Search results for: mechanics
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Nonlinear strain gradient and micromorphic one-dimensional elastic continua: Comparison through strong ellipticity conditions
PublicationWe discuss the strong ellipticity (SE) conditions for strain gradient and micromorphic continua considering them as an enhancement of a simple nonlinearly elastic material called in the following primary material. Recently both models are widely used for description of material behavior of beam-lattice metamaterials which may possess various types of material instabilities. We analyze how a possible loss of SE results in the behavior...
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Continuum models for pantographic blocks with second gradient energies which are incomplete
PublicationWe postulate a deformation energy for describing the mechanical behavior of so called pantographic blocks, that is bodies constituted by stacking of layers of pantographic sheets. We remark that the pantographic effect is limited in the plane of pantographic sheets and therefore only the second derivatives of transverse displacements along the pantographic fibers appear in the chosen deformation energy. We use this novel energy...
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Fluid–solid interaction on a thin platelet with high-velocity flow: vibration modelling and experiment
PublicationThe paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling...
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Strong ellipticity within the Toupin–Mindlin first strain gradient elasticity theory
PublicationWe discuss the strong ellipticity (SE) condition within the Toupin–Mindlin first strain gradient elasticity theory. SE condition is closely related to certain material instabilities and describes mathematical properties of corresponding boundary-value problems. For isotropic solids, SE condition transforms into two inequalities in terms of five gradient-elastic moduli.
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Local material symmetry group for first- and second-order strain gradient fluids
PublicationUsing an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients....
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Flexomagneticity in buckled shear deformable hard-magnetic soft structures
PublicationThis research work performs the first time exploring and addressing the flexomagnetic property in a shear deformable piezomagnetic structure. The strain gradient reveals flexomagneticity in a magnetization phenomenon of structures regardless of their atomic lattice is symmetrical or asymmetrical. It is assumed that a synchronous converse magnetization couples both piezomagnetic and flexomagnetic features into the material structure....
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Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect
PublicationGalerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material...
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Numerical modelling of the mesofracture process of sintered 316L steel under tension using microtomography
PublicationThis paper concerns numerical modelling of the deformation process, taking into account the local fracture of porous 316L sinters at the mesoscopic scale using the finite element method. Calculations are performed with the use of geometrical models, to map the realistic shape of the porous mesostructure of the material, obtained by means of computed microtomography. The microtomographic device has limited and insufficient measurement...
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublicationWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...
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A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions
PublicationThis work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the...
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On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model
PublicationWe study a time-dependent thermoelastic coupling within free vibrations of piezomagnetic (PM) microbeams considering the flexomagnetic (FM) phenomenon. The flexomagneticity relates to a magnetic field with a gradient of strains. Here, we use the generalized thermoelasticity theory of Lord–Shulman to analyze the interaction between elastic deformation and thermal conductivity. The uniform magnetic field is permeated in line with...
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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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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublicationThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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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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Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load
PublicationThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross-section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross-section. The first-order sensitivity variation of the frequencies is derived with...
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Surface effects of network materials based on strain gradient homogenized media
PublicationThe asymptotic homogenization of periodic network materials modeled as beam networks is pursued in this contribution, accounting for surface effects arising from the presence of a thin coating on the surface of the structural beam elements of the network. Cauchy and second gradient effective continua are considered and enhanced by the consideration of surface effects. The asymptotic homogenization technique is here extended to...
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Adaptation of the arbitrary Lagrange–Euler approach to fluid–solid interaction on an example of high velocity flow over thin platelet
PublicationThe aim of this study is to analyse the behaviour of a thin plate with air flow velocities of 0.3–0.9 Ma. Data from the experiment and numerical tools were used for the analysis. For fluid–solid interaction calculations, the arbitrary Lagrange–Euler approach was used. The results of the measurements are twofold. The first one is the measurement of the flow before and after vibrating plate, i.e. pure flow plate, and the second consists...
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Numerical Modeling of Steel Surface Hardening in the Process of High Energy Heating by High Frequency Currents
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Quality Improvement of Wear-Resistant Coatings in Plasma Spraying Integrated with High-Energy Heating by High Frequency Currents
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Perspective of High Energy Heating Implementation for Steel Surface Saturation with Carbon
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A new insight into understanding the Crow and Champagne preferred mode: a numerical study
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Simulation of Structure Formation Processes of Dissimilar Steels Welded Joints Using an Intermediate Layer
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Buckling Analysis of Cold Formed Silo Column
PublicationThe paper is devoted to stability analysis of different models of steel cold formed silo column. The steel cylindrical silos are often composed of corrugated walls and vertical open-sectional columns uniformly placed along the silo circumference. Both the whole 3D silo, a simplified model consisting of one column with a part of the silo walls, and a single column resting on elastic foundation provided by the silo walls were analyzed....
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Effect of a characteristic length on crack spacing in a reinforced concrete bar under tension
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Modelling and FE-simulation of plastic ductile damage evolution in plates and shells
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Modelling of in-plane wave propagation in a plate using spectral element method and Kane–Mindlin theory with application to damage detection
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Nutrient transport and acquisition by diatom chains in a moving fluid
PublicationThe role of fluid motion in delivery of nutrients to phytoplankton cells is a fundamental question in biological and chemical oceanography. In the study of mass transfer to phytoplankton, diatoms are of particular interest. They are non-motile, are often the most abundant components in aggregates and often form chains, so they are the ones expected to benefit most from enhancement of nutrient flux due to dissipating turbulence....
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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Robust four-node elements based on Hu–Washizu principle for nonlinear analysis of Cosserat shells
PublicationMixed 4-node shell elements with the drilling rotation and Cosserat-type strain measures based onthe three-field Hu–Washizu principle are proposed. In the formulation, apart from displacement and rotationfields, both strain and stress resultant fields are treated as independent. The elements are derived in the frame-work of a general nonlinear 6-parameter shell theory dedicated to the analysis of multifold irregular shells.The...
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Virtual spring damper method for nonholonomic robotic swarm self-organization and leader following
PublicationIn this paper, we demonstrate a method for self-organization and leader following of nonholonomic robotic swarm based on spring damper mesh. By self-organization of swarm robots we mean the emergence of order in a swarm as the result of interactions among the single robots. In other words the self-organization of swarm robots mimics some natural behavior of social animals like ants among others. The dynamics of two-wheel robot...
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Local buckling of composite channel columns
PublicationThe investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic...
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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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Structural response of existing spatial truss roof construction based on Cosserat rod theory
PublicationPaper presents the application of the Cosserat rod theory and newly developed associated finite elements code as the tools that support in the expert-designing engineering practice. Mechanical principles of the 3D spatially curved rods, dynamics (statics) laws, principle of virtual work are discussed. Corresponding FEM approach with interpolation and accumulation techniques of state variables are shown that enable the formulation...
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Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches
PublicationThis paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite...
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Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
PublicationIn this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...
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Selected local stability problems of channel section flanges made of aluminium alloys
PublicationThe paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
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Experimental and numerical studies of guided wave damage detection in bars with structural discontinuities
PublicationPraca dotyczy analizy propagacji fal podłużnych i poprzecznych w elementach prętowych z nieciągłościami strukturalnymi. Symulacje numeryczne przeprowadzone przy zastosowaniu metody elementów spektralnych zostały porównane z wynikami badań eksperymentalnych dla pręta w stanie nienaruszonym oraz dla prętów z rysą, spawem oraz dodatkową masą.
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Enriched buckling for beam-lattice metamaterials
PublicationWe discuss two examples of beam-lattice metamaterials which show attractive mechanical properties concerning their enriched buckling. The first one considers pantographic beams and the nonlinear solution is traced out numerically on the base of a Hencky’s model and an algorithm based on Riks’ arc-length scheme. The second one concerns a beam-lattice with sliders and the nonlinear solution is discussed in analytic way and, finally,...
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On the effective properties of foams in the framework of the couple stress theory
PublicationIn the framework of the couple stress theory, we discuss the effective elastic properties of a metal open-cell foam. In this theory, we have the couple stress tensor, but the microrotations are fully described by displacements. To this end, we performed calculations for a representative volume element which give the matrices of elastic moduli relating stress and stress tensors with strain and microcurvature tensors.
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Improved model of isothermal and incompressible fluid flow in pipelines versus the Darcy–Weisbach equation and the issue of friction factor
PublicationIn this article, we consider the modelling of stationary incompressible and isothermal one-dimensional fluid flow through a long pipeline. The approximation of the average pressure in the developed model by the arithmetic mean of inlet and outlet pressures leads to the known empirical Darcy–Weisbach equation. Most importantly, we also present another improved approach that is more accurate because the average pressure is estimated...
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Doświadczalne badania wytrzymałości zmęczeniowej stopów łożyskowych
PublicationW pracy przedstawiono wyniki badań nad wytrzymałością zmęczeniową warstw ślizgowych wykonanych z wybranych materiałów stosowanych w cienkościennych panwiach łożyskowych współczesnych maszyn. Badania przeprowadzono za pomocą urządzeń badawczych skonstruowanych i zbudowanych w Politechnice Gdańskiej. Przedstawiono zaobserwowane pęknięcia zmęczeniowe badanych próbek oraz oszacowano odpowiadające im krytyczne wartości naprężeń w warstwach...
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Procedura kontrolowanego wywrócenia żurawia stoczniowego
PublicationPrzedstawiono procedurę złomowania żurawia stoczniowego, wyposażeniowego. Procedurę tę przeprowadzono w przypadku żurawia uszkodzonego w wyniku katastrofy suwnicy bramowej. Może być również stosowana w przypadkach planowego złomowania wielkich dźwignic.
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
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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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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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An analysis of wind conditions at pedestrian level in the selected types of multi-family housing developments
PublicationThe following article addresses the issue of wind conditions around urban building development at pedestrian level. Factors that depend on those issues include wind comfort and air quality within urbanized spaces. The conditions specific of cities located in a temperate climate zone have been taken into account. The article is intended to identify aerodynamic phenomena characteristic of the three basic types of multi-family building...