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Search results for: BOUNDARY ELEMENT METHOD
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Method of lines for Hamilton-Jacobi functional differential equations.
PublicationInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublicationWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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Improving the accuracy of subgridding scheme in finite differences method based on Legendre polynomials expansion
PublicationIn this article the Legendre polynomials have been used to interpolate the field at the boundary of the meshes of different densities. The numerical verification of the proposed technique has been carried out in frequency domain. It has been shown that the accuracy of the presented method is very high and stable - the error monotonically decreases as a function of the refinement factor.
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Acoustic heating produced in the boundary layer
Publication: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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Soft – Partial Frequency Reuse Method for LTE-A
PublicationIn the paper a novel SPFR frequency reuse method is proposed which can be used for improvement of physical resources utilization efficiency in LTE-A. The proposed method combines both SFR and PFR giving the possibility of more flexible use of frequency band in different regions of a cell. First, a short study on the problem of frequency reuse in cells is discussed including bibliography overview....
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Analysis of hydrodynamic pressure fields of motorboats and pontoons in shallow water
PublicationThe article presents the results of calculations of the pressure fields generated by a motorboat at the bottom of a shallow sea. Calculations were made using the boundary elements method (BEM), arranged on the surface of the boat and the bottom of the sea. This method is described in [3], and applied on a free surface linearized boundary condition. Results for four different lengths of motorboats, from 2.85 m to 9.5 m, sea depth...
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Analiza i ocena smarności olejów w ujęciu energetycznym i działania układu tribologicznego = Analysis and evaluation of oil lubricity from the viewpoint of energy apects and of the tribological system action
PublicationBased on measurement results, an interpretation is presented of the tribological system boundary layer action in the form of a four-ball tester friction node. The evaluation was performed of the boundary layer action understood as transfer of energy Ep resulting from loading the tribological system in a determined time t with work Lp, which may lead to breaking the boundary layer. That energy and time are the values unequivocally...
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Method of evaluation of lubricating ability of lube oils and fuels in energetistic formulation
PublicationThe paper presents an interpretation of operation of a boundary layer of a lubricating medium. A model of the homogeneous Poisson process has been proposed to assess the deterioration process of the layer's operation. The assessment considers the original interpretation of operation of a boundary layer, as a lubricity measure of a boundary layer of any lubricant. In the submitted proposal the operation of a boundary layer is understood...
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Method of identification of the slide tribological system top layer condition by assessment of the t-02 four-ball tester friction node operation
Publicationa method is proposed of the assessment of t-02 four-ball tester friction node operation during extreme unit loads on the tribological system for identification of the top layer condition in that system lubricated with the tested lubricating oil. by identification of the friction node with a thermodynamic system, that operation is treated as an energy generating process of the created servo-layer structure. the friction node operation...
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Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method
PublicationIn this paper, bending analysis of rectangular functionally graded (FG) nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory (HSDT). The set of coupled equations are solved using the dynamic relaxation (DR) method combined with finite difference (FD) discretization technique...
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Thermal boundary conditions to simulate friction layers and coatings at sliding contacts
PublicationA brief review of the thermal boundary conditions specified at sliding interfaces was performed. New thermal boundary conditions were derived aimed at solving problems of sliding with account of surface layers representing friction layers and tribological coatings. Based on the assumption of linear temperature distributions in the surface layers, the proposed conditions enable one to simplify simulations by eliminating the surface...
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Scattering From a Cylindrical Object of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple and intuitive solution to scattering problems in shielded and open structures is presented. The main idea of the analysis is based on the direct field matching technique involving the usage of projection of the fields at the boundary on a fixed set of orthogonal basis functions. Different convex shapes and various obstacle materials are considered to verify the validity of the method in open and closed structures. The...
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Improvements to the two-phase sandwich method for calculating the melting points of pure metals
PublicationThe thermophysical properties of metal alloys are often investigated via molecular dynamics (MD) simulations.An exact and reliable estimation of the thermophysical parameters from the MD data requires a properly and carefullyelaborated methodology. In this paper, an improved two-phase sandwich method for the determination of the metal meltingtemperature is proposed, based on the solid-liquid equilibrium theory. The new method was...
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Comment on permeability conditions in finite element simulation of bone fracture healing
PublicationThe most popular model of the bone healing considers the fracture callus as poroelastic medium. As such it requires an assumption of the callus’ external permeability. In this work a systematic study of the influence of the permeability of the callus boundary on the simulated bone healing progress is performed. The results show, that these conditions starts to play significant role with the decrease of the callus size. Typically...
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On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...
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Numerical Analysis of Steady Gradually Varied Flow in Open Channel Networks with Hydraulic Structures
PublicationIn this paper, a method for numerical analysis of steady gradually varied fl ow in channel networks with hydraulic structures is considered. For this purpose, a boundary problem for the system of ordinary differential equations consisting of energy equation and mass conservation equations is formulated. The boundary problem is solved using fi nite difference technique which leads to the system of non-linear algebraic equations....
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Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
PublicationWe discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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Numerical analysis of crack propagation in silicone nitride
PublicationThe properties of ceramics, specifically low density, high hardness, high temperature capability and low coefficient of thermal expansion are of most interest to rolling element manufacturers. The influence of ring crack size on rolling contact fatigue failure has been studied using numerical fracture analysis. Such cracks are very often found on ceramic bearing balls and decrease fatigue life rapidly. The numerical calculation...
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Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple solution to propagation problem in open waveguides and dielectric fibers of arbitrary convex cross section is presented. The idea of the analysis is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. A complex root tracing algorithm is utilized to find the propagation coefficients of the investigated guides. Different convex...
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Numerical and experimental study on effect of boundary conditions during testing of stiffened plates subjected to compressive loads
PublicationThis study analyses the effect of boundary conditions during testing on the structural behaviour stiffened plates with different thicknesses subjected to compressive loads. The goal of the compressive tests is to analyse the ultimate strength of a stiffened plate. During the test, relevant physical quantities are measured and investigated. The supporting structure's behaviour is investigated by analysing the force-displacements...
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublicationApproximate analytical solution of two dimensional problem for sta- tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ- ing free convective heat transfer from isothermal surface of half innite vertical plate is presented. The problem formulation is based on the typ- ical for natural convection assumptions: the uid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component...
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Blade Section Prpfile Array Lifting Surface Design Method for Marine Screw Propeller Blade
PublicationThe lifting surface model is widely used in screw propeller design and analysis applications. It serves as a reliable tool for determination of the propeller blade mean line and pitch distribution. The main idea of this application was to determine the blade shape that would satisfy the kinematic boundary condition on its surface with the prescribed bound circulation distribution over it. In this paper a simplified lifting surface...
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Electrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theory
PublicationWe present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within density functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such...
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An optimal sliding mode control based on immune-wavelet algorithm for underwater robotic manipulator
PublicationIn this paper, a robust optimal Sliding Mode Controller (SMC) based on new algorithm of Artificial Immune System (AIS) is proposed for trajectory tracking of underwater manipulators. A new AIS algorithm is used to derive optimal values of surface parameters and boundary layer thickness in SMC with considering minimum torques and error. Surface parameters and boundary layer thickness are considered as antibody in AIS and Morlet...
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Modelowanie przepływu ustalonego niejednostajnego w sieciach kanałów otwartych z uwzględnieniem obiektów hydrotechnicznych
PublicationW pracy sformułowano zagadnienie brzegowe dla równania energii opisującego przepływ ustalony niejednostajny i przedstawiono sposób jego rozwiązania przy pomocy metody różnicowej. Zaproponowana metoda obliczeń nadaje się do analizy przepływu w dendrycznych i pierścieniowych sieciach kanałów otwartych. Ponadto na przykładzie przelewu prostokątnego zaproponowano metodę uwzględnienia w obliczeniach zabudowy hydrotechnicznej. Słowa...
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Implementation of Hermite-Ritz method and Navier’s Technique for Vibration of Functionally Graded Porous Nanobeam Embedded in Winkler-Pasternak Elastic Foundation Using bi-Helmholtz type of nonlocal elasticity
PublicationPresent study is devoted to investigating the vibration characteristics of Functionally Graded (FG) porous nanobeam embedded in an elastic substrate of Winkler-Pasternak type. Classical beam theory (CBT) or Euler-Bernoulli beam theory (EBT) has been incorporated to address the displacement of the FG nanobeam. Bi-Helmholtz type of nonlocal elasticity is being used to capture the small scale effect of the FG nanobeam. Further, the...
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublicationThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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GPR investigation of the strengthening system of a historic masonry tower
PublicationIn this paper the condition assessment of the strengthening system of a masonry tower was carried out by the GPR method. The study provided unique experimental data acquired during measurements of the reinforced concrete frame embedded in masonry walls. Conducted numerical and experimental investigations were focused on the phenomenon of the diffraction-refraction scattering of the electromagnetic energy. A hyperbola resulting...
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Mechanics of materials (PG_00057378), W/Ć, BM, II stop., sem1,3, lato, 2023/24
e-Learning CoursesThe aim of this course is providing knowledge in the field of analysis and solving problems of mechanics and strength of one-dimensional systems (bars, beams, frames) and selected two-dimensional systems (shields, plates); preparing the student to solve problems involving complex cases of material strength; developing the ability to assess the stability of structural elements (forms of stability loss, critical forces); consolidation...
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Mechanism of Solute and Thermal Characteristics in a Casson Hybrid Nanofluid Based with Ethylene Glycol Influenced by Soret and Dufour Effects
PublicationThis article models a system of partial differential equations (PDEs) for the thermal and solute characteristics under gradients (concentration and temperature) in the magnetohydrodynamic flow of Casson liquid in a Darcy porous medium. The modelled problems are highly non-linear with convective boundary conditions. These problems are solved numerically with a finite element approach under a tolerance of 10−8. A numerical algorithm...
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Hybrid Technique for the EM Scattering Analysis with the Use of Ring Domain Decomposition
PublicationA hybrid technique combining finite-element and mode-matching methods for the analysis of scattering problems in open space is presented here. The main idea is based on impedance matrix descriptions of the boundary surrounding the discrete computational domain and combine it with external field described analytically. The discrete analysis, which is the most time- and memory-consuming, is limited here only to the close proximity...
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2022-2023 - Wytrzymałość materiałów II, PG_00040052
e-Learning CoursesOpanowanie wiedzy i umiejętności rozwiązywania złożonych zagadnień wytrzymałości prętów, powłok oraz płyt, mechaniki pękania i wytrzymałości zmęczeniowej, drgań prętów, oraz wybranych zastosowań metody elementów skończonych. The aim of the lectures is to deliver to the students the knowledge and abilities to solve the complex problems concerning the bars, shells, 3D structures, mechanics of cracking and fatique strength, vibrations...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....
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Numerical simulation of hardening of concrete plate
PublicationThe paper presents a theoretical formulation of concrete curing in order to predict temperature evolution and strength development. The model of heat flow is based on a well-known Fourier equation. The numerical solution is implemented by means of the Finite Difference Method. In order to verify the model, the in situ temperature measurements at the top plate of a road bridge were carried out. A high agreement between numerical...
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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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Architectural Project I and II 2023/2024
e-Learning CoursesThe aim of the course is to teach the method of creating an architectural form in a style that reflects a given topic drawn in the form of an ideogram. Creating architecture in this way makes it possible to endow the architectural form with meanings contained in the art, so that it becomes an important element of the existential space. An important feature of the ideogram is its artistic value. In this way, it can additionally...
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Parallel Implementation of the Discrete Green's Function Formulation of the FDTD Method on a Multicore Central Processing Unit
PublicationParallel implementation of the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method was developed on a multicore central processing unit. DGF-FDTD avoids computations of the electromagnetic field in free-space cells and does not require domain termination by absorbing boundary conditions. Computed DGF-FDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublicationIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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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...
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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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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Wave propagation in damage assessment of ground anchors
PublicationThe inspection possibilities of ground anchors are limited to destructive test such as pull-out test. Guided wave propagation gives an opportunity to develop an inspection system dedicated to determine the condition of inspected element without violation of their integrity. In this paper the experimental study on wave propagation in laboratory models of ground anchors are presented. Experiments were conducted for different bonding...
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Evaluation of the Effectiveness of Methods for Delimitation of the Boundaries of Registered Parcels in the Process of Modernization of Land and Building Registration
PublicationIn the article, a comparative analysis of two methods for delimitation of the boundaries of registered parcels was carried out: the method of direct measurement in the field and the photogrammetric method. One of the analyzed factors was the attendance of parcels’ owners during the development of boundary recognition agreements. Research has shown that in this aspect the method of direct measurement...
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Modelling of some stealth features for a small navy ship at the concept design stage - part II
PublicationIn the paper a few problems associated with modelling the basic stealth features for a small ship at the concept design stage are introduced. One problem concerns the modification of the immersed ship hull using the rapid change of the ship loading condition. The second is associated with the modification of the ship boundary layer by the hull skin cover. The other stealth features of the ship are not presented in this paper. The...
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ARRAY OF MINIJETS – THERMAL AND HYDRAULIC PHENOMENA IN BOUNDARY LAYER
PublicationPresented work considers flow and thermal phenomena occurring in the system consisting of minijets array and heated with constant heat flux surface. Numerical analyses, based on the mass, momentum and energy conservation laws, were conducted. Focus was placed on the proper model construction, in which turbulence and boundary layer modelling was crucial. Calculations were done for various mass flow rates. The main calculations were...