Papers by Wojciech Sumelka
Bulletin of the Polish Academy of Sciences Technical Sciences
Heavy metal ions (e.g. cadmium, chromium, copper, nickel, arsenic, lead, zinc) have significantly... more Heavy metal ions (e.g. cadmium, chromium, copper, nickel, arsenic, lead, zinc) have significantly serious side effects on the human health. They can bind with proteins and enzymes, altering their activity, increasing neurotoxicity, generating reactive oxygen species (ROS), promote cellular stress and resulting in their damage. Furthermore, the size, shape and type of metal are important for considering nano-or microtoxicity. It then becomes clear that the levels of these metals in drinking water are an important issue. Herein, a new micro-mechanical sensor is proposed to detect and measure these hazardous metals. The sensor consists of a micro-beam inside a micro-container. The surface of the beam is coated with a specific protein that may bind heavy metals. The mass adsorbed is measured using the resonant frequency shift of the micro-beam. This frequency shift due to the admissible mass (which is considered acceptable for drinking water based on the World Health Organization (WHO) standard) of manganese (Mn), lead (Pb), copper (Cu) and cadmium (Cd) is investigated for the first, second and third mode, respectively. Additionally, the effects of micro-beam off-center positions inside the micro-container and the mass location are investigated.
Bulletin of the Polish Academy of Sciences Technical Sciences
Archives of Civil Engineering
This article presents the results of a numerical analysis of the road acoustic screen deteriorati... more This article presents the results of a numerical analysis of the road acoustic screen deterioration. Due to the fact that road noise barriers are located in an environment of very high corrosivity, the problem is the rusting of the metal cladding of component panels. The presented case study was, therefore, verified to fulfill the requirements presented in the Eurocode EN 1794-1. Static analysis for wind load and dynamic analysis for the load induced from vehicles was carried out. The analysis presented in the article proved the design errors and their contribution to the formation of severe corrosion, as well as demonstrating the importance of dynamic analysis in the design of acoustic screens.
Modern industrial standards require advanced constitutive modeling to obtain satisfactory numeric... more Modern industrial standards require advanced constitutive modeling to obtain satisfactory numerical results. This approach however, is causing significant increase in number of material parameters which can not be easily obtained from standard and commonly known experimental techniques. Therefore, it is desirable to introduce procedure decreasing the number of the material parameters. This reduction however, should not lead to misunderstanding the fundamental physical phenomena. This paper proposes the reduction of the number of material parameters by using ANN approximation. Recently proposed viscoplasticity formulation for anisotropic solids (metals) developed by authors is used as an illustrative example. In this model one needs to identify 28 material parameters to handle particular metal behaviour under adiabatic conditions as reported by Glema et al (
The problems of solid mechanics and acoustics are discussed. The interest is focused on wave effe... more The problems of solid mechanics and acoustics are discussed. The interest is focused on wave effects. Small size elements and short time increments generate large computational model. It is often to large in comparison with accessible computer power. The computations of limited part of whole domain are considered. The omitted part of large problem is not neglected, but recompensed. A surrounding area is introduced for local region of mechanical or acoustic response. The subset of boundary conditions defined for surrounding area is verified to give adequate wave propagation, dissipation and dispersion. The problems of mechanics and acoustic are studied in the paper from the point of view of wave propagation effects. For numerical computations the space and time domains undergo discretization into many elements and time increments. Such the discretization generates large computational model. The motivation of research comes from constrains in obtaining the numerical solution. The number of nodes, degree of freedom are too huge to finish computations in reasonable time or to use data storage devices. The same questions rise for multiscale analysis. In the paper there is a proposition to reduce the size of computational model. The subject of interest is limited to relatively small part of whole domain. The main attention is concentrated on the question, how to implement the influences coming from large domain. The substitution of omitted part is proposed by area surrounding the local region of interest. The idea is presented in Fig. 1. The local region with the same characteristic as in original problem is surrounded by the region with postulated geometry and material properties. We are motivated to clarify how to define the additional region to substitute wave effects of mechanical or acoustic process and to identify the material behavior of solid in additional region with its dissipative and dispersive parameters. The intention of replacement is to provide adequate boundary conditions for local region. The problem of dynamic tension of steel specimen is presented. The viscoplastic material is applied for surrounding region. There are two main parameters of subset: dimension (width) and viscosity. The parametric study of those variables is carried out. The results show wide range of wave behavior (Fig. 1). The viscosity of surrounding area is the parameter controlling wave reflections and energy transmitted outside the local region.
The analysis of deformation process of an anisotropic ductile material (mainly metals) subjected ... more The analysis of deformation process of an anisotropic ductile material (mainly metals) subjected to impact loading is presented. The problem is formulated within the theory of continuum mechanics and in the framework of thermodynamics. The macroscopic anisotropy is induced by the evolution of microstructure. Experimental observations show the nucleation, growth and coalescence of microcracks and microvoids. During the deformation process microstructure undergoes the modification in which direction of microvoids and microcracks growth and the direction of new defects nucleation influence then the deformation increment. Anisotropy of microstructure is incorporated in the problem formulation and numerical analysis. The information about direction in evolution of the microstructure is described in the model by second order tensorial field. The microdamage tensor was introduced [1, 3]. The microdamage tensor becomes one of internal state variables defined in constitutive formulation and its evolution is computed in deformation process. The classical volume fraction porosity is related to microdamage tensor, in such a way that the norm of microdamage tensor is the porosity scalar [2, 4]. The microdamage tensor belongs to microdamage tensorial field and all properties of sec
Symmetry
This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neu... more This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the oscillating circuit and generalize the spring–mass device equation. The proposed approach transforms the given nonlinear fractional differential equation (FDE) into an unconstrained minimization problem. The simulated annealing (SA) algorithm minimizes the mean square error. The proposed techniques examine various non-integer order problems to verify the theoretical results. The numerical results show that the proposed approach yields better results than existing methods.
Buildings
Over the last century, the seismic behavior of reinforced concrete (RC) beam–column joints has dr... more Over the last century, the seismic behavior of reinforced concrete (RC) beam–column joints has drawn many researchers’ attention due to their complex stress state. Such joints should possess sufficient capacity and ductility to ensure integrity and safety when subjected to cyclic loading during seismic events. In the literature, while most studies have focused on the behavior of concentric beam–column joints, few studies investigated the response of eccentric beam–column joints, in which the beam’s centerline is offset from the centerline of the column. Recent earthquakes demonstrated severe damage in eccentric beam–column joints due to their brittle torsional behavior, which may threaten the ductility required for the overall structural performance. To investigate the effect of brittle failure on the strength, ductility, and stability of eccentric beam–column joints, nonlinear finite element (FE) models were developed and validated. The FE model was employed to study the effect of ...
This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considerin... more This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.
Fractals
The human immunodeficiency virus (HIV) is a major global public health issue and causes millions ... more The human immunodeficiency virus (HIV) is a major global public health issue and causes millions of deaths around the globe. The most severe phase of HIV infection is known as AIDS. In recent years, a number of mathematical models based on classical integer-order derivative have been developed to analyze the insight dynamics of HIV/AIDS. This paper presents the transmission dynamics of HIV/AIDS using fractional order (FO) and a fractal-fractional order compartmental model with the power-law kernel. In the first phase, the proposed model is formulated using the Caputo-type fractional derivative. The basic properties such as the solution positivity and existence as well as uniqueness of the fractional model are presented. The equilibria and the basic reproductive number [Formula: see text] are evaluated. Further, using fractional stability concepts the stability of the model (both local and global) around the equilibrium is presented in the disease-free case. In addition, the fraction...
Fractals
A numerical method for the solution of nonlinear variable-order (VO) fractional differential equa... more A numerical method for the solution of nonlinear variable-order (VO) fractional differential equations (FDEs) is proposed in this paper. To determine the numerical solution of nonlinear VO FDEs, we used the Haar wavelet collocation method (HWCM) with a combination of Caputo fractional derivatives. For checking the efficiency of the HWCM, some examples are given. The maximum absolute error and mean square root errors of each test problem are computed for a different number of collocation points (CPs) to check the validity and applicability of the presented technique. The comparison of the exact and approximate solution is shown in figures for various numbers of CPs.
Materials
Architectural soda-lime silicate glass (SLS) is increasingly taking on complex shapes that requir... more Architectural soda-lime silicate glass (SLS) is increasingly taking on complex shapes that require more detailed numerical analysis. Glass modeling is a thoroughly described topic with validated constitutive models. However, these models require a number of precise material parameters for SLS glass, and these are very sensitive to changes in glass composition. The currently available information is based on SLS glass tested in the late 1990s. As a result, most current publications are based on the above data. The object of this work was to analyze the available sources and update the information on selected key parameters for modeling. Using the currently utilized SLS glass in construction, the coefficient of thermal expansion (CTE), glass transition temperature, and the Young’s modulus have been experimentally investigated. The updated material parameters will allow for more accurate modeling of the SLS glass currently used in construction, and in consequence will make the prototyp...
Energies
This article models a system of partial differential equations (PDEs) for the thermal and solute ... more This 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 (finite element approach) is provided and a numerical procedure is discussed. Convergence is also observed via 300 elements. Simulations are run to explore the dynamics of flow and the transport of heat and mass under parametric variation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, simulations are recorded. Remarkable changes in temperature and concentration are noted when Dufour and Soret numbers are varied.
Energies, 2021
In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1... more In this paper, the applicability of the space-fractional non-local formulation (sFCM) to design 1D material bodies with a specific dynamic eigenvalue spectrum is discussed. Such a formulated problem is based on the proper spatial distribution of material length scale, which maps the information about the underlying microstructure (it is important that the material length scale is one of two additional material parameters of sFCM compared to the classical local continuum mechanics—the second one, the order of fractional continua—is treated herein as a scaling parameter only). Technically, the design process for finding adequate length scale distribution is not trivial and requires the use of an inverse optimization procedure. In the analysis, the objective function considers a subset of eigenvalues reduced to a single value based on Kreisselmeier–Steinhauser formula. It is crucial that the total number of eigenvalues considered must be smaller than the limit which comes from the rati...
Materials, 2022
Auxetic structures can be used as protective sacrificial solutions for impact protection with lig... more Auxetic structures can be used as protective sacrificial solutions for impact protection with lightweight and excellent energy-dissipation characteristics. A recently published and patented shock-absorbing system, namely, Uniaxial Graded Auxetic Damper (UGAD), proved its efficiency through comprehensive analytical and computational analyses. However, the authors highlighted the necessity for experimental testing of this new damper. Hence, this paper aimed to fabricate the UGAD using a cost-effective method and determine its load–deformation properties and energy-absorption potential experimentally and computationally. The geometry of the UGAD, fabrication technique, experimental setup, and computational model are presented. A series of dog-bone samples were tested to determine the exact properties of aluminium alloy (AW-5754, T-111). A simplified (elastic, plastic with strain hardening) material model was proposed and validated for use in future computational simulations. Results sh...
Fractals, 2021
In this paper, we develop a numerical method for the solution of nonlinear fractional integral eq... more In this paper, we develop a numerical method for the solution of nonlinear fractional integral equations (NFIEs) based on Haar wavelet collocation technique (HWCT). Under certain conditions, we also prove the uniqueness and existence as well as Hyers–Ulam (HU) stability of the solution. With the help of the mentioned technique, the considered problem is transformed to a system of algebraic equations which is then solved for the required results by using Broyden algorithm. To check the validation and convergence of the proposed technique, some examples are given. For different number of collocation points (CPs), maximum absolute and mean square root errors are computed. The results show that for solving these equations, the HWCT is effective. The convergence rate is also measured for different CPs, which is nearly equal to [Formula: see text]
Archives of Mechanics, 2017
Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into... more Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into the governing equations of the differential operator type of linear solid materials. FDMs are more general than those of integer derivative models (IDMs) so they are more fixable to describe physical phenomena. In this paper the inhomogeneous nonlocal theory has been introduced based on conformable fractional derivatives (CFD) to study the critical point instability of micro/nano beams under a distributed variable-pressure force. The phase of distributed variable-pressure force is used for electrostatic force, electromagnetic force and so on. This model has two free parameters: i) parameter to control the order of inhomogeneity in constitutive relations that gives a general form to the model, and ii) a nonlocal parameter to consider size dependence effects in micron and sub-micron scales. As a case study the theory has been used to model micro cantilever (C-F) and doubly-clamped (C-C) s...
The problems of solid mechanics and acoustics are discussed. The interest is focused on wave effe... more The problems of solid mechanics and acoustics are discussed. The interest is focused on wave effects. Small size elements and short time increments generate large computational model. It is often to large in comparison with accessible computer power. The computations of limited part of whole domain are considered. The omitted part of large problem is not neglected, but recompensed. A surrounding area is introduced for local region of mechanical or acoustic response. The subset of boundary conditions defined for surrounding area is verified to give adequate wave propagation, dissipation and dispersion. The problems of mechanics and acoustic are studied in the paper from the point of view of wave propagation effects. For numerical computations the space and time domains undergo discretization into many elements and time increments. Such the discretization generates large computational model. The motivation of research comes from constrains in obtaining the numerical solution. The numb...
Computational Mechanics, 2021
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Papers by Wojciech Sumelka