Some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids

The paper concerns eigenvalue problems for elastic bodies with voids in contact with massive rigid plane punches. The linear theory of elastic materials with voids according to the Cowin–Nunziato model is used. A variational principle is constructed which has the properties of minimality, similar to the well-known variational principle for problems with pure elastic media. The discreteness of the spectrum and completeness of the eigenfunctions are proved. As a consequence of variational principles, the properties of an increase or a decrease in the natural frequencies, when the mechanical and “porous” boundary conditions and the modulus of elastic solid with voids change, are established. A finite element method is proposed for numerical solution of eigenvalue problems for elastic media with voids. Some effective block algorithms for finite element eigenvalue problems with partial coupling are described. Numerical experiments are presented for determining the first eigenfrequencies of an axisymmetric elastic body with voids.     

On the adaptive finite element method of steady-state rolling contact for hyperelasticity in finite deformations

In this paper, we present an adaptive finite element method for steady-state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with Coulomb friction. A general formulation of rolling contact geometry is derived from the point of view of differential geometry. Solvability conditions for the rolling contact problems are discussed. We use Newton's method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem. We provide a numerical example to illustrate the method.     

A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells

A variational principle is formulated for the inverse problem of full-field reconstruction of three-dimensional plate/shell deformations from experimentally measured surface strains. The formulation is based upon the minimization of a least-squares functional that uses the complete set of strain measures consistent with linear, first-order shear-deformation theory. The formulation, which accommodates for transverse shear-deformation, is applicable for the analysis of thin and moderately thick plate and shell structures. The main benefit of the variational principle is that it is well-suited for C⁰-continuous displacement finite element discretizations, thus enabling the development of robust algorithms for application to complex civil and aeronautical structures. The methodology is especially aimed at the next generation of aerospace vehicles for use in real-time structural health monitoring systems.     

On persistent excitations for the identification of switched linear dynamical systems over finite fields

This paper discusses the issue of the Persistent Excitation (PE) conditions in the context of identification for dynamical systems defined over a finite field. The work is motivated by the fact that the asymptotical property of the PE conditions for dynamical systems defined over the field of real numbers is no longer valid in the case of systems defined over finite fields. The special class of switched linear discrete-time systems for which the mode is assumed to be unknown is considered. A necessary and sufficient condition that provides the minimum amount of data required for the identification is first proposed. Next, a necessary condition is derived that gives the structural condition the system must satisfy, regardless of the availability of data. Finally, some computational aspects are discussed and examples are given to illustrate the validity of the proposed results.     

A treatment of discontinuities for nonlinear systems with linearly degenerate fields

In this paper we propose an artificial compression technique to avoid the numerical diffusion that standard numerical methods present in contact discontinuities. The main idea is to replace contact discontinuities by shocks. For nonlinear 1D systems we replace locally linearly degenerate fields by genuinely nonlinear fields, in such a way the solution does not vary. We apply this technique to a family of numerical schemes and we deduce that this can be seen as a discretization of the system modified by a new term, when we are in a jump of a contact discontinuity. We have also extended this technique for the multidimensional case. We prove by applying the artificial compression technique that the numerical scheme is stable under the same CFL condition. We also present different numerical schemes: Sod’s problem for 1D Euler equations, transport of a discontinuity, a stationary contact discontinuity and in the multidimensional case the transversal transport of two different geometries. We observe that in all cases the numerical diffusion is reduced.     

Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE framework

In this article we consider the representation of a finite-energy non-stationary random field with a finite number of samples. We pose the problem as an optimal sampling problem where we seek the optimal sampling interval under the mean-square error criterion, for a given number of samples. We investigate the optimum sampling rates and the resulting trade-offs between the number of samples and the representation error. In our numerical experiments, we consider a parametric non-stationary field model, the Gaussian–Schell model, and present sampling schemes for varying noise levels and for sources with varying numbers of degrees of freedom. We discuss the dependence of the optimum sampling interval on the problem parameters. We also study the sensitivity of the error to the chosen sampling interval.     

An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method

In this paper, a new approach is developed to solve elastoplastic problems by the finite element method. This approach involves two steps: (1) A mechanical formulation using the principle of virtual work and an implicit incremental form of the constitutive equations. This form is obtained by an approximate integration of the flow rules over the increment and includes the yield criterion itself. (2) A resolution algorithm to solve the nonlinear equations obtained by the mechanical formulation: Two resolution algorithms based on the Newton-Raphson method are proposed and compared. As the mechanical formulation is no more bound to the resolution algorithm, the results obtained by these two algorithms are the same and are path independent. Two numerical examples are presented: A thick cylinder under an internal pressure and a tensile sample. The numerical results obtained by the presented approach are compared with those obtained by the classical I.S.M. The comparison shows that the accuracy of the results does not vary when the load increment size increases as in the I.S.M. For a given accuracy this method requires about 15 times less computer time than the I.S.M. for the same memory space. This approach is easy to implement in a program based on the I.S.M. and has been extended to compressible and viscoplastic materials.     

A new method for the coupling of finite element and boundary element discretized subdomains of elastic bodies

A new and efficient approach for the coupling of subregions of elastic solids discretized by means of finite elements (FE) and boundary elements (BE), respectively, is presented. The method is characterized by so-called ‘bi-condensation’ of nodal degrees of freedom followed by the transformation of the resulting BEM-related traction-displacement equations for the interface(s) of the BE subregion(s) and the FE subdomain(s) to ‘FEM-like’ force-displacement relations which are assembled with the FEM-related force-displacement equations for the interface(s). The presented ‘local FE coupling approach’ is computationally more economic than a global coupling approach since it only requires the inversion of BEM-related coefficient matrices referred to the interfaces of BE subregions and FE subdomains. Depending on whether the principle of virtual displacements or the principle of minimum of potential energy is used for the generation of force-displacement equations for the coupling interface(s), unsymmetric or symmetric coefficient matrices are obtained. Since the two principles are mechanically equivalent, identical results would be achieved in the limit of finite discretizations.The numerical investigation has shown that, depending on the problem and the discretization, the results obtained on the basis of symmetric coefficient matrices may be poor. This applies to ‘edge problems’ characterized by discontinuous tractions along the edges. On the basis of unsymmetric coefficient matrices, however, satisfactory results are obtained even for relatively coarse discretizations.     

On different finite element methods for approximating the gradient of the solution to the helmholtz equation

We consider the numerical solution of the Helmholtz equation by different finite element methods. In particular, we are interested in finding an efficient method for approximating the gradient of the solution. We first approximate the gradient by the standard Ritz-Galerkin method. As a second method a two-stage method due to Aziz and Werschulz (1980) is presented. It is shown that this method gives the same accuracy in the computed gradient and in the computed solution also in the nonconforming case. Finally, a direct method with asymptotic error estimates is given. It turns out that the presented direct method is of lowest computational complexity. Test examples are presented to illustrate the accuracy of the methods.     

A magnetic resonance compatible surgical manipulator: part of a unified support system for the diagnosis and treatment of heart disease

A prototype of a magnetic resonance (MR)-compatible surgical manipulator was designed and evaluated. The manipulator is designed so as to fit into vertical magnetic field open-configuration MR imagers. Moreover, it is designed to work without being fixed to an MR imager, and its electrical circuits and lines of actuators and sensors are independent of the room shield so that it could be installed in various kinds of settings at many MR imager sites without any additional construction. The MR compatibility of the manipulator was evaluated: no noticeable deformation was observed in the MR images even when the manipulator was in motion. Although the signal-to-noise deterioration ratio was higher than that previously reported, the MR images were thought to be good enough for recognizing the whole structure of a targeted organ and for following the relative position of the manipulator tip with regard to the target, i.e. MR tracking.     

On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers

The paper is concerned with the numerical simulation of compressible flow with wide range of Mach numbers. We present a new technique which combines the discontinuous Galerkin space discretization, a semi-implicit time discretization and a special treatment of boundary conditions in inviscid convective terms. It is applicable to the solution of steady and unsteady compressible flow with high Mach numbers as well as low Mach number flow at incompressible limit without any modification of the Euler or Navier–Stokes equations.     

A unified setting for decoupling with preview and fixed-lag smoothing in the geometric context

Exact decoupling with preview, perfect tracking of previewed references, unknown-input state observation with fixed lag, and left inversion with fixed lag are considered from a unifying perspective where exact decoupling with preview is the basic problem. Necessary and sufficient constructive conditions for decoupling with finite preview are proved in the geometric framework. Structural and stabilizability conditions are considered separately and the use of self-bounded controlled invariant subspaces allows the dynamic compensator with the minimal unassignable dynamics to be straightforwardly derived. A steering along zeros technique is devised to guarantee decoupling with stability also in the presence of unstable unassignable dynamics of the minimal self-bounded controlled invariant.     

On the absence of global solutions for quantum versions of Schrödinger equations and systems

We, first, consider the quantum version of the nonlinear Schrödinger equation

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |u(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

where $0<q<1$, $i^q$ is the principal value of $i^q$, $D_{q|t}$ is the $q$-derivative with respect to $t$, $\Delta$ is the Laplacian operator in ${\mathbb{R}}^N$, $\lambda \in ??\left\{0\right\}$, $p>1$, and $u(t,x)$ is a complex-valued function. Sufficient conditions for the nonexistence of global weak solution to the considered equation are obtained under suitable initial data. Next, we study the system of nonlinear coupled equations

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |v(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

$i^q{D}_{q|t}v(t,x)+\Delta v(qt,x)=\lambda |u(qt,x){|}^m,t>0,x\in {\mathbb{R}}^N,$     

Formal and incremental construction of distributed algorithms: On the distributed reference counting algorithm

The development of distributed algorithms and, more generally, distributed systems, is a complex, delicate and challenging process. Refinement techniques of (system) models improve the process by using a proof assistant, and by applying a design methodology aimed at starting from the most abstract model and leading, in an incremental way, to the most concrete model, for producing a distributed solution. We show, using the distributed reference counting (DRC) problem as our study, how models can be produced in an elegant and progressive way, thanks to the refinement and how the final distributed algorithm is built starting from these models. The development is carried out within the framework of the event B method and models are validated with a proof assistant.     

A unified approach to the change of resolution: space and gray-level

It is shown that by defining a suitable measure for the comparison of images, changes in resolution can be treated with the same tool as changes in color resolution. A gray-tone image, for example, can be compared to a half-tone image having only two colors (black and white), but of higher spatial resolution. A graph-theoretical definition of the basic measure used is introduced. This is followed by application to spatial resampling and gray-level requantization. This results in a hybrid treatment of resolution, and the possibility of trading spatial for gray-level resolution and vice versa.<>     

On the control of noise in finite element tidal computations: A semi-implicit approach

Numerical solution of the two-dimensional shallow water equations is achieved by coupling the finite element method in space with finite difference time stepping schemes. Solutions obtained with an efficient leapfrog model are found to contain severe short-wavelength oscillations in space when compared to analytic solutions. An alternative semi-implicit formulation in the time domain, which retains most of the economical advantages of the leapfrog scheme is developed and tested. A significant reduction in the mode-to-node oscillations and improved agreement with analytical solutions are obtained. Both linear triangles and quadratic isoparametric quadrilaterals are examined. Emphasis is on the numerical behavior of the schemes tested and a comparison with a field case is not attempted.     

试论大学生思想政治工作的预见性

阐述了大学生思想政治工作具有预见性的必要性和可能性;提出了大学生思想政治工作要做到具有预见性,应注意从掌握需要、掌握客观环境因素、善于观察这三方面入手.     

Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position

Suggested by the structure of the visual nervous system, a new algorithm is proposed for pattern recognition. This algorithm can be realized with a multilayered network consisting of neuron-like cells. The network, “neocognitron”, is self-organized by unsupervised learning, and acquires the ability to recognize stimulus patterns according to the differences in their shapes: Any patterns which we human beings judge to be alike are also judged to be of the same category by the neocognitron. The neocognitron recognizes stimulus patterns correctly without being affected by shifts in position or even by considerable distortions in shape of the stimulus patterns.