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The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced polymer-based moderately-thick plates subjected to in-plane biaxial compressive loads in elastic and thermal environments in the framework of first-order shear deformation plate theory (FSDPT) is investigated. First, the temperature-dependent properties of CNTs and nanocomposites are defined and their constitutive relations are established, then the stability and strain compatibility equations in elastic media are derived in the framework of the FSDPT. Then, by applying the Galerkin method to the basic equations, a closed-form solution is obtained for the critical biaxial compressive loads. The specific numerical analyzes and interpretations are made for various plate sizes and CNT patterns on the Winkler elastic foundation and in thermal environments within FSDPT and classical plate theory (CPT).

Carbon fiber composites have emerged as a transformative technology, offering a fascinating alternative to traditional materials like aluminum and steel. Their unique combination of high strength, stiffness, and reduced density makes them an ideal choice for lightweight structural components, an attribute that aligns with the pursuit of fuel-efficient and eco-friendly aircraft designs. With the continuous race between countries and research organizations to find new materials that satisfies the above-mentioned characteristics, this article highlights the utilization of a new Ultra-Light Carbon-based Composite (ULCC) in the aeronautical sector developed within the industrial research project TERSA (Radar technologies for autonomus flying vehicles or TEcnologie Radar per Sistemi aerei a pilotaggio remoto (SAPR) Autonomi in italian). The composite material has been developed with the aim of achieving superior performance and efficiency compared to existing products on the market. To evaluate its effectiveness, first, the mechanical properties of the ULCC have been compared to T300/Epoxy and T1000/Epoxy, two of the materials commonly used in aeronautical industry and unmanned aerial vehicle (UAV). Second, finite element models were employed to verify and analyze the dynamic properties of aeronautical structural components made of ULCC. The results indicate that the new carbon-based composite exhibits remarkable strength-to-weight ratio, enhanced durability, and offering significant advantages in terms of weight reduction and overall performance. These findings validate its potential as a viable alternative in aeronautical industry.

A failure criterion fully considering the anisotropy and hydration of shale is essential for shale formation stability evaluation. Thus, a novel failure criterion for hydration shale is developed by using Jaeger’s shear failure criterion to describe the anisotropy and using the shear strength reduction caused by clay minerals hydration to evaluate the hydration. This failure criterion is defined with four parameters in Jaeger’s shear failure criterion (S1, S2, α and φ), three hydration parameters (k, ωsh and σs) and two material size parameters (d and l0). The physical meanings and determining procedures of these parameters are described. The accuracy and applicability of this failure criterion are examined using the published experimental data, showing a cohesive agreement between the predicted values and the testing results, R2 = 0.916 and AAREP (average absolute relative error percentage) of 9.260%. The error (|Dp|) is then discussed considering the effects of β (angle between bedding plane versus axial loading), moisture content and confining pressure, presenting that |Dp| increases when β is closer to 30°, and |Dp| decreases with decreasing moisture content and with increasing confining pressure. Moreover, |Dp| is demonstrated as being sensitive to S1 and being steady with decrease in the data set when β is 0°, 30°, 45° and 90°.

A strategy based on material homogenization and heuristic optimization for the structural identification of composite materials is proposed. The objective is the identification of the constitutive properties of a micropolar continuum model employed to describe the mechanical behaviour of a composite material made of rigid blocks and thin elastic interfaces. The micropolar theory (Cosserat) has been proved to be capable of properly accounting for the particles arrangements as well as their size and orientation. The constitutive parameters of the composite materials, characterized by different textures and dimensions of the rigid blocks, are identified through a homogenization procedure. Thus, the identification is repeated exploiting the static or modal response of the composite materials and using the Differential Evolution algorithm. The benchmark structures assumed as target are represented by discrete models implemented in ABAQUS where the blocks and the elastic interfaces are modelled by rigid bodies and elastic interfaces, respectively. The obtained results show that proposed strategies provide accurate results paving the way to the experimental validation and in field applications.

The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal environment, is investigated by means of the first-order shear deformation theory (FSDT). The nanocomposite material is modeled as homogeneous and heterogeneous and is based on a carbon nanotube (CNT)-reinforced polymer with the linear variation of the mechanical properties throughout the thickness. In the heterogeneous case, the mechanical properties are modeled as the linear function of the thickness coordinate. The basic equations are derived as partial differential equations and solved in a closed form, using the Galerkin procedure, to determine the critical combined loads for the selected structure in thermal environments. To test the reliability of the proposed formulation, comparisons with the results obtained by finite element and numerical methods in the literature are accompanied by a systematic study aimed at testing the sensitivity of the design response to the loading parameters, CNT models, and thermal environment.

In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin’s procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment.

All-atom molecular dynamics simulations are conducted to elucidate the fracture mechanism of polylactic acid nanofibres doped with metallic nanoparticles. Extensional deformation is applied on polymer nanofibres decorated with spherical silver nanoparticles on the surface layer. In the obtained stress–strain curve, the elastic, yield, strain softening and fracture regions are recognized, where mechanical parameters are evaluated by tracking the stress, strain energy and geometrical evolutions. The energy release rate during crack propagation, which is a crucial factor in fracture mechanics, is calculated. The results show that the presence of doping nanoparticles improves the fracture properties of the polymer nanofibre consistently with experimental observation. The nanoparticles bind together polymer chains on the surface layer, which hinders crack initiation and propagation. The effect of the distribution of nanoparticles is studied through different doping decorations. Additionally, a discussion on the variation of internal energy components during uniaxial tensile loading is provided to unravel the deformation mechanism of nanoparticle-doped nanofibres.

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]

The structural performance of any building design is often dependent on the geometrical shape, which affects its behavior and stability. Structural consideration and optimization in the conceptual stage of the design process can lead to better solutions and design exploration. In this paper, a design approach for generating and structurally optimizing the geometrical form in the conceptual design phase is presented. The method is applied to a canopy of an ecological island (waste collection center in Rome, Italy). We demonstrate how parametric structural design can facilitate the decision-maker to generate and analyze the optimal design solutions rapidly in the conceptual stage of the design process. Fully parametric models are created in a Rhinoceros3D® environment and interfaced with in-house built algorithms, and Finite Element simulations are performed in DubalRFEM. An ecological island’s canopy has been completely redesigned with a Genetic Algorithm and a Dynamic Relaxation Algorithm, resulting in a free-form shape-resistant structure. Finally, the shape-optimized canopy meets various requirements (structural, functional, formal) that improve structural efficiency and design collaboration, such as in the role of the architect and engineer in the design process and in the relationship between the designer and design tools.

The buckling behavior of sandwich shells with functionally graded (FG) coatings operating under different external pressures was generally investigated under simply supported boundary conditions. Since it is very difficult to determine the approximation functions satisfying clamped boundary conditions and to solve the basic equations analytically within the framework of first order shear deformation theory (FOST), the number of publications on this subject is very limited. An analytical solution to the buckling problem of FG-coated cylindrical shells under clamped boundary conditions subjected to uniform hydrostatic pressure within the FOST framework is presented for the first time. By mathematical modeling of the FG coatings, the constitutive relations and basic equations of sandwich cylindrical shells within the FOST framework are obtained. Analytical solutions of the basic equations in the framework of the Donnell shell theory, obtained using the Galerkin method, is carried out using new approximation functions that satisfy clamped boundary conditions. Finally, the influences of FG models and volume fractions on the hydrostatic buckling pressure within the FOST and classical shell theory (CT) frameworks are investigated in detail.

Tungsten trioxide/graphene oxide (WO3/GO) nanocomposites have been successfully synthesized using in situ and ex situ chemical approaches. Graphite and tungsten carbide (WC) were employed to perform in situ synthesis, and WO3 and GO were employed to perform the ex situ synthesis of WO3/GO nanocomposites. GO, which was required for ex situ synthesis, is synthesized via the modified and improved Hummers method. XRD, SEM/EDS, and FTIR are used for the characterization of the nanocomposite. From the XRD of the WO3/GO nanocomposites, it was observed that WO3 distributed uniformly on graphene oxide sheets or was incorporated between the sheets. The photocatalytic activities of WO3/GO nanocomposites were evaluated by methylene blue (MB) adsorption and visible light photocatalytic degradation activities by UV-vis spectroscopy. The results showed that the efficiency of the photocatalytic activity of the nanocomposite depends on different synthesis methods and the morphology resulting from the changed method. WO3/GO nanocomposites synthesized by both methods exhibited much higher photocatalytic efficiencies than pure WO3, and the best degradation efficiencies for MB was 96.30% for the WO3/GO in situ synthesis nanocomposite.

This study presents the solution for the thermal buckling problem of moderately thick laminated conical shells consisting of carbon nanotube (CNT) originating layers. It is assumed that the laminated truncated-conical shell is subjected to uniform temperature rise. The Donnell-type shell theory is used to derive the governing equations, and the Galerkin method is used to find the expression for the buckling temperature in the framework of shear deformation theories (STs). Different transverse shear stress functions, such as the parabolic transverse shear stress (Par-TSS), cosine-hyperbolic shear stress (Cos-Hyp-TSS), and uniform shear stress (U-TSS) functions are used in the analysis part. After validation of the formulation with respect to the existing literature, several parametric studies are carried out to investigate the influences of CNT patterns, number and arrangement of the layers on the uniform buckling temperature (UBT) using various transverse shear stress functions, and classical shell theory (CT).

The mechanical response of materials such as fiber and particle composites, rocks, concrete, and granular materials, can be profoundly influenced by the existence of voids. The aim of the present work is to study the dynamic behavior of hexagonal microstructured composites with voids by using a discrete model and homogenizing materials, such as micropolar and classical Cauchy continua. Three kinds of hexagonal microstructures, named regular, hourglass, and skew, are considered with different length scales. The analysis of free vibration of a panel described as a discrete system, as a classical and as a micropolar continuum, and the comparison of results in terms of natural frequencies and modes show the advantage of the micropolar continuum in describing dynamic characteristics of orthotropic composites (i.e., regular and hourglass microstructures) with respect to the Cauchy continuum, which gives a higher error in frequency evaluations for all three hexagonal microstructured materials. Moreover, the micropolar model also satisfactorily predicts the behavior of skewed microstructured composites. Another advantage shown here by the micropolar continuum is that, like the discrete model, this continuum is able to present the scale effect of microstructures, while maintaining all the advantages of the field description. The effect of void size is also investigated and the results show that the first six frequencies of the current problem decrease by increasing in void size.

It is known that the presence of microstructures in solids such as joints and interfaces has an essential influence on the studies of the development of advanced materials, rock mechanics, civil engineering, and so on. However, microstructures are often neglected in the classical local (Cauchy) continuum model, resulting in inaccurate descriptions of the behavior of microstructured materials. In this work, in order to show the impact of microstructures, an implicit ‘non-local’ model, i.e., micropolar continuum (Cosserat), is used to numerically investigate the effects of direction and scale of microstructures on the tension problem of a composite plate with a circular hole. The results show that distributions of field variables (such as displacements and stresses) have an obvious directionality with respect to the microstructures’ direction. As the scale of microstructures increases, such a direction effect becomes more evident. Unlike the isotropic material where stress concentration occurs at the vertex of the hole and the stress concentration factor is close to 3, for the microstructured composite, the stress concentration can be observed at any location depending on the microstructures’ directions, and the concentration factor can exceed 3 to a maximum close to 9 as the increasing scale of microstructures. In addition, differences in the mechanical behavior between Cosserat and Cauchy models can be also observed; such differences are more evident for the material showing a pronounced orthotropic nature.

High performance thermosetting resins are targeted in many exigent applications, such as aerospace and marine fields, for the development of lightweight structural composites. Till now, these industries only rely on petroleum-based materials for their supposedly better performances. However, the latest developments in the field suggest otherwise. In fact, many reports confirmed that sustainable and ecofriendly thermosetting polymers can display similar or even better performances. Additionally, exploring alternative renewable feedstock’s to meet the ever increasing demands of these industries is an essential step towards sustainable development. Aiming to unravel the potential of these materials, the present review summarizes the most relevant chemical routes allowing the preparation of fully or partially bio-based thermosetting resins. Meanwhile, the overall performances of these exceptional materials are also compared with their petroleum-based counterparts.

The current work presents a material characterization for bio composites used for automotive industrial applications. The mechanical properties are utilized in the design of components of an electric micro-car for the green innovation of automotive industry. The composite material is homogenized as equivalent orthotropic medium and its mechanical properties verified through laboratory testing. Finally a finite element model of some composite parts are analyzed by considering classical materials and innovative bio-composites. The comparison shows the valuable structural performances of the natural-based composites with respect to classical ones both in terms of cost, economical impact and mechanical performances.

Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and updated numerical calculations to be performed using improved theories at design time to reliably apply such elements. The main goal of this study is to model, mathematically and within an analytical solution, the thermoelastic stability problem of composite cylinders reinforced by carbon nanotubes (CNTs) under a uniform thermal loading within the shear deformation theory (ST). The influence of transverse shear deformations is considered when forming the fundamental relations of CNT-patterned cylindrical shells and the basic partial differential equations (PDEs) are derived within the modified Donnell-type shell theory. The PDEs are solved by the Galerkin method, and the formula is found for the eigenvalue (critical temperature) of the functionally graded nanocomposite cylindrical shells. The influences of CNT patterns, volume fraction, and geometric parameters on the critical temperature within the ST are estimated by comparing the results within classical theory (CT).

The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach approximating functions at collocation nodes are obtained by using radial basis functions which depend on shape parameters. The selection of such parameters can strongly influences the accuracy of the numerical technique. Therefore the authors are presenting some numerical benchmarks which involve the solution of nanoplates by employing an optimization approach for the evaluation of the undetermined shape parameters. Stability is discussed as well as numerical reliability against solutions taken for the existing literature.

Exposure to ionizing radiation (IR) during diagnostic medical procedures brings certain risks, especially when experiencing recurrent exposures. The fabrication of nano-based composites, doped with different nanoparticles, have been suggested as effective shielding materials to replace conventional lead-based ones in material sciences and nanotechnology. In this study, commercially available fabrics, used to produce scrubs and gowns for clinical staff, are modified utilizing graphene oxide (GO) nanoparticles using a layer-by-layer (LBL) technique. GO was obtained from graphite through environmentally friendly technology by using a modified–improved Hummers’ method without NaNO3. Lightweight, flexible, air- and water-permeable shielding materials are produced that are wearable in all-day clinical practice. The nanoparticles are kept to a minimum at 1 wt%; however, utilizing the LBL technique they are distributed evenly along the fibers of the fabrics to achieve as much shielding effect as possible. The evaluation of samples is accomplished by simulating real-time routine clinical procedures and the radiographic programs and devices used daily. The GO-coated nanocomposite fabrics demonstrated promising results for X-ray shielding.

Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CNT-reinforced composites, and their interaction with the ground, there is a need to renew the dynamic response calculations under moving pressures and to create new mathematical solution methods during their design. The aim of this study was to analyze the influences of elastic foundations (EFs) and material gradient on the dynamic response of infinitely long carbon nanotube (CNT)-based polymer pipes under combined static and moving pressures. The CNT-based polymer pipes resting on the EFs were exposed to the axial and moving pressures. The uniform and heterogeneous reinforcement distributions of CNTs, which varied linearly throughout the thickness of polymer pipes, were considered. After setting the problem, the fundamental equations derived to find new analytical expressions for dynamic coefficients and critical velocity, which are dynamic characteristics of cylindrical pipes reinforced by the uniform and linear distributions of CNTs, were solved in the framework of the vibration theory. Finally, numerical computations were performed to examine the effects of EFs on the critical parameters depending on the characteristics of the pipes, the speed of moving pressures, the shape of the distribution of CNTs, and the change in volume fractions.

It has been demonstrated that materials with microstructure, such as particle composites, show a peculiar mechanical behavior when discontinuities and heterogeneities are present. The use of non-local theories to solve this challenge, while preserving memory of the microstructure, particularly of internal length, is a challenging option. In the present work, composite materials made of rectangular rigid blocks and elastic interfaces are studied using a Cosserat formulation. Such materials are subjected to dynamic shear loads. For anisotropic media, the relative rotation between the local rigid rotation and the microrotation, which corresponds to the skewsymmetric part of strain, is crucial. The benefits of micropolar modeling are demonstrated, particularly for two orthotropic textures of different sizes.

The main purpose of the study is to investigate the vibration behaviors of carbon nanotube (CNT) patterned double-curved construction elements using the shear deformation theory (SDT). After the visual and mathematical models of CNT patterned double-curved construction elements are created, the large amplitude stress–strain relationships and basic dynamic equations are derived using the first order shear deformation theory (FSDT). Then, using the Galerkin method, the problem is reduced to the nonlinear vibration of nanocomposite continuous systems with quadratic and cubic nonlinearities. Applying the Grigolyuk method to the obtained nonlinear differential equation, large-amplitude frequency-amplitude dependence is obtained. The expressions for nonlinear frequencies of homogenous and inhomogeneous nanocomposite construction members such as plates, panels, spherical and hyperbolic-paraboloid (hypar) shells in the framework of FSDT are found in special cases. The accuracy of the results of the current study has been confirmed by comparing them with the reliable results reported in the literature. Original analyses are carried out to examine the effects of nonlinearity, CNT patterns and volume fraction changes on frequencies in the framework of shear deformation and classical shell theories.

This work aims to present the dynamic character of microstructured materials made of hexagonal-shape particles interacting with elastic interfaces. Several hexagonal shapes are analyzed to underline the different constitutive behavior of each texture. The mechanical behavior at the macro scale is analyzed by considering a discrete model assumed as a benchmark of the problem and it is compared to a homogenized micropolar model as well as a classical one. The advantages of the micropolar description with respect to the classical one are highlighted when internal lengths and anisotropies of microstuctured materials are taken into consideration. Comparisons are presented in terms of natural frequencies and modes of vibrations.

The authors are presenting a novel formulation based on the Differential Quadrature (DQ) method which is used to approximate derivatives and integrals. The resulting scheme has been termed strong and weak form finite elements (SFEM or WFEM), according to the numerical scheme employed in the computation. Such numerical methods are applied to solve some structural problems related to the mechanical behavior of plates and shells, made of isotropic or composite materials. The main differences between these two approaches rely on the initial formulation – which is strong or weak (variational) – and the implementation of the boundary conditions, that for the former include the continuity of stresses and displacements, whereas in the latter can consider the continuity of the displacements or both. The two methodologies consider also a mapping technique to transform an element of general shape described in Cartesian coordinates into the same element in the computational space. Such technique can be implemented by employing the classic Lagrangian-shaped elements with a fixed number of nodes along the element edges or blending functions which allow an “exact mapping” of the element. In particular, the authors are employing NURBS (Not-Uniform Rational B-Splines) for such nonlinear mapping in order to use the “exact” shape of CAD designs.

Nanoplates have been extensively utilized in the recent years for applications in nanoengineering as sensors and actuators. Due to their operative nanoscale, the mechanical behavior of such structures might also be influenced by inter-atomic material interactions. For these reasons, nonlocal models are usually introduced for studying their mechanical behavior. Sensor technology of plate structures should be formulated with coupled mechanics where elastic, magnetic and electric fields interact among themselves. In addition, the effect of hygro-thermal environments are also considered since their presence might effect the nanoplate behavior. In this work a trigonometric approach is developed for investigating smart composite nanoplates using a strain gradient nonlocal procedure. Convergence of the present method is also reported in terms of displacements and electro-magnetic potentials. Results agree well with the literature and open novel applications in this field for further developments.

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

Authors of the present Special Issue are gratefully acknowledged for writing papers of very high standard [...]

The macroscopic behavior of materials with anisotropic microstructure described as micropolar continua is investigated in the present work. Micropolar continua are characterized by a higher number of kinematical and dynamical descriptors than classical continua and related stress and strain measures, namely the micro-rotation gradient (curvature) and the relative rotation with their work conjugated counterparts, the micro-couple, and the skew-symmetric part of the stress, respectively. The presence of such enriched strain and stress fields can be detected especially when concentrated forces and/or geometric discontinuities are present. The effectiveness of the micropolar model to represent the mechanical behavior of materials made of particles of prominent size has been widely proved in the literature, in this paper we focus on the capability of this model to grossly capture the behavior of anisotropic solids under concentrated loads for which the relative strain, that is a peculiar strain measure of the micropolar model, can have a salient role. The effect of material anisotropy in the load diffusion has been investigated and highlighted with the aid of numerical parametric analyses, performed for two dimensional bodies with increasing degrees of anisotropy using a finite element approach specifically conceived for micropolar media with quadratic elements implemented within Comsol Multiphysics© framework. The present studied cases show that a significant diffusion and redistribution of the load is due to an increasing in the level of material anisotropy.

Recent progresses in nanotechnology have clearly shown that the incorporation of nanomaterials within concrete elements leads to a sensible increase in strength and toughness, especially if used in combination with randomly distributed short fiber reinforcements, as for ultra high-performance fiber-reinforced concrete (UHPFRC). Current damage models often are not able to accurately predict the development of diffuse micro/macro-crack patterns which are typical for such concrete structures. In this work, a diffuse cohesive interface approach is proposed to predict the structural response of UHPFRC structures enhanced with embedded nanomaterials. According to this approach, all the internal mesh boundaries are regarded as potential crack segments, modeled as cohesive interfaces equipped with a mixed-mode traction-separation law suitably calibrated to account for the toughening effect of nano-reinforcements. The proposed fracture model has been firstly validated by comparing the failure simulation results of UHPFRC specimens containing different fractions of graphite nanoplatelets with the available experimental data. Subsequently, such a model, combined with an embedded truss model to simulate the concrete/steel rebars interaction, has been used for predicting the load-carrying capacity of steel bar-reinforced UHPFRC elements enhanced with nanoplatelets. The numerical outcomes have shown the reliability of the proposed model, also highlighting the role of the nano-reinforcement in the crack width control.

The current work presents a study on hollow cylinder composite beams, since hollow cylinder cross-sections are one of the principal geometry in many engineering fields. In particular, the present study considers the use of these profiles for scaffold design in offshore engineering. Composite beams cannot be treated as isotropic ones due to couplings mainly present among traction, torsion, bending and shear coefficients. This research aims to present a simple approach to study composite beams as they behave like isotropic ones by removing most complexities related to composite material design (e.g., avoid the use of 2D and 3D finite element modeling). The work aims to obtain the stiffness matrix of the equivalent beam through an analytical approach which is valid for most of the laminated composite configurations present in engineering applications. The 3D Euler–Bernoulli beam theory is considered for obtaining the correspondent isotropic elastic coefficients. The outcomes show that negligible errors occur for some equivalent composite configurations by allowing designers to continue using commercial finite element codes that implement the classical isotropic beam model.

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials.

The present paper talks about the free vibration analysis of simply supported Single- and Double-Walled Carbon Nanotubes (SWCNTs and DWCNTs). Refined 2D Generalized Differential Quadrature (GDQ) shell methods and an exact 3D shell model are compared. A continuum approach (based on an elastic three-dimensional shell model) is used for natural frequency investigation of SWCNTs and DWCNTs. SWCNTs are defined as isotropic cylinders with an equivalent thickness and Young modulus. DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of van der Waals interactions. Layer wise approaches are mandatory for the analysis of van der Waals forces in DWCNTs. The effect of van der Waals interaction between the two cylinders is shown for different DWCNT lengths, diameters and vibration modes. The accuracy of beam models and classical 2D shell models in the free vibration analysis of SWCNTs and DWCNTs is also investigated.

Coal contains a large number of fractures, whose characteristics are difficult to describe in detail, while their spatial distribution patterns may follow some macroscopic statistical laws. In this paper, several fracture geometric parameters (FGPs) were used to describe a fracture, and the coal seam was represented by a two-dimensional stochastic fracture network (SFN) which was generated and processed through a series of methods in MATLAB. Then, the processed SFN image was able to be imported into COMSOL Multiphysics and converted to a computational domain through the image function. In this way, the influences of different FGPs and their distribution patterns on the permeability of the coal seam were studied, and a finite element model to investigate gas flow properties in the coal seam was carried out. The results show that the permeability of the coal seam increased with the rising of fracture density, length, aperture, and with the decrease of the angle between the fracture orientation and the gas pressure gradient. It has also been found that large-sized fractures have a more significant contribution to coal reservoir permeability. Additionally, a numerical simulation of CBM extraction was carried out to show the potential of the proposed approach in the application of tackling practical engineering problems. According to the results, not only the connectivity of fractures but also variations of gas pressure and velocity can be displayed explicitly, which is consistent well with the actual situation.

The Strong Formulation Finite Element Method (SFEM) is a numerical solution technique for solving arbitrarily shaped structural systems. This method uses a hybrid scheme given by the Differential Quadrature Method (DQM) and the Finite Element Method (FEM). The SFEM takes the best from DQM and FEM giving a highly accurate strong formulation based technique with the adaptability of finite elements. The present study investigates the stability and accuracy of SFEM when applied to 1D and 2D structural components, such as rods, beams, membranes and plates using analytical and semi-analytical well-known solutions. The numerical results show that the present approach can be very accurate using a small number of grid points and elements, when it is compared to standard FEM.

The aim of the present work was to investigate the mechanical behavior of orthotropic composites, such as masonry assemblies, subjected to localized loads described as micropolar materials. Micropolar models are known to be effective in modeling the actual behavior of microstructured solids in the presence of localized loads or geometrical discontinuities. This is due to the introduction of an additional degree of freedom (the micro-rotation) in the kinematic model, if compared to the classical continuum and the related strain and stress measures. In particular, it was shown in the literature that brick/block masonry can be satisfactorily modeled as a micropolar continuum, and here it is assumed as a reference orthotropic composite material. The in-plane elastic response of panels made of orthotropic arrangements of bricks of different sizes is analyzed herein. Numerical simulations are provided by comparing weak and strong finite element formulations. The scale effect is investigated, as well as the significant role played by the relative rotation, which is a peculiar strain measure of micropolar continua related to the non-symmetry of strain and work-conjugated stress. In particular, the anisotropic effects accounting for the micropolar moduli, related to the variation of microstructure internal sizes, are highlighted.

As required by regulations, Finite Element Analyses (FEA) can be used to investigate the behavior of joints which might be complex to design due to the presence of geometrical and material discontinuities. The static behavior of such problems is mesh dependent, thus these results must be calibrated by using laboratory tests or reference data. Once the Finite Element (FE) model is correctly setup, the same settings can be used to study joints for which no reference is available. The present work analyzes the static strength of reinforced T-joints and sheds light on the following aspects: shell elements are a valid alternative to solid modeling; the best combination of element type and mesh density for several configurations is shown; the ultimate static strength of joints can be predicted, as well as when mechanical properties are roughly introduced for some FE topologies. The increase in strength of 12 unreinforced and reinforced (with collar or doubler plate) T-joints subjected to axial brace loading is studied. The present studies are compared with the literature and practical remarks are given in the conclusion section.

Jackets are the most common structures in the Adriatic Sea for extracting natural gas. These structural typologies are suitable for relative low water depths and flat sandy sea floors. Most of them have been built in the last 50 years. When the underground source finishes, these structures should be moved to another location or removed if they have reached their design life. Nevertheless, another solution might be considered: change the future working life of these platforms by involving renewable energy and transforming them into offshore wind towers. The present research proposal aims to investigate the possibility of converting actual structures for gas extraction into offshore platforms for wind turbine towers. This simplified analysis is useful for initial design phases and tender design, or generally when available information is limited. The model proposed is a new simplified tool used to study the structural analysis of the jacket structure, developed and summarized in 10 steps, firstly adopted to study the behavior of the oil and gas structure and then for the retrofitted wind tower configuration.

The present work considers a computational study on laminated composite plates by using a linear theory for moderately thick structures. The present problem is solved numerically because analytical solutions cannot be found for such plates when lamination schemes are general and when all the stiffness constants are activated at the constitutive level. Strong and weak formulations are used to solve the present problem and several comparisons are given. The strong form is dealt with using the so-called Strong Formulation Finite Element Method (SFEM) and the weak form is solved using commercial Finite Element (FE) packages. Both techniques are based on the domain decomposition technique according to geometric discontinuities. The SFEM solves the strong form inside each element and needs the implementation of kinematic and static inter-element conditions, whereas the FE solves the weak form and the continuity conditions among the elements are given in terms of displacements only. The results are reported in graphical form in terms of the first three natural frequencies. The accuracy and stability of SFEM and FE are thoroughly discussed.

A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami’s function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software.

The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.