Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak-and strong-form finite element solutions

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

Special Issue on Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

none2The advancement in manufacturing technology and scientific research have improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity, and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical, and/or mechanical uncertainties in nonconventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for the design of complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural aspects, involving static, dynamic, buckling, and damage/fracturing problems at different scales.Tornabene, Francesco; Dimitri, RossanaTornabene, Francesco; Dimitri, Rossan

The strong formulation finite element method: stability and accuracy

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 former is used for solving the differential equations inside each element and the latter employs the mapping technique to study domains of general shape. A general brief review on the current methodology has been reported in the book [1] and recalled in the works [2,3], where a stress and strain recovery procedure was implemented. The aim of this manuscript is to present a general view of the static and dynamic behaviors of one- and two-dimensional structural components solved by using SFEM. It must be pointed out that SFEM is a generalization of the so-called Generalized Differential Quadrature Finite Element Method (GDQFEM) presented by the authors in some previous papers [4-8]. Particular interest is given to the accuracy, stability and reliability of the SFEM when it is applied to simple problems. Since numerical solutions - of any kind - are always an approximation of physical systems, all the numerical applications are compared to well-known analytical and semi-analytical solutions of one- and two-dimensional systems. Ultimately, this work presents typical aspects of an innovative domain decomposition approach that should be of wide interest to the computational mechanics community

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

In the present manuscript, a Layer-Wise (LW) generalized model is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads. The unknown field variable is modelled employing polynomials of various orders, each of them defined within each layer of the structure. As a particular case of the LW model, an Equivalent Single Layer (ESL) formulation is derived too. Different approaches are outlined for the assessment of external forces, as well as for non-conventional constraints. The doubly-curved shell is composed by superimposed generally anisotropic laminae, each of them characterized by an arbitrary orientation. The fundamental governing equations are derived starting from an orthogonal set of principal coordinates. Furthermore, generalized blending functions account for the distortion of the physical domain. The implementation of the fundamental governing equations is performed by means of the Generalized Differential Quadrature (GDQ) method, whereas the numerical integrations are computed employing the Generalized Integral Quadrature (GIQ) method. In the post-processing phase, an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations. A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes, calculated by the present methodology, have been successfully compared to those ones obtained from refined finite element three-dimensional simulations. Even though the present LW approach accounts for a two-dimensional assessment of the structural problem, it is capable of well predicting the three-dimensional response of structures with different characteristics, taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations

Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory

In this paper, the damped forced vibration of single-walled carbon nanotubes (SWCNTs) is analyzed using a new shear deformation beam theory. The SWCNTs are modeled as a flexible beam on the viscoelastic foundation embedded in the thermal environment and subjected to a transverse dynamic load. The equilibrium equations are formulated by the new shear deformation beam theory which is accompanied with higher-order nonlocal strain gradient theory where the influences of both stress nonlocality and strain gradient size-dependent effects are taken into account. In this new shear deformation beam theory, there is no need to use any shear correction factor and also the number of unknown variables is the only one that is similar to the Euler-Bernoulli beam hypothesis. The governing equations are solved by utilizing an analytical approach by which the maximum dynamic deflection has been obtained with simple boundary conditions. To validate the results of the new proposed beam theory, the results in terms of natural frequencies are compared with the results from an available well-known reference. The effects of nonlocal parameter, half-wave length, damper, temperature and material variations on the dynamic vibration of the nanotubes, are discussed in detail. Keywords: Forced vibration, Single walled carbon nanotube, A new refined beam theory, Higher-order nonlocal strain gradient theory, Dynamic deflectio