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Search results for: NUMERICAL STABILITY
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Some remarks about numerical stability in nonlinear dynamics on the basic of truss structures.
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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On convergence and stability of a numerical scheme of Coupled Nonlinear Schrödinger Equations
PublicationRozważamy rozwiązania numeryczne układu sprężynowych równań nieliniowych Schrödingera. Udowodniliśmy stabilność i zbieżność. Testujemy za pomocą rozwiązań solitonowych.
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Simplified numerical model for global stability of corrugated silos with vertical stiffeners
PublicationArtykuł omawia wyniki stateczności globalnej silosów z blachy falistej z pionowymi usztywnieniami. Zaproponowano uproszczony model numeryczny metody elementów skończonych do określenia stateczności. Wyniki numeryczne były bardziej dokładnie niż metody zaproponowane w Eurokodzie.
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Stability Assessment of Coastal Cliffs Incorporating Laser Scanning Technology and a Numerical Analysis
PublicationWe investigated the cli coast in Jastrzebia Gora, Poland. The measurements that were taken between 2014 and 2018 by applying terrestrial, mobile, and airborne laser scanning describe a huge geometric modification involving dislocations in a 2.5 m range. Dierential maps and a volumetric change analysis made it possible to identify the most deformed cli’s location. Part of the monitoring of coastal change involved the measurement...
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Stability and bearing capacity of arch-shaped corrugated shell elements: experimental and numerical study
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Numerical analysis of influence of intermediate stiffeners setting on the stability behaviour of thin-walled steel tank shell
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Numerical Issues and Approximated Models for the Diagnosis of Transmission Pipelines
PublicationThe chapter concerns numerical issues encountered when the pipeline flow process is modeled as a discrete-time state-space model. In particular, issues related to computational complexity and computability are discussed, i.e., simulation feasibility which is connected to the notions of singularity and stability of the model. These properties are critical if a diagnostic system is based on a discrete mathematical model of the flow...
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Stability of an Innovative Cold-Formed GEB Section
PublicationThis paper is focused on the numerical analysis and experimental test of stability of the cold-formed profile with an innovative GEB cross-section. For the shell model of the axially compressed member, the linear buckling analysis and the nonlinear static analysis were carried out. In the numerical research, the buckling load and the limit load for variable section heights were obtained. Some of the results were compared with the...
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Stability and limit load analysis of a cold-formed channel section column
PublicationThe paper presents stability and limit load analysis of a steel column 1440 mm high of a cold-formed channel section, subjected to a combination of compression and bending. Experimental results were compared to the resistance of a code procedure and to the outcome of numerical non-linear analysis. Comparison was made of numerical solutions by means of static (Riks) and dynamic (Explicit and Implicit) methods. Perfectly elastic...
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Stability analysis of a dike constructed of anthropogenic materials
PublicationNumerical analyses of stability are presented for a hypothetical dikes constructed of dredged materials and bottom ash, in varying proportions. The paper is related to the international research project DredgDikes, which focused on the use of anthropogenic materials in dikes construction and flood protection. The aim of this project was to investigate the possibility of using anthropogenic materials from rivers and sea dredging...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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ANALYSIS OF BRACE STIFFNESS INFLUENCE ON STABILITY OF THE TRUSS
PublicationThe paper is devoted to the numerical and experimental research of stability of a truss with side elastic supports at the top chord. The structure is a model of a real roof truss scaled by factor ¼. The linear buckling analysis and non-linear static analysis were carried out. The buckling length factor for the compressed top chord was calculated and the limit load for the imperfect truss shell model with respect to brace stiffness...
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LINEAR CHARACTERISTICS OF THE SLOSHING PHENOMENON FOR THE PURPOSE OF ON-BOARD SHIP'S STABILITY ASSESSMENT
PublicationThe paper presents results of experimental research and numerical simulations of the sloshing phenomenon. The research was focused on computation of the heeling moment affecting stability of a vessel. The proposed linearisation enables application of the results to the assessment of the ship's stability. The dependence of the heeling moment upon localisation of a tank in the ship's hull is analysed. The heeling moment obtained...
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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Thermal ablation modeling via the bioheat equation and its numerical treatment
PublicationThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
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A Method of Assessment of the Liquid Sloshing Impact on Ship Transverse Stability
PublicationLiquid sloshing phenomenon taking place in partly filled ships? tanks directly affects the stability of a vessel. However, only static calculations are carried out onboard ships nowadays and static transfer of liquid weight is taken into account in the course of routine stability calculation. The paper is focused on a dynamic heeling moment due to liquid sloshing in tanks onboard ships. The set of numerical simulations of liquid...
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Stability of an imperfect truss loaded by wind
PublicationThe present paper is devoted to the numerical research of stability of a truss loaded by wind and stiffened by elastic supports located at the top chord. The lateral braces or lateral and torsional braces were taken into account. In this paper, the linear buckling analysis re- sults for the beam and shell model were presented. Two different shapes of initial geometric imperfections were considered in the non-linear static analysis...
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Effect of excitation intensity on slope stability assessed by a simplified approach
PublicationThe paper concerns the selection of a design accelerograms used for the slope stability assessment under earthquake excitation. The aim is to experimentally verify the Arias Intensity as an indicator of the excitation threat to the slope stability. A simple dynamic system consisting of a rigid block on a rigid inclined plane subjected to horizontal excitation is adopted as a slope model. Strong ground motions recorded during earthquakes...
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The Impact of Sloshing Liquids on Ship Stability for Various Dimensions of Partly Filled Tanks
PublicationLiquid sloshing phenomenon taking place in partly filled ships' tanks directly affects the stability of a vessel. However, only static calculations are carried out onboard ships nowadays and static transfer of liquid weight is taken into account in the course of routine stability calculation. The paper is focused on a dynamic heeling moment due to liquid sloshing in tanks onboard ships. A number of numerical simulations of liquid...
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Stability and load bearing capacity of a truss with elastic braces
PublicationThe present paper is devoted to the numerical and experimental investigations of stability of a truss stiffened by elastic braces. The model of a real roof truss scaled by factor ¼ was investigated. In the research the linear buckling and non-linear static analysis of the truss shell and beam model with geometric and material non-linearity is presented. The initial imperfections were assumed in the form of the first buckling mode....
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublicationThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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Stability of a truss under upward wind loading
PublicationThe present paper is devoted to the numerical investigations of stability of a truss under upward wind load. The truss is braced at its the upper cord. A structural variant including lateral braces, or lateral and torsional braces is considered. The research presents the problems of linear buckling and non-linear static analysis of the truss shell and beam model with geometric and material non-linearity are presented. The initial...
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Numerical tests of time-stepping schemes in the context of FEM for 6-field shell dynamics
PublicationThe paper deals with integration of dynamic equations of irregular shells performed with relatively long time steps. Numerical instability appearing often in this kind of analysis motivated the authors to present some studies based on numerical tests referring to convergence problems of finite element analysis as well the applied stability conditions. The analysis is carried out on simulations of shell dynamics with the where the...
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Stability and load bearing capacity of a braced truss under upward wind loading
PublicationThe paper is focused on the numerical and experimental investigation of stability of a steel truss under upward wind loading. The structure was stiffened by elastic braces situated at the top and bottom chord. Usually the lateral (translational) brace stiffness is considered. However, the rotational stiffness of braces caused by interaction between torsional stiffness of the truss top chord and bending stiffness of the roof elements...
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Stability and load bearing capacity of a braced truss under upward wind loading
PublicationThe paper is focused on the numerical and experimental investigation of stability of a steel truss under upward wind loading. The structure was stiffened by elastic braces situated at the top and bottom chord. Usually the lateral (translational) brace stiffness is considered. However, the rotational stiffness of braces caused by interaction between torsional stiffness of the truss top chord and bending stiffness of the roof elements...
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublicationThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case
PublicationThis paper addresses the problem of model-based global stability analysis of discrete-time Takagi–Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the classical common quadratic Lyapunov...
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Numerical analysis and in situ tests of the Grot Rowecki Bridge in Warsaw
PublicationThe paper presents the FEM analysis of the reconstructed the Grot-Rowecki Bridge over Vistula river in Warsaw. The bridge has seven spans and consists of two independent structures with the longest spans of 120 m. After reconstruction the bridge is over 10 m wider. The numerical, nonlinear analysis has been con-ducted on a global and local FEM models. These models are defined so as they strictly comply with global structural bridge...
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Analysis of sloping brace stiffness influence on stability and load bearing capacity of a truss
PublicationThe paper is focused on the numerical study of stability and load bearing capacity of a truss with side elastic braces. The structure is made in reality. The rotational and sliding brace stiffnesses were taken into account. Linear buckling analysis and non-linear static analysis with geometric and material nonlinearity were performed for the beam and shell model of the truss with respect to the angle of sloping braces. As a result...
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Testing Stability of Digital Filters Using Multimodal Particle Swarm Optimization with Phase Analysis
PublicationIn this paper, a novel meta-heuristic method for evaluation of digital filter stability is presented. The proposed method is very general because it allows one to evaluate stability of systems whose characteristic equations are not based on polynomials. The method combines an efficient evolutionary algorithm represented by the particle swarm optimization and the phase analysis of a complex function in the characteristic equation....
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Numerical and quantitative analysis of HIV/AIDS model with modified Atangana-Baleanu in Caputo sense derivative
PublicationFractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu’s of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels....
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Thermo-elastic non-linear analysis of multilayered plates and shells
PublicationGeometrically nonlinear FEM analysis of multilayered composite plates and shells is performed in order to resolve the stability problem of the structures being under the influence of temperature field. The Riks-Wempner-Ramm algorithm with a specially modified multi-choice unloading condition has been implemented in authors’ numerical code. As the representation of multilayered medium the Equivalent Single Layer approach with the...
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Extended Newmark method to assess stability of slope under bidirectional seismic loading
PublicationThe paper concerns the dynamic behavior of a simple slope model subjected to simultaneous horizontal and vertical excitations. The proposed method is based on Newmark’s sliding block concept, however, four new features are introduced. The most important assumption is that the normal component of dynamic excitations affects the resisting force both before and after the initiation of the relative slope motion, making it time-dependent....
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Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field
PublicationThis paper considers a single-walled composite nano-shell (SWCNS) exposed in a torsional critical stability situation. As the magnetic field affects remarkably nanostructures in the small size, a three-dimensional magnetic field is assessed which contains magnetic effects along the circumferential, radial and axial coordinates system. Based on the results of the nonlocal model of strain gradient small-scale approach and the first-order...
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Experimental and numerical study on deformed steel columns subjected to impact load during earthquakes
PublicationThe soft-storey failure is one of the most typical types of damage observed in buildings during earthquakes. The failure of an upper soft storey of a structure results in large impact load acting on the lower floors and if the resistance of the structural members of the lower storeys is not sufficient it may further lead to progressive collapse of the whole building. The aim of the present paper is to investigate the dynamic behaviour...
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Thermal ablation modeling via bioheat equation
PublicationWe consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublicationIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublicationWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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ANALYSIS OF THE p53 PROTEIN GENE EXPRESSION MODEL
PublicationWe study the asymptotic behaviour of the solutions of the p53-Mdm2 model proposed by Monk (2003). The p53 gene is crucial for cellular inhibition of the angiogenesis process, while Mdm2 is a negative regulator of the p53 tumor-suppressor. We investigate the stability of the positive steady state and perform some numerical experiments.
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Method of lines for physiologically structured models with diffusion
PublicationWe deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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Solving the Problem of Dynamic Adaptability of Artificial Intelligence Systems that Control Dynamic Technical Objects
PublicationThis paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object...
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Geo-engineering computer simulation seems attractive but is it the real world?
PublicationCorrect formulation of the differential equation system for equilibriom conditions of subsoil, especially in terms of controlled numerical calculation, is discussed. The problem of solution stability is also considered. The solution of problems, which are ill-posed, have no practical value in the majority of cases and is this way the engineering prognosis can lead to real disaster. The object of this paper is quite relevant if...
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Running characteristics of aerodynamic bearing with self-lifting capability at low rotational speed
PublicationAn aerodynamic journal bearing that is capable of self-generating squeeze-film pressure is presented and its dynamic characteristics investigated numerically and experimentally. A numerical method based on a time marching static model was applied to assess the orbit trajectory path of the rotor upon a perturbation. Experimental results were obtained to validate the effect of the self- generated squeeze-film pressure on the stability...
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Analysis of EN 1993-1-6 guidelines about determining amplitudes of equivalent imperfections of steel cylindrical shells subjected to uniform external pressure
PublicationCivil engineering structures should be designed with reference to relevant standards. One of them is a Eurocode 3 standard EN 1993-1-6:2007: Design of steel structures Part 1-6: Strength and Stability of Shell Structures. According to this standard, the value of buckling load can be determined using different approaches: classical hand calculations (stress design) and geometrical and material non-linear analysis of an imperfect...
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Buckling of thin-walled columns accounting for initial geometrical imperfections
PublicationThe paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The...
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublicationIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...