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We formulate a series of strong ellipticity inequalities for equilibrium equations of the gradient elasticity up to the Nth order. Within this model of a continuum, there exists a deformation energy introduced as an objective function of deformation gradients up to the Nth order. As a result, the equilibrium equations constitute a system of 2 N -order nonlinear partial differential equations (PDEs). Using these inequalities for a boundary-value problem with the Dirichlet boundary conditions, we prove the positive definiteness of the second variation of the functional of the total energy. In other words, we establish sufficient conditions for infinitesimal instability. Here, we restrict ourselves to a particular class of deformations which includes affine deformations. [ABSTRACT FROM AUTHOR]

We 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 the transverse axis. Using the strain gradient approach, the beam yields microstructural properties. The analytical solving process has been gotten via applying sine Fourier technique on displacements. Graphical illustrations are assigned to shape numerical examples concerning variations in essential physical quantities. It was observed that the flexomagnetic effect could be extraordinary if the thermal conductivity of the material is higher or the thermal relaxation time of the heat source is lesser. This theoretical study will provide the way of starting studies on magneto-thermoelastic small-scale piezo-flexomagnetic structures based on the heat conduction models. [ABSTRACT FROM AUTHOR]

We discuss conservation laws for thin structures which could be modeled as a material minimal surface, i.e., a surface with zero mean curvatures. The models of an elastic membrane and micropolar (six-parameter) shell undergoing finite deformations are considered. We show that for a minimal surface, it is possible to formulate a conservation law similar to three-dimensional non-linear elasticity. It brings us a path-independent J -integral which could be used in mechanics of fracture. So, the class of minimal surfaces extends significantly a possible geometry of two-dimensional structures which possess conservation laws. [ABSTRACT FROM AUTHOR]

The 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 and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration. [ABSTRACT FROM AUTHOR]

We 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 dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by Eremeyev et al. (2020 Z angew Math Phys 71 (6): 1–16) to the case of domains with edges and when external line forces are applied. Let us note that the interest paid to Lipschitz polyhedra-type domains is at least twofold. First, it is known that geometrical singularity of the boundary may essentially influence singularity of solutions. On the other hand, the analysis of weak solutions in polyhedral domains is of great significance for design of optimal computations using a finite-element method and for the analysis of convergence of numerical solutions. [ABSTRACT FROM AUTHOR]

Using 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. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua. [ABSTRACT FROM AUTHOR]

In 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. Dispersion equations for both models have been obtained in algebraic form for two types of anti-plane wave, i.e. a Love-type wave and a new type of surface wave (due to micropolarity). The angular frequency and phase velocity of anti-plane waves have been analysed through a numerical study within cut-off frequencies. The obtained results may find suitable applications in thin film technology, non-destructive analysis or biomechanics, where the models discussed here may serve as theoretical frameworks for similar types of phenomena. [ABSTRACT FROM AUTHOR]

On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs. [ABSTRACT FROM AUTHOR]

For two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat curve beam model, we get 2D and 3D semi-discrete models. These models consist of systems of ordinary differential equations describing the statics of a collection of fibers with certain geometrical constraints. Using a specific homogenization technique, we introduce two- and three-dimensional equivalent continuum models which correspond to the six-parameter shell model and the micropolar continuum, respectively. We call two models equivalent if their approximations coincide with each other up to certain accuracy. The two- and three-dimensional constitutive equations of the networks are derived and discussed within the micropolar continua theory. [ABSTRACT FROM AUTHOR]

Here 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 are more localised near the free surface. For the strain-gradient elasticity model there is a range of wavenumbers where the amplitude of displacements decays very slowly. [ABSTRACT FROM AUTHOR]

It is worth mentioning stress and strain gradient elasticity, surface elasticity, media with internal degrees of freedom, and nonlocal continua among others. 32967152 10 Tocci Monaco G., Fantuzzi N., Fabbrocino F., Luciano R. Critical temperatures for vibrations and buckling of magneto-electro-elastic nonlocal strain gradient plates. Recent advances in technologies of design, manufacturing and further studies of new materials and structures result in an essential extension of classic models of continuum and structural mechanics. [Extracted from the article]

The aim of this paper is to develop a robust layer-wise theory for structural analysis of curved glass and photovoltaic panels. By the analogy to the existing theories of plates, governing equations for doubly curved layers including kinematic relations, equilibrium conditions and constitutive equations are introduced. Applying assumptions of shear rigidity of skin layers and moments-free core layer as well as approximations of thin shallow shell, a reduced form of governing differential equations is proposed. Compared to the classical theories of shells the derived system includes an additional second order differential equation. As a result, additional boundary conditions should be satisfied for any edge of the shell. The importance of these extensions is demonstrated for long cylindrical panel with for two examples of simple supports: one with free edges, where relative in-plane displacements of skins are allowed, and one with framed edges, where cross-section rotations of all layers are assumed the same. For both cases closed-form analytical solutions related to a shell strip approximation are presented. Displacement bounds in monolithic and layered cases are derived, and the dependence of deformation and stress characteristics on the radius of curvature and types of supports are illustrated. [ABSTRACT FROM AUTHOR]

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area. [ABSTRACT FROM AUTHOR]

In the present work, the flexomagnetic (FM) behaviour of a vibrating squared multi-physic beam in finite dimensions. It is assumed that the bending and shear deformations cause rotary inertia. In the standard type of the Timoshenko beam the rotary inertia originated from shear deformations has been typically omitted. It means the rotary inertia resulting from shear deformation is a new concept considered here. Thus, the novelty in this work is that the effect of shear deformation's rotary inertia (SDRI) on the FM response will be considered in detail. When it comes to nanosize, the well-posed nonlocal elasticity assumption of Eringen can be worth choosing. In this study, the weak form (differential) of strain-driven nonlocal theory is taken into hand for easiness. The procedure of solution will be in regard to the advantage of the Galerkin weighted residual technique based on an analytical flow for the meta beam located at simply-simply supported ends. Several separate studies will show how SDRI and FM can influence each other. The observations give some new achievements in the series of studies on FM. It has been earned that the SDRI can directly impress the flexomagnetic feature of small-scale actuators. [ABSTRACT FROM AUTHOR]

We discuss the material symmetry group of the micropolar continuum and related consistently simplified constitutive equations. Following Eremeyev and Pietraszkiewicz (Int J Solid Struct 2012; 49: 1993–2005; Generalized continua as models for materials, Heidelberg: Springer, 2013, 77–90) we extend the definition of the group proposed by Eringen and Kafadar (Continuum physics, vol. 4, New York, NY: Academic Press, 1976, 1–75) by taking into account the microstructure curvature tensor as well as different transformation properties of polar (true) and axial (pseudo) tensors. Our material symmetry group consists of ordered triples of tensors which make the strain energy density of the micropolar continuum invariant under change of the reference placement. Within micropolar solids we discuss the isotropic, hemitropic, orthotropic, transversely isotropic and clinotropic materials and give explicitly the consistently reduced representations of the strain energy density. [ABSTRACT FROM AUTHOR]

In the last years, the rapid increase in the technical capability to control and design materials at the nanoscale has pushed toward an intensive exploitation of new possibilities concerning optical, chemical, thermoelectrical and electronic applications. As a result, new materials have been developed to obtain specific physical properties and performances. In this general picture, it was natural that the attention toward mechanical characterization of the new structures was left, in a sense, behind. Anyway, once the theoretically designed objects proceed toward concrete manufacturing and applications, an accurate and general description of their mechanical properties becomes more and more scientifically relevant. The aim of the paper is therefore to discuss new methods and techniques for modeling the behavior of nanostructured materials considering surface/interface properties, which are responsible for the main differences between nano- and macroscale, and to determine their actual material properties at the macroscale. Our approach is intended to study the mechanical properties of materials taking into account surface properties including possible complex inner microstructure of surface coatings. We use the Gurtin-Murdoch model of surface elasticity. We consider the inner regular and irregular surface thin coatings (i.e., ordered or disordered nanofibers arrays) and present few examples of averaged 2D properties of them. Since the actual 2D properties depend not only on the mechanical properties of fibers or other elements of a coating, but also on the interaction forces between them, the analysis also includes information on the geometry of the microstructure of the coating, on mechanical properties of elements and on interaction forces. Further we use the obtained 2D properties to derive the effective properties of solids and structures at the macroscale, such as the bending stiffness or Young's modulus. [ABSTRACT FROM AUTHOR]

Courant’s minimax variational principle is considered in application to the six-parameter theory of prestressed shells. The equations of a prestressed micropolar shell are deduced in detail. Courant’s principle is used to study the dependence of the least and higher eigenfrequencies on shell parameters and boundary conditions. Cases involving boundary reinforcements and shell junctions are also treated. [ABSTRACT FROM AUTHOR]

Abstract: Laminated plates with glass skin layers and a core layer from soft polymers are widely used in the civil engineering. Photovoltaic panels currently available on the market are composed from stiff front and back layers and a solar cell layer embedded in a soft polymeric encapsulant. In this paper a layer-wise theory for the structural analysis of glass and photovoltaic laminates is developed. Starting from governing equations for individual layers, kinematical constraints and appropriate interaction forces, a twelfth order system of partial differential equations is derived. The primary variables in the theory include the Airy stress function, the deflection function and the vector of relative in-plane displacements of skin layers. For symmetric laminates a system of uncoupled differential equations with respect to scalar potentials is presented. Three of them correspond to the first order shear deformation plate. The new additional second order differential equation provides a correction function according to the layer-wise theory. Closed form analytical solutions for a plate strip are derived to illustrate the essential influence of this correction for laminates with soft core layer. The importance of additional boundary conditions is shown for examples of free and framed plate edges. [Copyright &y& Elsevier]

In this paper a direct non-local peridynamics theory for thin plates is developed. Peridynamic points are assumed to behave like rigid bodies with independent translation and finite rotation degrees of freedom. The non-local mechanical interaction between points is characterized by force and moment vectors. The balance equations including the linear momentum, the angular momentum and the energy are presented. Peridynamic deformation states of the plate are introduced including the actual bond vector (relative translation of two points within the bond) and the relative finite rotation tensor (actual relative orientation of two points in the bond). The corresponding power-conjugate bond force and bond moment states are derived. The framework to develop constitutive equations for the plate peridynamic states is addressed. Special cases of the theory including plates with zero drilling moments, membranes, soft interlayers as well as stiff plate layers with small relative rotations are considered. [ABSTRACT FROM AUTHOR]

Solvability and uniqueness of solutions to the problems of equilibrium, vibration and dynamics in a weak setup for classical and nonclassical models of linear elasticity are established in a unified framework sufficiently flexible to accommodate new elastic models. [ABSTRACT FROM PUBLISHER]

Abstract: We extend the material symmetry group of the non-linear polar-elastic continuum by taking into account microstructure curvature tensors as well as different transformation properties of polar and axial tensors. The group consists of an ordered triple of tensors which makes the strain energy density of polar-elastic continuum invariant under change of reference placement. An analog of the Noll rule is established. Four simple specific cases of the group with corresponding reduced forms of the strain energy density are discussed. Definitions of polar-elastic fluids, solids, liquid crystals and subfluids are given in terms of members of the symmetry group. Within polar-elastic solids we discuss in more detail isotropic, hemitropic, cubic-symmetric, transversely isotropic, and orthotropic materials and give explicitly corresponding reduced representations of the strain energy density. For physically linear polar-elastic solids, when the density becomes a quadratic function of strain measures, reduced representations of the density are established for monoclinic, orthotropic, cubic-symmetric, hemitropic and isotropic materials in terms of appropriate joint scalar invariants of stretch, wryness and undeformed structure curvature tensors. [Copyright &y& Elsevier]

The article reports that the special issue is dedicated to Professor Dr Eron L. Aero on the occasion of his 80th birthday.

Considering the viscoelastic behavior of polymer foams a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. The material properties are changing in the thickness direction. Solving some problems of the global structural analysis it will be demonstrated that in some cases the results significantly differ from the results based on the Kirchhoff-type theory. [ABSTRACT FROM AUTHOR]

Our analysis incorporates the geometrically nonlinear bending of the Euler-Bernoulli ferromagnetic nanobeam accounting for a size-dependent model through assuming surface effects. In the framework of the flexomagnetic phenomenon, the large deflections are investigated referring to von-Kármán nonlinearity. Employing the nonlocal effects of stress coupled to the gradient of strain generates a scale-dependent Hookean stress–strain scheme related to the small scale. Taking into account the supports of the nanobeam in two cases, that is, totally fixed and hinged, the deformations are predicted. A constant static lateral load is postulated uniformly along the length of the beam, which forces the deformation. As the analysis is based on the one-dimensional media, the electrodes are embedded so that they give off a transverse magnetic field creating a longitudinal force. The newly developed mathematical model is computed by means of the differential quadrature method together with the Newton-Raphson technique. The computational section discusses and reveals the numerical results in detail for the characteristics and parameters involved in the design of beam-like magnetic nanosensors. As shown later, the conducted research presents that there is a strong linkage between the surface effect and the flexomagneticity behavior of the bulk. [ABSTRACT FROM AUTHOR]

In this paper, the equation governing the buckling of a magnetic composite nanoplate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the nanoplate, the nonlocal strain gradient theory has been used by taking into account the classical plate theory. The axial magnetic force, which is originated from the magnetic field, is investigated. After extracting the governing differential equation, the critical buckling load is obtained for different support conditions. The effect of nonlocal parameter, sheet aspect ratio and the effect of one-dimensional magnetic field on critical load are discussed. It was earned that if the nanoplate is rectangular so that the value of aspect ratio is less than one, the flexomagnetic response will be more noticeable. [ABSTRACT FROM AUTHOR]

It was with Maugin that Francesco dell'Isola met Paul Germain for the first time. It is in this perspective that some of dell'Isola's works in the field of Economics, such as dell'Isola and del Monte [[18]] or his recent book [[19]], should be framed. Graph We are very pleased to dedicate this Special Issue of I Mathematics and Mechanics of Solids i to Francesco dell'Isola for celebrating his 60th birthday. Francesco dell'Isola's academic formation can be ascribed to a double matrix: the primary Italian one, for which it is even possible to draw up a genealogy, and the French one, mediated by his numerous collaborations with French scientists and inspired by his fruitful contact, as a young scholar, with Paul Germain. [Extracted from the article]

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant. [ABSTRACT FROM AUTHOR]

A drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic-polynomial higher-order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect effect of thickness variations. As a result of compounding the proposed beam model in linear Lagrangian strains and variational of energy, the system of equations is obtained. The Galerkin method is here expanded for several edge conditions to obtain elastic critical buckling values. First, the importance of the higher-order beam theory, as well as stretching effect, is assessed in assorted tabulated comparisons. Next, with validations based on the existing and open literature, the proposed shape function is evaluated to consider the desired accuracy. Some comparative graphs by means of well-known shape functions are plotted. These comparisons reveal a very good compliance. In the final section of the paper, based on an inappropriate mixture of the SUS304 and Si 3 C 4 as the first type of FGM beam (Beam-I) and, Al and Al 2 O 3 as the second type (Beam-II), the results are pictured while the beam is kept in four states, clamped–clamped (C–C), pinned–pinned (S–S), clamped-pinned (C–S) and in particular cantilever (C–F). We found that the defect impresses markedly an FGM beam with boundary conditions with lower degrees of freedom. [ABSTRACT FROM AUTHOR]

For micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua we have six degrees of freedom (DOF) that are three DOFs for translations and three DOFs for rotations. So the corresponding kinetic energy density nontrivially depends on linear and angular velocity. Here we define the local material symmetry group as a set of ordered triples of tensors which keep both kinetic energy density and strain energy density unchanged during the related change of a reference placement. The triples were obtained using transformation rules of strain measures and microinertia tensors under replacement of a reference placement. From the physical point of view, the local material symmetry group consists of such density-preserving transformations of a reference placement, that cannot be experimentally detected. So the constitutive relations become invariant under such transformations. Knowing a priori a material's symmetry, one can establish a simplified form of constitutive relations. In particular, the number of independent arguments in constitutive relations could be significantly reduced. [ABSTRACT FROM AUTHOR]

Among 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 this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam. [ABSTRACT FROM AUTHOR]

The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton's principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material. [ABSTRACT FROM AUTHOR]

Large deformations and stress analyses in two types of space structures that are intended for people to live in space have been studied in this research. The structure under analysis is assumed to rotate around the central axis to create artificial gravitational acceleration equal to the gravity on the Earth's surface. The analysis is fully dynamic, which is formulated based on the energy method by using the first-order shear deformation shell theory in two systems, cylindrical and torus. Also, the nonlinear von Kármán strain field has been assumed. The obtained set of partial differential equations has been solved using the semi-analytical polynomial solution method (SAPM). The main purpose of this paper is to study the effects of unusual conditions in the space outside the Earth's atmosphere (which is a complete vacuum environment without pressure) on the strength of the analyzed structure. The numerical results of the governing equations have been evaluated using those of other studies and the simulation efficiency performed in this research has been proven. Finally, the effect of important parameters on the numerical results, including the angular velocity of the structure (which causes artificial gravity), the amount of imposed mechanical and hygro-thermal loads, the structure size and material specifications have been investigated in more detail. • Large dynamic deformations of torus-shaped and cylindrical space structures are studied. • Artificial gravity due to rotations is taken into account. • Hygro-thermal effects are also considered. • Functionally graded structures are analyzed. [ABSTRACT FROM AUTHOR]

Within the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which occurs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we considered here both large translations and rotations. The constitutive relations contain some additional micropolar parameters with so-called coupling factor that relates Cosserat shear modulus with the Cauchy shear modulus. The discussed instability relates to the bifurcation from the static solution without rotations to solution with non-zero rotations. So we call it rotational instability. We present an elementary discrete model which captures the rotational instability phenomenon and the results of numerical analysis within the shell model. The dependence of the bifurcation condition on the micropolar material parameters is discussed. [ABSTRACT FROM AUTHOR]

We discuss experimental and numerical studies of the deformation and destruction of fine-grained concrete B22.5 under dynamic loading. The experiments were carried out using the Kolsky (or split-Hopkinson pressure bar) method, and its modifications in the strain rate range from 400 to 2000 s−1. The rate dependences of ultimate stresses and fracture energy in tension and compression are obtained. Based on experimental data, the identification of the dynamic component of two models from the LS-DYNA computational complex was carried out: *MAT_CONCRETE_DAMAGE and *MAT_CSCM. The results of a comparative analysis of the identified models based on single-element modeling and comparison with experimental data are presented. It is shown that the obtained experimental strain rate dependences of the fracture characteristics can significantly improve the predictive ability of the model compared to the default parameter set. Information about the rate dependence of the fracture energy in *MAT_CSCM model makes it possible to more realistically simulate the behavior of the material beyond the ultimate stress. [ABSTRACT FROM AUTHOR]

In this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained. Boundary elements with mixed approximation of geometry and field variables with the standard nodal collocation procedure are used for spatial discretization. In order to obtain time-domain solutions, the classic Durbin's method is applied for numerical inversion of Laplace transform. Problem of alleviating Gibbs oscillations is addressed. Dynamic boundary element analysis of the model problem involving trigonal material is performed to test presented formulation. Obtained results are compared with finite element solutions. [ABSTRACT FROM AUTHOR]

This paper presents a thermodynamic theory for elastic rods using the model of directed curves. In this model, the thin rod-like bodies are described as deformable curves with a triad of rigidly rotating vectors attached to each point. To account for the thermal effects in rods, we introduce two independent temperature fields: the absolute temperature field and the temperature deviation field. We present a complete derivation of the non-linear equations of thermoelastic rods, starting from the principles of thermodynamics. Finally, we prove the uniqueness of solution to the linearized equations of thermoelastodynamics for rods. [ABSTRACT FROM AUTHOR]

One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory. [ABSTRACT FROM AUTHOR]

In the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic, and any non-geometric structure with functional cross-section, can be modeled mechanically with only one partial differential equation system. The obtained equations have been solved by applying SAPM semi-analytical solution method. In order to present a comprehensive research, dynamic nonlinear analysis is considered. The variation of material properties through the thickness has been assumed as functionally graded and its effect on the strength of the shell structure with the functional cross-section has been investigated. The numerical results have been compared with available papers and also with FEM results for some structures that there is no paper available for validation. Different types of shell structures have been studied in terms of cross-sectional shape and properties. Finally, the effects of some important factors on the results such as boundary conditions, nonlinear analysis, dynamic analysis, and rotation of the structure around its central axis have been conducted thoroughly. This study and its original governing equations can be considered as a comprehensive reference for mechanical analysis of various shell structures with functional cross-sectional shape. [ABSTRACT FROM AUTHOR]

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i.e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out. [ABSTRACT FROM AUTHOR]

This paper introduced the use of two new adsorbents, Akrosorb soda-lime and Bentonite clay, for refinery flare flue gas capture and storage. This study also developed a novel pilot plant model with 409.7149 kg/h capacity refinery flare emission capture with a novel adsorption column configuration using Akrosorb soda-lime and Bentonite clay adsorbents. The flare flue gas adsorption unit was designed, fabricated, test run, and commissioned. The adsorption column temperature is 28 ± 10 °C and has a pressure of 131.7 kPa. The novel plant RSM optimization result shows that 93.24% of CO2 and 62.18% of CO were absorbed, while 86.14% of NOx and 55.87% of HC were absorbed. The established optimum conditions of CO2, NOx, HC, and CO removal efficiency are 22 °C, 2 atm, and 60 min. The variation in flare gas emission could impact the removal efficiency of the plant. The results show the maximum adsorption ability or capacity of 314.30 mg/g, and 68.90 mg/g was reached at 60 min for Akrosorb soda-lime and molded Bentonite adsorbents. Therefore, the developed novel technology for CO2 and other GHG capture is technically feasible and friendly. The combined usage of both adsorbents will enhance the capture of GHG at a low cost compared to using Akrosorb alone as an adsorbent. [ABSTRACT FROM AUTHOR]

• The collapse mechanisms of R.C. existing bridges piers subjected to corrosion effects has been analyzed considering static and dynamic loads. • An analytical approach has been considered to introduce the corrosion effects in the finite element model implementation. • Linear and non-linear numerical analyses have been carried out considering an existing R.C. bridge located in Northern Italy in order to evaluate its safety level under different load cases. • Different interventions have been proposed to prevent the collapse of the bridge. The evaluation of the structural behaviour of existing reinforced concrete (RC) bridges represents one of the most current structural engineering research topics due to their strategic importance, especially if they are subjected to corrosion effects which can lead to a significant reduction of load-bearing capacity of the main structural elements (e.g., the piers). In the last decades, different types of numerical approaches have been proposed for the evaluation of the structural behaviour of these strategic infrastructures, especially after the recent collapses that have affected this type of structures during last years. In this paper, the structural behaviour of an existing RC bridge subjected to corrosion effects due to carbonation is analysed by means of an efficient procedure based on the implementation of a Finite Element Model (FEM) where the main structural elements are implemented using only Timoshenko beam elements. The safety level of the bridge has been evaluated considering different load conditions (e.g. traffic load, seismic action, etc.) calculated according to the Italian Design Code (NTC2018). Finally, a retrofitting intervention is proposed in order to guarantee and adequate safety level of the bridge under the considered different load combinations. [ABSTRACT FROM AUTHOR]

Dynamic tests of fine-grained fired dioxide-zirconia ceramics under compression under uniaxial stress conditions were carried out. The influence of the specimen length on the obtained strength and deformation properties of ceramics is investigated. The thickness of the specimen has a significant impact on the course of the obtained dynamic stress–strain diagrams: short specimens have a much more sloping area of active loading branch. The main contribution to the modulus of the load branch resulting from tests of brittle porous media is made by the geometry of the specimens and the porosity of the material. When choosing the length of specimens for dynamic tests, the optimal geometry of the tested specimens is preferable in accordance with the Davies–Hunter criterion, when the contributions of axial and radial inertia are mutually compensated, and the contribution of the effects of friction in the resulting diagram is minimal. When choosing the geometry of specimens of brittle porous media, the structure of the material should be taken into account so that the size of the specimen (both length and diameter) exceeds the size of the internal fractions of the material by at least five times. [ABSTRACT FROM AUTHOR]

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton's principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton's technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions. [ABSTRACT FROM AUTHOR]

In the present research, wood flour reinforced polyethylene polymer composites with a coupling agent were prepared by injection molding. The effects of wood flour size, aspect ratios, and mold injection temperature on the composites' mechanical properties were investigated. For the preparation of the polymer composites, five different formulations were created. The mechanical properties including tensile strength and the modulus, flexural strength and the modulus, and impact energy were measured. To investigate the changes in the properties resulting from different compositions, mechanical static and impact testing was performed. The obtained results indicate that by reducing the flour size, the tensile strength and modulus, flexural strength, and impact energy were reduced. In contrast, the flexural modulus increased. Furthermore, with the increment of injection molding temperature, the tensile strength and the modulus and the impact energy of the specimens were reduced. On the other hand, the flexural strength and the modulus increased. Thus, an optimized amount of injection molding temperature can provide improvements in the mechanical properties of the composite. [ABSTRACT FROM AUTHOR]

In this study, the effect of wood powder and nanoclay particle content on composites' mechanical behavior made with polyethylene matrix has been investigated. The wood flour as a reinforcer made of wood powder was at levels of 30, 40, and 50 wt.%, and additional reinforcement with nanoclay at 0, 1, 3, and 5 wt.%. Furthermore, to make a composite matrix, high-density polyethylene was used at levels of 70, 60, and 50% by weight. Wood-plastic composite (WPC) specimens were manufactured in injection molding. After preparing the specimens, tensile and bending tests were performed on samples. The mechanical properties such as tensile and flexural strength and flexural modulus were measured. Results showed that nanoclay particle content increases flexural modulus, flexural strength, modulus of elasticity, and tensile strength. The experimental test results show that Young's moduli increased with the volume of wood flour. The biggest modulus of elasticity was achieved in the samples having 50 wt.% of wood powder. Furthermore, the highest value of tensile strength was achieved at the level of 30 wt.%. The highest flexural strength was for the sample containing 50% wood powder by weight. Additionally, a numerical model was made utilizing the Abaqus software using the finite element method (FEM). Comparing the numerical and experimental results, it was found that they are compatible in the linear-elastic and plastic state of the material. There are no crucial differences between experiment and FEM. [ABSTRACT FROM AUTHOR]

Wave diffusion in the composite soil layer with the lined tunnel structure is often encountered in the field of seismic engineering. The wave function expansion method is an effective method for solving the wave diffusion problem. In this paper, the wave function expansion method is used to present a semi-analytical solution to the shear horizontal (SH) wave scattering problem of a circular lined tunnel under the covering soil layer. Considering the existence of the covering soil layer, the great arc assumption (that is, the curved boundary instead of the straight-line boundary) is used to construct the wavefield in the composite soil layer. Based on the wave field and boundary conditions, an infinite linear equation system is established by adding the application of complex variable functions. The finite term is intercepted and solved, and the accuracy of the solution is analyzed. Although truncation is inevitable, due to the Bessel function has better convergence, a smaller truncation coefficient can achieve mechanical accuracy. Based on numerical examples, the influence of SH wave incident frequency, soil parameters, and lining thickness on the dynamic stress concentration factor of lining is analyzed. Compared with the SH wave scattering problem by lining in a single medium half-space, due to the existence of the cover layer and the influence of its stiffness, the dynamic stress of the lining can be increased or inhibited. In addition, the lining thickness has obvious different effects on the dynamic stress concentration coefficient of the inner and outer walls of different materials. [ABSTRACT FROM AUTHOR]

A new mathematical model is developed for the analytical study of two cracks in the upper plane of dissimilar materials under various mechanical loadings, i.e., shear, normal, tearing and mixed stresses with different geometry conditions. This problem is developed into a new mathematical model of hypersingular integral equations (HSIEs) by using the modified complex potentials (MCPs) function and the continuity conditions of the resultant force and displacement with the crack opening displacement (COD) function as the unknown. The newly obtained mathematical model of HSIEs are solved numerically by utilizing the appropriate quadrature formulas. Numerical computations and graphical demonstrations are carried out to observe the profound effect of the elastic constants ratio, mode of stresses and geometry conditions on the dimensionless stress intensity factors (SIFs) at the crack tips. [ABSTRACT FROM AUTHOR]

Commercial aircraft have well-designed and optimized systems, the result of a huge experience in the field, due to the large fleet of aircraft in operation. For light, utility, or sports aircraft, with a multitude of shapes, tasks, and construction types, there are different solutions that seek to best meet the requirements of the designed aircraft. In this sense, for a sport plane, an increased maneuverability is desired, and the system that controls flaps and wing must be properly designed. A new flap mechanism command solution is proposed and justified in the paper, for use in sports and recreational aviation, in order to achieve angles of braking greater than 40°, take-off and landing in a shorter time and over a shorter distance, as well as the gliding of the aircraft in critical flight conditions or when fuel economy is needed. A finite element model is used to verify the optimized command system for the flap and wing and to check if the strength structure of the aircraft is properly designed. The main result consists of the new design command system for flaps and wings and in verifying, by calculation, the acceptability of the new mechanism proposed from the point of view of the strength of the materials. [ABSTRACT FROM AUTHOR]

In this article, a method is proposed for determining parameters of the exponentialy varying shear modulus of a functionally graded half-space. The method is based on the analytical solution of the problem of pure shear of an elastic functionally graded half-space by a strip punch. The half-space has the depth-wise exponential variation of its shear modulus, whose parameters are to be determined. The problem is reduced to an integral equation that is then solved by asymptotic methods. The analytical relations for contact stress under the punch, displacement of the free surface outside the contact area and other characteristics of the problem are studied with respect to the shear modulus parameters. The parameters of the functionally graded half-space shear modulus are determined (a) from the coincidence of theoretical and experimental values of contact stresses under the punch and from the coincidence of forces acting on the punch, or (b) from the coincidence of theoretical and experimental values of displacement of the free surface of the half-space outside the contact and coincidence of forces acting on the punch, or (c) from other conditions. The transcendental equations for determination of the shear modulus parameters in cases (a) and (b) are given. By adjusting the parameters of the shear modulus variation, the regions of "approximate-homogeneous" state in the functionally graded half-space are developed. [ABSTRACT FROM AUTHOR]