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Search results for: ELASTIC MATRIX
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Transverse surface waves on a cylindrical surface with coating
PublicationWe discuss the propagation of transverse surface waves that are so-called whispering-gallery waves along a surface of an elastic cylinder with coating. The coating is modelled in the framework of linearized Gurtin–Murdoch surface elasticity. Other interpretations of the surface shear modulus are given and relations to so-called stiff interface and stiff skin model are discussed. The dispersion relations are obtained and analyzed.
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublicationWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a tin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equatio is derived with aid of the principle of stationary potential energy. The critical load for simply supported bar is found in an analytical form and it is copared with the FEM solution. Sufficient accuracy of the...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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A Note on Reduced Strain Gradient Elasticity
PublicationWe discuss the particular class of strain-gradient elastic material models which we called the reduced or degenerated strain-gradient elasticity. For this class the strain energy density depends on functions which have different differential properties in different spatial directions. As an example of such media we consider the continual models of pantographic beam lattices and smectic and columnar liquid crystals.
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Generalized Taylor formula and shell structures for the analysis of the interaction between geosythetics and engineering structures of transportation lines
PublicationThe analysis of the interaction between geosynthetics and engineering structures (e.g. railroad bed, soil foundation, pipeline) assumes that the geosynthetic form elastic membranes or shell laid on different types of foundations. The mathematical description of that problems in continuous domain employs Laplace operator Δ or d’Alembert operator □. In this paper we demonstrate the analysis based on generalize Taylor formula, and...
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Theoretical and experimental study on scattering of low-energy electrons by dimethyl and diethyl ethers
PublicationWe report a joint theoretical and experimental investigation on low-energy electron scattering by dimethyl and diethyl ethers. The experimental elastic differential cross sections were measured at impact energies from 1 eV up to 30 eV and scattering angle range of 10◦ to 130◦. Theoretical elastic differential, integral and momentum-transfer cross sections are calculated at impact energies up to 30 eV, employing the Schwinger multichannel...
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The Point Estimate Method in a Reticulated Shell Reliability Analysis
PublicationThe objective of this paper is to present an application of the point estimate method (PEM) to determine the probabilistic moments for engineering structures. Reliability analysis is illustrated by two examples: an estimation of the critical force in linear elastic buckling analysis and a reticulated shell limit load determinations. Calculations were also made using Monte Carlo method. It has been shown the practical usefulness...
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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublicationThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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Modeling of Composite Shells in 6-Parameter Nonlinear Theory with Drilling Degree of Freedom
PublicationWithin the framework of a 6-parameter nonlinear shell theory, with strain measures of Cosserat type, constitutive relations are proposed for thin elastic composite shells. The material law is expressed in terms of five engineering constants of classical anisotropic continuum plus an additional parameter accounting for drilling stiffness. The theory allows for unlimited displacements and rotations. A number of examples are presented...
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On the Bending of Multilayered Plates Considering Surface Viscoelasticity
PublicationWe discuss the bending resistance of multilayered plates taking into account surface/interfacial viscoelasticity. Within the linear surface viscoelasticity we introduce the surface/interfacial stresses linearly dependent on the history of surface strains. In order to underline the surface viscoelasticity contribution to the bending response we restrict ourselves to the elastic behaviour in the bulk. Using the correspondence principle...
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A study on transverse shear correction for laminated sandwich panels
PublicationThe paper presents a study on an application of the First Order Shear Deformation Theory in a linear static analysis of elastic sandwich panels. A special attention has been given to the issue of the transverse shear correction. Two benchmark examples of sandwich plate problems with known reference solutions have been selected for a comparative analysis performed with own Finite Element codes. Interesting results allowed for drawing...
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SIMULATION OF PROCEED® SURGICAL MESH APPLIED TO VENTRAL HERNIA REPAIR
PublicationIn the present research, Proceed® implant is considered. The system is subjected to short-time dynamic pressure load, similar to post-operative cough naturally occurring in human abdomen. The model refers to a clinical case of 5cm of hernia operated by Proceed implant fixed by 15 joints every 3cm around the orifice. The simulations of the implanted mesh are performed by means of the Finite Element Method. The implant is modelled...
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Using Minimum Actuators to Control Shape and Stress of a Double Layer Spherical Model Under Gravity and Lateral Loadings
PublicationSpherical domes are picturesque structures built in developed countries to attract tourists. Due to horizontal and vertical overloading, the structures’ attractive shapes may be disturbed, and some members' stress may exceed the elastic level. In this paper, the shape and stress of a deformed double-layer spherical numerical model due to simultaneous lateral and vertical loadings are controlled, meanwhile, the number of actuators...
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Mechanical Behavior of Bi-Layer and Dispersion Coatings Composed of Several Nanostructures on Ti13Nb13Zr Alloy
PublicationTitanium implants are commonly used because of several advantages, but their surface modification is necessary to enhance bioactivity. Recently, their surface coatings were developed to induce local antibacterial properties. The aim of this research was to investigate and compare me-chanical properties of three coatings: multi-wall carbon nanotubes (MWCNTs), bi-layer composed of an inner MWCNTs layer and an outer TiO2 layer, and...
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The influence of the grid density of measurement points on damage detection in an isotropic plate by the use of elastic waves and laser scanning Doppler vibrometry
PublicationDamage detection in structural components, especially in mechanical engineering, is an 2 important element of engineering practice. There are many methods of damage detection, in which 3 changes in various parameters caused by the presence of damage are analysed. Recently, methods 4 based on the analysis of changes in dynamic parameters of structures, i.e. frequencies or mode shapes 5 of natural vibrations, as well as changes in...
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Analiza konstrukcji nawierzchni asfaltowych oparta o teorię lepkosprężystości
PublicationPrzedmiotem artykułu jest analiza przykładowej konstrukcji nawierzchni drogowej podatnej w oparciu o liniową teorię lepkosprężystości. Do symulacji pracy warstw asfaltowych wykorzystano model Burgersa, a obliczenia wykonano przy użyciu programu VEROAD (Visco-Elastic RoadAnalysis Delft). Autor poddaje analizie odkształcenia na spodzie warstw asfaltowych oraz ich deformacje odwracalne i trwałe, a także bada wpływ temperatury.
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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Can we really solve an arch stability problem?
PublicationWe bring attention to the problem of solving nonlinear boundary-value problems for elastic structures such as arches and shells. Here we discuss a classical problem of a shear-deformable arch postbuckling. Considering a postbuckling behaviour of a circular arch we discuss the possibility to find numerically a solution for highly nonlinear regimes. The main attention is paid to the problem of determination of all solutions. The...
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FEM-based wave propagation modelling for SHM: Certain numerical issues in 1D structures
PublicationThe numerical modelling of structural elements is an important aspect of modern diagnostic systems. However, the process of numerical implementation requires advanced levels of consideration of multiple aspects. Important issues of that process are the positive and negative aspects of solution applied methods. Therefore the aim of this article is to familiarise the reader with the most important aspects related to the process of...
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A Monte Carlo Strategy to simulate Positrons and Positronium in biological Materials
PublicationWe present an algorithm for Monte Carlo simulations of positron tracks in biological materials. The algorithm takes into account the cross-section data for elastic and inelastic collisions between positrons and molecules and processes like direct annihilation, ionization and positronium formation. In the case of positronium formation, the algorithm considers the interactions of positronium with molecules. The algorithm can be used...
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Mechanical properties of Precontraint 1202 S2 based on uniaxial tensile and creep tests
PublicationThe purpose of the paper is the estimation of the polyvinyl chloride – polyester-coated fabric (Precontraint 1202 S2) mechanical properties under uniaxial tensile tests as well as short- and long-time creep tests. The uniaxial tests are the basis of non-linear elastic description while the creep tests are used for the evaluation of the stiffness parameters in time and for the identification of the standard viscoelastic model. The...
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Fracture Energy of Bonded Joints with 2D Elastic Adhesive Layer
PublicationWhen bonded joint is subjected to mode I fracture loading, the adhesive joints analytical solutions treats the adhesive layer, usually, as not existing or 1D Hooke elastic layer. In the case of 1D elastic layer, represented as Hookes spring element, is acting, only, in direction contrary to the applied load. Basing on the information yielded from sensitive laser profilometry technique, where deflections of bonded part of the joint...
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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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On refined constitutive equations in the six-field theory of elastic shells
PublicationWithin the resultant six-field shell theory, the second approximation to the complementary energy density of an isotropic elastic shell undergoing small strains is constructed. In this case, the resultant drilling couples are expressed explicitly by the stress resultants and stress couples as well as by amplitudes of the quadratic and cubic distributions of an intrinsic deviation vector. The refined 2D strain-stress and stress-strain...
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Low energy elastic electron scattering from benzonitrile (C6H5CN)
PublicationWe present experimental differential elastic scattering cross sections (DCSs) for low energy electron scattering from benzonitrile along with integral and momentum-transfer cross sections that are determined from these DCSs. The measurements of DCSs are obtained using the relative flow method with helium as the standard gas, in a crossed electron-molecular gas beam arrangement. Our measurements are made at incident electron energies...
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The Role of Molecular Structure in Monte Carlo Simulations of the Secondary Electron Yield and Backscattering Coefficient from Methacrylic Acid
PublicationIn this paper, we show the influence of the chemical structure of four different conformers on the secondary electron emission and backscattering of an electron beam from a gel of methacrylic acid. The conformers have different permanent dipole moments, which determines the cross sections for elastic collisions with electrons. The cross sections are used in Monte Carlo simulations of an electron beam, which enters the gel of methacrylic...
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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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Diagnostics of historic columns using wave propagation
PublicationThis paper presents a numerical analysis of elastic wave propagation in columns of historical buildings for diagnostics purposes. Numerical calculations were performed using the finite element method in the Abaqus software package. The analysis was carried out for three types of brick columns: a full column, a column filled with debris, and a column empty inside. The excitation was in the form of a wave packet and signals of propagating...
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Numerical FDM modelling of wave propagation in concrete structure
PublicationThe article presents application of finite difference method to damage detection and its size evaluation in concrete structure by elastic wave propagation method. The simulations of wave propagation in concrete structure were performed for six different damage scenarios. Damages were modelled as areas with changed material properties. Investigation focused on the influence of damage size on the energy of wave reflection. Presented...
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Laminated plates and shells - first ply failure analysis within 6-parameter shell theory
PublicationThis work describes Tsai-Wu and Hashin criteria modifications, dictated by nonlinear 6-parameter shell theory with asymmetric strain measures and drilling rotation. The material law is based on standard orthotropic elastic constants for a non-polar continuum, under plane state of stress. First ply failure loads of cylindrical panel subjected to pressure and flat compressed plate are estimated by means of Finite Element Analysis....
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Application of the distributed transfer function method and the rigid finite element method for modelling of 2-D and 3-D systems
PublicationIn the paper application of the Distributed Transfer Function Method and the Rigid Finite Element Method for modelling of 2-D and 3-D systems is presented. In this method an elastic body is divided into 1-D distributed parameter elements (strips or prisms). The whole body (divided into strips or prism) is described by a set of coupled partial differential equations. Solving this equations in the state space form it is possible...
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Similarity Measures for Face Images: An Experimental Study
PublicationThis work describes experiments aimed at finding a straightforward but effective way of comparing face images.We discuss properties of the basic concepts, such as the Euclidean, cosine and correlation metrics, test the simplest version of elastic templates, and compare these solutions with distances based on texture descriptors (Local Ternary Patterns). The influence of selected image processing methods (e.g. bilateral ltering)...
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The influence of chemical composition of amide block on the thermal properties and structure of terpoly(ester-b-ether-b-amide) elastomers
PublicationMultiblock terpolymers-(PBT-b-PTMO-b-PA12,10)(n)- constituting the polymer systems, in which one of the three blocks (PBT) does not dissolve in PA12,10 block (hard phase) and, depending on its molecular weight is slightly soluble in PTMO block (soft phase), have been obtained. The DSC method was applied to investigate the thermal properties of these polymers and it was found that PBT block acts as an element that produces stiffness...
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Cavity-expansion approximation for projectile impact and penetration into sand
PublicationA one-dimensional problem of a spherical cavity expanding at a constant velocity from zero initial radius in an infinite granular medium, which has the first-kind self-similar solution, is considered. We are solving this dynamic spherical cavity-expansion problem to model rigid spheres penetrating into a granular media. Elastic–plastic deformation of the granular media is described in a barotropic approximation, using the high-pressure...
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Elastic scattering of electrons from chloroform
PublicationWe present experimental and theoretical cross sections for elastic electron scattering from CHCl3. This is an important target because of its relevance to environmental chemistry and the plasma etching industry as a source of chlorine radicals. The experimental results were obtained at incident electron energies ranging from 0.5 to 800 eV in the 10deg-130deg scattering angle range. Theoretically, the scattering cross sections in...
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublicationIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...
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Cross section calculations for electron scattering from platinum chemotherapeutic compounds
PublicationCross section for electron impact ionization of carboplatin, C6H12N2O4Pt, and oxaliplatin, C8H14N2O4Pt, have been calculated within binary-encounter-Bethe model for energies from the ionization threshold up to 5000 eV. Cross section for elastic electron scattering from carboplatin and oxaliplatin molecules have also been derived using independent atom method (IAM) and additivity rule for collision energies ranging from 50 eV to...
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Mechanical properties for preliminary design of structures made from PVC coated fabric
PublicationIn this paper, laboratory tests necessary for the identification of non-linear elastic immediate properties of the PVC coated polyester fabric (like AF 9032) are described. The material parameters are specified on the basis of the uniaxial tensile tests in the warp and weft directions as well as on the base of the biaxial tensile tests. For the identification process techniques based on the least squares method are used. The authors...
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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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Experimental Research on Insufficient Water Lubrication of Marine Stern Tube Journal Bearing with Elastic Polymer Bush
PublicationWater-lubricated bearings with polymer bushes are steadily gaining popularity due to their advantages, including environmental friendliness, relatively simple construction and long-term operation. Nevertheless, in practice instances of damage to such bearings occur due to insufficient or absent flow of the lubricating agent. In this study, experimental tests established that elastic polymer bush bearing is capable of operating...
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Detection of defects in PMMA beam using shear waves - numerical simulation and experiment
PublicationTest doświadczalny falami sprężystymi jest częścią systemu diagnostycznego belek. Autorzy badają pole przyspieszeń wywołane przepływem fal ultradźwiękowych i jego modyfikacje wynikające z wprowadzonych uszkodzeń belki. Artykuł porównuje wyniki eksperymentalne z symulacjami numerycznymi MES. The experimental test introduced in the paper is the part of the diagnostic system utilizing the elastic waves. The authors investigate the...
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On the use of uniaxial one-parameter damage laws for estimating fatigue life under multiaxial loading
PublicationThe goal of this paper is to evaluate the capabilities of different one-parameter fatigue laws to estimate crack initiation in notched components under multiaxial loading. Fatigue damage is accounted for through stress-based, strain-based, and energy-based approaches while the cyclic plasticity at the notch-controlled process zone is estimated using linear-elastic simulations. The results show that energy-based formulations established...
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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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On stress singularity near the tip of a crack with surface stresses
PublicationIn the framework of the simplified linear Gurtin–Murdoch surface elasticity we discuss a singularity of stresses and displacements in the vicinity of a mode III crack. We show that inhomogeneity in surface elastic properties may significantly affect the solution and to change the order of singularity. We also demonstrate that implicitly or explicitly assumed symmetry of the problem may also lead to changes in solutions. Considering...
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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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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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FEM ANALYSIS AND EXPERIMENTAL TESTS OF RIGID RISER HANGING SYSTEM
PublicationThe article presents the analysis, project, and experimental examination of an original rigid riser for Coil Tubing Pipes. The principle of riser operation is based on the use of friction forces. The research included the FEM analysis of the designed riser, calculations of the required bolt tensions, and checking the effect of the clamping force on stress distribution in the pipeline. The results of computer simulation were verified...
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Design of septic tanks placed on cohesive soils
PublicationThe paper presents a short review of literature with regard to design and erection of the reinforced concrete and concrete tanks. The authors investigated the underground septic tank with of 10 m3 capacity placed on cohesive soils. The authors compared the values of internal forces for soils in drained and undrained conditions with different geotechnical parameters: loamy sand of liquidity index IL = 0.1 and IL = 0.7 and clay with...
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Investigation of abdomen surface deformation due to life excitation: implications for implant selection and orientation in laparoscopic ventral hernia repair
PublicationVentral hernia is a common medical problem. Statistically there are around 10% recurrences of the sickness. The authors' former investigation proved edges of the hernia orifice displacements to be one of the factors causing recurrence. Thus, experimental investigation of the abdomen surface deformation due to some normal activities of people is studied.The extreme strains, their localization and directions are identified. The acquired...