement.Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy,the designed HWENO limiters can simultaneously obtain uniform high order accuracy and sharp,essentially non-oscillatory shock transition.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

A unified analysis of a micro-beam, droplet and CNT ring adhered on a substrate: Calculation of variation with movable boundaries

In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube (CNT) ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thoroughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materials, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.     

Recent advances in inkjet printing synthesis of functional metal oxides

Inkjet printing(IJP) synthesis has emerged as a useful technique for the fabrication of functional metal oxides in the fields of nanotechnology and materials science.In this paper,we will review the fundamental state-of-the-art principles of the special ink formulations used for IJP synthesis of functional metal oxides and the applications of these oxides.     

The Schrödinger equation in theory of plates and shells with orthorhombic anisotropy

This work is the continuation of the discussion of Refs. [1-5]. In this paper:[A] The Love-Kirchhoff equations of vibration problem with small deflection for orthorhombic misotropic thin shells or orthorhombic anisotropic thin plates on Winkler’s base are classified as several of the same solutions of Schrodmger equation, and we can obtain the general solutions for the two above-mentioned problems by the method in Refs. [1] and [3-5].[B] The. von Karman-Vlasov equations of large deflection problem for shallow shells with orthorhombic anisotropy (their special cases are the von Harmon equations of large deflection problem for thin plates with orthorhombic anisotropy) are classified as the solutions of AKNS equation or Dirac equation, and we can obtain the exact solutions for the two abovementioned problems by the inverse scattering method in Refs. [4-5].The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or rib-reinforced plates and shells as special cases is included in this paper.     

Porosity Effects on Mechanical Properties of 3D Random Fibrous Materials at Elevated Temperatures

In this study,we prepare the specimens of three-dimensional random fibrous(3D RF)material along its through-the-thickness(TTT)and in-plane(IP)directions.The experimental tests of tensile and compressive properties as well as fracture toughness of 3D RF material are performed at elevated temperatures.Then,the porosity(83%,87%and 89%)and temperature dependence of the tensile and compressive strength,elastic modulus,fracture toughness and fracture surface energy of the 3D RF materials for both the TTT and IP directions are analyzed.From the results of the tensile strength and elastic modulus versus material porosities at various temperatures,we find that tensile strength and elastic modulus for the TTT direction are more sensitive to the porosity,but not for the IP direction.Fracture toughness increases firstly and then decreases at a certain critical temperature.Such critical temperature is found to be the lowest for the porosity of 83%.On the other hand,at below 1073 K,the temperature-dependent fracture surface energies with three porosities for the TTT direction show similar variation trends.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

New discrete element models for elastoplastic problems

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.     

Hamiltonian parametric element and semi-analytical solution for smart laminated plates

Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.     

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.     

Flow and heat transfer over hyperbolic stretching sheets

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numerical results are obtained by a series expansion method and a local non-similarity (LNS) method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.     

SELECTION OF OBJECTIVE FUNCTIONS AND APPLICATION OF GENETIC ALGORITHMS IN DAMPING DESIGN OF PIPE SYSTEM

The vibration failure of pipe system of aeroengine seriously influences the safety of aircraft. Its damping design is determined by the selection of the design target, method and their feasibility. Five objective functions for the vibration design of a pipeline or pipe system are introduced, namely, the frequency, amplitude, transfer ratio, curvature and deformation energy as options for the optimization process. The genetic algorithms (GA) are adopted as the optimization method, in which the selection of the adaptive genetic operators and the method of implementation of the GA process are crucial. The optimization procedure for all the above objective functions is carried out using GA on the basis of finite element software-MSC/NASTRAN.The optimal solutions of these functions and the stress distribution on the structure are calculated and compared through an example, and their characteristics are analyzed. Finally we put forward two new objective functions, curvature and deformation energy for pipe system optimization. The calculations show that using the curvature as the objective function can reflect the case of minimal stress, and the optimization results using the deformation energy represent lesser and more uniform stress distribution. The calculation results and process showed that the genetic algorithms can effectively implement damping design of engine pipelines and satisfy the efficient engineering design requirement.     

THE PROPERTIES AND APPLICATIONS OF THE INTEGRATING FACTOR IN THE OUALITATIVE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

In this article, we indicated that all the problems. such as theclassification of the singular point and the determination of thestability of limit cycle, can be solved by the application of the in-tegral factor. Especially we gave a criterion for deciding the cen-ter and the focus, Which is appropriate for the singular point ofthe first order as well as that of the higher order.In the qualitative theory of ordinary differential equations,allthe problems, such as the classification of singular point of thefirst order and higher order, and the determination of stability oflimit cycle, are important problems to be solved by different ways,the distinction between a focus and a center of singular point of thehigher order is an unsolved problem. In this paper, we show that allthe problems mentioned above can be solved by the use of the integra-ting factor. A criterion is given to decide the center and the fo-cus, and this criterion is applicable to the singular point of thefirst order as well as the higher o