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Search results for: NONLINEAR MARKOV PROCESS
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On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Comparison of Two Nonlinear Predictive Control Algorithms for Dissolved Oxygen Tracking Problem at WWTP
PublicationThe wastewater treatment plant is classified as a complex system, due to its nonlinear dynamics, large uncertainty of disturbance inputs, multiple time scales in the internal process dynamics, and multivariable structure. The aeration process, in turn, is an important and expensive part of wastewater treatment plant operation. All operating parameters of the aeration in biological processes are to be precisely controlled to provide...
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Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
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Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...
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Nonlinear Influence of Sound on the Vibrational Energy of Molecules in a Relaxing Gas
PublicationDynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublicationThe nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k>1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics...
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublicationThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...
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Nonlinear Interaction of Magnetoacoustic Modes in a Quasi-Isentropic Plasma Flow
PublicationThe nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till . The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting....
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NONLINEAR VIBRATION ANALYSIS OF BEAM AND PLATE WITH CLOSED CRACK: A REVIEW
PublicationThe effect of nonlinearity is high sensitivity in damage detection, especially for closed cracks and delamination. This review illustrates the results of several researchers dealing with nonlinear effects caused by the closure of cracks in the structure, i.e., beam and plate structures. Early detection of damage is an important aspect for the structure and, therefore, continuous progress is being made in developing new and effective...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Mixed integer nonlinear optimization of biological processes in wastewater sequencing batch reactor
PublicationWastewater treatment plays a key role for humanity. The waste entering lakes, rivers, and seas deteriorates daily quality of life. Therefore, it is very important to improve the efficiency of wastewater treatment. From a control point of view, a biological wastewater treatment plant is a complex, non-linear, multidimensional, hybrid control system. The paper presents the design of the optimizing hierarchical control system applied...
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Hidden Markov Models for Visual Processing of Marketing Leaflets
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On the mixing property and the ergodic principle for nonhomogeneous Markov chains
PublicationW pracy rozważane są różne typy zachowania granicznego nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym. Badana jest struktura geometryczna zbioru łańcuchów Markowa w normowej i mocnej topologii operatorowej.
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Optimal asynchronous estimation of 2D Gaussian-Markov processes
PublicationW artykule rozważa się problem estymacji trajektorii dwuwymiarowych ciągłoczasowych procesów Gaussa-Markowa na podstawie zaszumionych pomiarów wykonywanych w nierównomiernie rozłożonych chwilach czasu. W przypadku takiego problemu, w każdym cyklu pracy algorytmu należy dokonać dyskretnoczasowej predykcji (analogicznie jak w przypadku filtru Kalmana). Niestety zadanie to może być złożone obliczeniowo. Aby rozwiązać ten problem,...
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Nonlinear increase in bubbles radii caused by sound in a bubbly liquid
PublicationThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is considered. The reasons for interaction are both nonlinearity and dispersion. In the field of intense sound, a decrease in the mixture density is predicted. That corresponds to the well-established growth of bubbles volumes due to rectified diffusion. The nonlinear interaction of modes as a reason for a bubble to grow due to sound, is discovered. The...
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Generalized Euler method for nonlinear first order partial differential equations.
PublicationKlasyczne rozwiązania nieliniowych równań różniczkowych cząstkowych pierwszego rzędu są aproksymowane w tej pracy za pomocą rozwiązań quasiliniowych układów równań różnicowych. Podstawowa idea pracy jest oparta na teorii charakterystyk. Podane są warunki wystarczające dla zbieżności metody. Dowód stabilności schematu różnicowego wykorzystuje metodę porównawczą z nieliniowymi oszacowaniami typu Perrona dla danych funkcji.Podane...
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Optical rotation in the lithium triborate nonlinear crystal
PublicationA dual-wavelength polarimetric technique at 633 and 661 nm has been used for the characterization of a nonlinear lithium triborate (LiB3O5) nonenantiomorphous biaxial crystal. The mismatch of the crystallographic and optical coordinate systems was taken into account. The optical rotatory power for light propagation along one of the optical axes is ρ = 7.06° mm−1. The gyration tensor component along the bisector between the x and...
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Limiting distribution of the three-state semi-Markov model of technical state transitions of ship power plant machines and its applicability in operational decision-making.
PublicationThe article presents the three-state semi-Markov model of the process {W(t): t 0} of state transitions of a ship power plant machine, with the following interpretation of these states: s1 – state of full serviceability, s2 – state of partial serviceability, and s3 – state of unserviceability. These states are precisely defined for the ship main engine (ME). A hypothesis is proposed which explains the possibility of application...
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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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Towards More Realistic Probabilistic Models for Data Structures: The External Path Length in Tries under the Markov Model
PublicationTries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel- Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing...
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On the Nonlinear Effects of Magnetoacoustic Perturbations in Optically Thin Quasi-Isentropic Plasmas
PublicationNonlinear effects of planar magnetosound perturbations in a plasma are discussed. Plasma is non-adiabatic due to optically thin radiation and external heating. For these reasons, thermal instability of a plasma may appear which makes it acoustically active. The plasma is assumed to be initially homogeneous ideal gas with infinite electrical conductivity permeated by a straight magnetic field which is orthogonal to the trajectories...
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The knowledge and process continuum
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Nonlinear fuzzy control of the dissolved oxygen in activated sludge processes
PublicationWastewater treatment plant is generally a complex, multivariable, time varying and nonlinear large scale industrial system. Moreover, interactions between the components are very strong. The dissolved oxygen tracking problem is one of the most complex and fundamental issues of biological processes. Air for the aerated tanks is supplied by aeration system (blowers, pipes, diffusers). It is a complex dynamic system. The new control...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Certain family of analytical solutions of nonlinear von Neumann equations
PublicationIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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Employment of a Nonlinear Adaptive Control System for Improved Control of Dissolved Oxygen in Sequencing Batch Reactor
PublicationA proper control in a complex system, such as Wastewater Treatment Plant (WWTP) with each year is becoming increasingly important. High quality control can minimize an environmental impact as well as reduce operational costs of the WWTP. One of the core issues is providing adequate dissolved oxygen (DO) concetration for microorganisms used in a treatment process. An aeration process of the wastewater realised by an system consisting...
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Direct estimation of linear and nonlinear functionals of quantum state
PublicationWe present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of...
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublicationIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
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Accuracy of Trajectory Tracking Based on Nonlinear Guidance Logic for Hydrographic Unmanned Surface Vessels
PublicationA new trend in recent years for hydrographic measurement in water bodies is the use of unmanned surface vehicles (USVs). In the process of navigation by USVs, it is particularly important to control position precisely on the measuring profile. Precise navigation with respect to the measuring profile avoids registration of redundant data and thus saves time and survey costs. This article addresses the issue of precise navigation...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Nonlinear secondary arc model use for evaluation of single pole auto-reclosing effectiveness
PublicationPurpose – The purpose of this paper is to discuss two evaluation methods of single pole autoreclosing process effectiveness in HV transmission lines. Secondary arc current and recovery voltage results obtained by load flow calculation are compared to the results obtained by the time domain simulations. Moreover, a nonlinear secondary arc implementation is presented. Design/methodology/approach – A computer simulation studies were...
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An invariance principle for the law of the iterated logarithm for some Markov chains
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass
PublicationThe planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces exchanged between the point-mass and the string are taken into account via Lagrange...
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Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
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Nonlinear and linear impedance of bismuth vanadate ceramics and its relation to structural properties
PublicationThe nonlinear and linear electrical properties, topography, and microstructure of bismuth-vanadate ceramics, were studied. The structurewas observed with the use of X-ray diffraction (XRD), scanning electronmicroscopy (SEM), atomic force microscopy (AFM) and confocal microscopy methods. The obtained results showed that ceramic is porous. Two phase transitionswere determinedwith the use of DSC measurements. The linear and nonlinear ac...
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Elastoplastic material law in 6-parameter nonlinear shell theory
PublicationWe develop the elastoplastic constitutive relations for nonlinear exact 6-parameter shell theory. A J2-type theory with strain hardening is formulated that takes into account asymmetric membrane strain measures. The incremental equations are solved using implicit Euler scheme with closest point projection algorithm. The presented test example shows the correctness of the proposed approach. Influence of micropolar material parameters...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Mechatronic design o strongly nonlinear systems on a basis of three wheeled mobile platform
PublicationRemarkable grow in demand both of mobile platform operability performance and reduction of project leading time development encourage to apply modern algorithms and reliable engineering tools for the design process. The paper discusses the mechatronic design applied for the surveillance system based on the energy performance index algorithm. The exploited mechatronic techniques i.e. virtual prototyping, Hardware-In-the-Loop Simulation...
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On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
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Searching of the buried objects into the sea bottom by means of nonlinear acouctic methods
PublicationThe main goal of this paper is to introduce the methodology of preparing the area for investigations that will be carried out at the sea. As the first step there is recognition of the basic method both in the theory as well as experimental investigation. There were taken into account the nonlinear methods. These ones are very promising methods that have very interesting features, very convenient for examinations of the seabed structure....
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Nonlinear Model of Synchronous Generator for Autonomous Electrical Power Systems Analysis
PublicationThis paper presents the nonlinear lookup table model for synchronous generator (SG) analysis. The saturation effects of the SG magnetic circuit have been considered. The saturated characteristic of the SG magnetic circuit are based on the open circuit saturation curve for magnetizing inductances. The model has been implemented into the Synopsys/Saber software using the MAST modelling language. To implement the no-load voltage characteristic...
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Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas
PublicationTwo dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place. are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into...
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Ship Dynamic Positioning Based on Nonlinear Model Predictive Control
PublicationThe presented work explores the simulation test results of using nonlinear model predictive control algorithm for ship dynamic positioning. In the optimization task, a goal function with a penalty was proposed with a variable prediction step. The results of the proposed control algorithm were compared with backstepping and PID. The effect of estimation accuracy on the control quality with the implemented algorithms was investigated....
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Nonlinear Excitation of the Non-Wave Perturbations by the Magnetoacoustic Waves in the Non-Isentropic Plasma
PublicationNonlinear excitation of slow modes by the planar magnetosonic perturbations in a plasma is discussed. Plasma is an open system due to radiation and external heating. This may stipulate enhancement of wave perturbations and hence the acoustical activity of plasma. Plasma is assumed to be a homogeneous ideal gas with infinite electrical conductivity. The straight magnetic field is orthogonal to the velocity of fluid’s...
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Nonlinear Fuzzy Control System for Dissolved Oxygen with Aeration System in Sequencing Batch Reactor
PublicationBiological processes at a wastewater treatment plant are complex, multivariable, time varying and nonlinear. Moreover, interactions between the components are very strong. Control of dissolved oxygen is one of most important task at the plant. The level of dissolved oxygen in aerobic tanks has significant influence on behaviour and activity of microorganisms at the plant. Air for aerated tanks is supplied by the aeration system...
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Elastoplastic nonlinear FEM analysis of FGM shells of Cosserat type
PublicationThe paper is a continuation of [1] where the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter (the drilling degree of freedom) was presented. Here the formulation is extended to the elasto-plastic range. The material law is based on Cosserat plasticity and employs the well-known Tamura-Tomota-Ozawa (TTO) [2] mixture...