Problem of information equivalent functional schemes in aided inertial navigation systems

It has already been shown [1] that the problem of aiding inertial navigation systems (INS) by using information supplementing the inertial information can be solved both by estimating the INS errors from its output data and by introducing a feedback in the INS navigation algorithm. In the framework of the linear theory, it was also shown that any combination of these two schemes is information equivalent to one of them if the problem is solved as a pure estimation problem. The procedure of constructing the corresponding algorithms was described. Although the problem has been solved sufficiently completely, our meetings with the designers show that there is no clarity in its understanding. This understanding is especially important if the aiding problem is solved by using coarse sensors of source information, for example, MEMS sensors, which is actual at present. The material presented below should be considered as an additional explantation of the previously presented materials. Here illustrative examples are especially important.     

An Eulerian approach for simulating frictional heating in disc-pad systems

Thermal stresses as a result from frictional heating must be considered when designing disc brakes, clutches or other rotating machine components with sliding contact conditions. The rotational symmetry of the disc in these kind of applications makes it possible to model these systems using an Eulerian approach instead of a Lagrangian framework. In this paper such an approach is developed and implemented. The disc is formulated in an Eulerian frame where the convective terms are defined by the angular velocity. By utilizing the Eulerian framework, a node-to-node formulation of the contact interface is obtained, producing most accurate frictional heat power solutions. The energy balance of the interface is postulated by introducing an interfacial temperature. Both frictional power and contact conductances are included in this energy balance. The contact problem is solved by a non-smooth Newton method. By adopting the augmented Lagrangian approach, this is done by rewriting Signorini’s contact conditions to an equivalent semi-smooth equation. The heat transfer in the disc is discretized by a Petrov–Galerkin approach, i.e. the numerical difficulties due to the non-symmetric convective matrix appearing in a pure Galerkin discretization is treated by following the streamline-upwind approach. In such manner a stabilization is obtained by adding artificial conduction along the streamlines. For each time step the thermo-elastic contact problem is first solved for the temperature field from the previous time step. Then, the heat transfer problem is solved for the corresponding frictional power. In such manner a temperature history is obtained sequentially via the trapezoidal rule. In particular the parameter is set such that both the Crank–Nicolson and the Galerkin methods are utilized. The method seems very promising. This is demonstrated by solving a two-dimensional benchmark as well as a real disc brake system in three dimensions.     

Formation of the residual stress field under local thermal actions

The one-dimensional process of material deformation due to local heating and subsequent cooling is analyzed in the framework of the classical theory of elastoplastic deformations. The problem of formation of residual stresses in a thin plate made of an elastoplastic material under a given thermal action is solved. The graphs of fields of residual stresses and displacements are constructed.     

Thermomechanical response of non-local porous material

A thermomechanical model of a porous material is presented. The constitutive model is based on the Gurson model, formulated within a thermodynamic framework and adapted to large deformations. The thermodynamic framework yields a heat equation that naturally includes the mechanical dissipation. To introduce a length scale, the Gurson model was enhanced through non-local effects of the porosity being taken into account. A numerical integration scheme of the constitutive model and the algorithmic stiffness tensor are derived. The integration of the plastic part of the deformation gradient is based on an exponential update operator, an eigenvalue decomposition is also being used to reduce the number of equations that need to be solved. The coupled problem that arises is dealt with by employing a staggered solution method. To examine the capabilities of the model, shear band formation in a thick disc and crack growth in a thick notched disc were investigated.     

Discretization of an admixture flux within the framework of the fractal model of anomalous diffusion

Within the framework of the fractal mobile-immobile medium model describing non-Fickian effects occurring in admixture seepage due to particle adhesion to the solid matrix, an expression for the admixture flux is derived. Flow discretization intended for finite-difference calculations is proposed and used as a basis for a conservation-law scheme for solving the model equations with account for admixture sources. Several one-dimensional test problems of admixture propagation in an imposed seepage flow are solved using the approach developed.     

Inhomogeneous deformation in metallic glasses

The present study provides a theoretical framework for the inhomogeneous deformation in metallic glasses. The free volume concentration is adopted as the order parameter, which is a function of position and time. The three processes that can change the local free volume concentration are diffusion, annihilation, and stress-driven creation. The rate functions for free volume generation and plastic flow depend on the underlying microscopic model, but the framework is generally valid for different models. A simple shear problem is solved as an example. A linear stability analysis is performed on the basis of the homogeneous solution. An inhomogeneous solution is obtained with a finite amplitude disturbance to the initial free volume distribution. Numerical simulation shows the development of the inhomogeneous deformation and strain localization.     

Thermoelastoplastic Deformation of a Multilayer Ball

The problem of centrally symmetric deformation of a multilayer elastoplastic ball in the process of successive accretion of preheated layers to its outer surface is considered in the framework of small elastoplastic deformations. The problems of residual stress formation in the elastoplastic ball with an inclusion and a cavity are solved under various mechanical boundary conditions on the inner surface and for prescribed thermal compression distributions. The graphs of residual stress and displacement fields are constructed.     

Stability of an Elastic Layer Stack Between Two Half-Spaces Under Compressive Loads

A stability problem is solved for a multicomponent medium consisting of a layer stack and two structurally homogeneous half-spaces. The analysis is made within the framework of the piecewise-homogeneous model and the three-dimensional linearized theory of stability for small subcritical strains. The properties of isolated elements of the medium are determined within the framework of the orthotropic linearly elastic model. Specific numerical results are obtained for the case of plane strain     

Temperature distributions in a periodically stratified layer with slant lamination

The paper deals with the two-dimensional stationary temperature distribution in a composite layer. The nonhomogenous body is assumed to be composed of periodically repeated two-layered laminae. The layering is inclined with an arbitrary angle to the boundary planes. The lower and upper boundary planes are assumed to be kept at given temperatures. The considered problem is solved within the framework of the homogenized model with microlocal parameters, where the continuity thermal conditions on interfaces are satisfied.     

Stability of Cylindrical Shells with Microdamages

Problems on bifurcational stability of cylindrical shells are formulated and solved within the framework of the Kirchhoff–Love hypotheses with regard for damageability in the precritical stress state. The damageability of the material is due to the inhomogeneity of its microstrength and is modeled by empty quasispherical pores whose distribution over the shell volume is statistically homogeneous and isotropic. The problems are solved for shells under axial and radial compression.     

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

In this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen relies on a partitioned strategy that allows us to solve the strongly coupled fluid–structure interaction problem. It is then possible to re-use the existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian–Eulerian (ALE) framework, and the finite volume is used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern the 2D validation case but also 3D problems with a large number of equations to be solved.     

Exact solution for mixed boundary value problems at anisotropic piezoelectric bimaterial interface and unification of various interface defects

The special mixed boundary value problem in which a debonded conducting rigid line inclusion is embedded at the interface of two piezoelectric half planes is solved analytically by employing the 8-D Stroh formalism. Different from existing interface insulating crack model and interface conducting rigid line inclusion model, the presently analyzed model is based on the assumption that all of the physical quantities, i.e., tractions, displacements, normal component of electric displacements and electric potential, are discontinuous across the interface defect. Explicit solutions for stress singularities at the tips of debonded conducting rigid line inclusion are obtained. Closed form solutions for the distribution of tractions on the interface, surface opening displacements and jump in electric potential on the debonded inclusion are also obtained, in addition real form solutions for these physical quantities are derived. Various forms of interface defect problems encountered in practice are solved within a unified framework and the stress singularities induced by those interface defects are discussed in detail. Particularly, we find that the analysis of interface cracks between the embedded electrode layer and piezoelectric ceramics can also be carried out within the unified framework.     

Finite deformation solution of a dynamic problem of combined compressive and shear loading for an elastic-plastic half-space

A self-similar problem involving combined compressive and shear loading of a non work-hardening elastic-plastic half-space is solved, for large deformations, within the framework proposed earlier by J.R. Willis (1969). The thermodynamic system, which was left open in the general framework, is taken to be that proposed recently by G.W. Swan and C.K. Thornhill (1974). Results are presented for oblique loading of a block of low carbon steel. For an imposed normal velocity of the order of 1,100 m s^?1, a smooth shear wave behind the shock that is formed is possible only for small transverse velocities, perhaps no greater than 14 m s^?1, depending upon the value assumed for the yield stress. Larger transverse velocities would give rise to a thin layer of intense shear near the surface of the block, whose study would require allowance for both work-hardening and temperature-dependent yield stress.     

Effect of Irradiation on the Stability and Natural Vibrations of Containment Shells

An approximate approach is proposed to solve the problem on the natural vibrations and stability of an NPP reactor containment. Radiation alters the mechanical properties of such shells and causes volumetric expansion of their material. The problems are solved within the framework of the Timoshenko kinematic hypotheses by reducing shells inhomogeneous throughout the thickness to homogeneous shells with reduced tension–compression, shear, and flexural rigidities     

Nonlinear analysis of the finite-amplitude oscillations of a charged liquid layer on a rigid spherical core for the multimodal initial deformation of the free surface

Within the framework of the analytical asymptotic procedure, in the quadratic approximation in the small dimensionless amplitude of the capillary oscillation of a charged electroconductive fluid layer on the surface of a rigid spherical core, the problem of calculation of the free surface shape at an arbitrary moment is solved for a multimodal initial deformation. The conditions under which the internal nonlinear resonant interaction between the liquid layer oscillation modes and the intermodal energy exchange are realized are analyzed for both the degenerate and the secondary combinational resonances.     

Neural network ℋ<Subscript>∞</Subscript> chaos synchronization

This paper proposes a new neural network ?_∞ synchronization (NNHS) scheme for unknown chaotic systems. In the proposed framework, a dynamic neural network is constructed as an alternative to approximate the chaotic system. Based on this neural network and linear matrix inequality (LMI) formulation, the NNHS controller and the learning law are presented to reduce the effect of disturbance to an ?_∞ norm constraint. It is shown that finding the NNHS controller and the learning law can be transformed into the LMI problem and solved using the convex optimization method. A numerical example is presented to demonstrate the validity of the proposed NNHS scheme.     

Flow in a viscous jet escaping through a supersonic nozzle into a semi-infinite ambient space

The problem of an axisymmetric gas flow in a supersonic nozzle and in the jet escaping from the nozzle to a quiescent gas is solved within the framework of Navier-Stokes equations. The calculated pressure distribution is compared with that measured in the jet by a Pitot tube. The influence of the jet pressure ratio, Reynolds number, and half-angle of the supersonic part of the nozzle on nozzle flow and jet flow parameters is studied. It is shown that the distributions of gas-dynamic parameters at the nozzle exit are nonuniform, which affects the jet flow. The flow pattern for an overexpanded jet shows that jet formation begins inside the nozzle because of boundary-layer displacement from the nozzle walls. This result cannot be obtained with the inviscid formulation of the problem.     

Flow of a viscous fluid down a slope

A thin layer of viscous fluid flowing down a slope under gravity is considered. The stability of this flow is studied in the framework of a shallow water model. A number of equations of shallow water motion are derived with consideration of the viscous friction. The corresponding Cauchy problem is solved analytically. It is shown that the uniform flow may be unstable with respect to small initial perturbations. A criterion of instability is proposed.     

Exact geometry based quasi-conforming analysis for Euler-Bernoulli beam

The problem of quick analysis using exact geometry data was proposed by Hughes et al. and the isogeometric analysis framework was introduced as a solution. In this letter, the exact geometry concept is combined into the quasi-conforming framework and a novel method, i.e., the exact geometry based quasi-conforming analysis is proposed. In present method the geometry is exactly described by non-uniform rational B-spline bases, while the solution space by traditional polynomial bases. Present method combines the merits of both isogeometric analysis and quasi-conforming finite element method. In this letter Euler-Bernoulli beam problem is solved as an example and the results show that the present method is effective and promising.