Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures

The advancement in manufacturing technology and scientific research has 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 of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing 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 members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales

Higher-order free vibration analysis of porous functionally graded plates

none5siThe present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications.Merdaci S.; Adda H.M.; Hakima B.; Dimitri R.; Tornabene F.Merdaci, S.; Adda, H. M.; Hakima, B.; Dimitri, R.; Tornabene, F

Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications

Quasi-3D beam models for the computation of eigenfrequencies of functionally graded beams with arbitrary boundary conditions

The present article deals with the free vibration analysis of three-dimensional metallic and functionally graded beams with arbitrary boundary conditions. The investigation is carried out by using refined variable-kinematics quasi-3D beam theories hierarchically generated by using the method of power series expansion of displacement components. Each displacement variable, in the displacement field, can be expanded at any desired order independently from the others and regarding to the results accuracy and the computational cost. The weak-form of the governing equations is derived via the Principle of the Virtual Displacements (PVD), while the Ritz method is used as solution technique. Algebraic Ritz functions, orthogonalised by using the Gram–Schmidt process, are employed in the analysis. Convergence and accuracy of the proposed formulation have been thoroughly examined. A comprehensive assessment of the developed beam models, for various boundary conditions, is also provided. The effect of significant parameters such as length-to-thickness ratio (slenderness ratio), volume fraction index and material properties, on the natural frequencies and mode shapes, is discussed

Advanced modelling of multilayered composites and functionally graded structures by means of Unified Formulation

Most of the engineering problems of the last two centuries have been solved thanks to structural models for both beams, and for plates and shells. Classical theories, such as Euler-Bernoulli, Navier and De Saint-Venant for beams, and Kirchhoff-Love and Mindlin-Reissner for plates and shells, permitted to reduce the generic 3-D problem, in onedimensional one for beams and two-dimensional for shells and plates. Refined higher order theories have been proposed in the course of time, as the classical models do not consent to obtain a complete stress/strain field. Carrera Unified Formulation (UF) has been proposed during the last decade, and allows to develop a large number of structural theories with a variable number of main unknowns by means of a compact notation and referring to few fundamental nuclei. This Unified Formulation allows to derive straightforwardly higher-order structural models, for beams, plates and shells. In this framework, this thesis aims to extend the formulation for the analysis of Functionally Graded structures, introducing also the thermo-mechanical problem, in the case of functionally graded beams. Following the Unified Formulation, the generic displacements variables are written in terms of a base functions, which multiplies the unknowns. In the second part of the thesis, new bases functions for shells modelling, accounting for trigonometric approximation of the displacements variables, are considere

Vibration and post-buckling of a functionally graded beam subjected to non-conservative forces

Vibration and post-buckling of beams made from functionally graded materials (FGM) subjected to uniformly and tangentially compressing follower forces are studied in this paper. Based on the accurately and geometrically nonlinear theory for extensible beams, the dynamic governing equations for FGM beams under non-conservative load are formulated. By using a shooting method to solve the non-linearly differential equations numerically, the responses of post-buckling and free vibration in the vicinity of post-buckling configuration are obtained, in which the hinged-fixed boundary conditions of beam are considered. Effects of material gradient parameter on the critical buckling, post-buckling and lower frequencies of the FGM beam are discussed in details

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton’s principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1

Analytical Solution for Bending and Free Vibrations of an Orthotropic Nanoplate based on the New Modified Couple Stress Theory and the Third-order Plate Theory

In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton’s principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1

Multimode Nonlinear Vibration Analysis of Stiffened Functionally Graded Double Curved Shells in a Thermal Environment

The motivation of the current work is to develop a multi-modal analysis of the nonlinear response of stiffened double curved shells made of functionally graded materials under thermal loads. The formulation is based on the first order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain-displacement relationships. The nonlinear equations of motion of stiffened double curved shell based on the extended Sanders’s theory were derived using Galerkin’s method. The resulting system of infinite nonlinear ordinary differential equations, that includes both cubic and quadratic nonlinear terms, was solved using a nonlinear dynamic software XPPAUT to obtain the force-amplitude relationship. The effect of both, longitudinal and transverse stiffeners, was considered using the Lekhnitsky’s technique and the material properties are temperature dependent and vary in the thickness direction according to the linear rule of mixture. In order to obtain accurate natural frequency in thermal environments, critical buckling temperature differences are carried out, resulting in closed form solutions. The effect of temperature’s variation as well as power index, functionally graded stiffeners, geometrical parameters, temperature depended materials and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed. This dissertation showed that the nonlinear study of problems of thin-walled structures with even stiffeners is of paramount importance. It was also found that the difference between single-mode and multi-mode analyses could be very significant for nonlinear problems in a thermal environment. Hence, multimode vibration analysis is necessary for structures of this nature