Static and free vibration analysis of anisotropic doubly-curved shells with general boundary conditions

In the present work, a two-dimensional model based on a higher order Layer-Wise (LW) approach is presented for the static and dynamic analysis of doubly-curved anisotropic shell structures. The Equivalent Single Layer (ESL) methodology is also obtained as particular case of LW. Each lamina of the stacking sequence is modelled as an anisotropic continuum. The fundamental equations account for both surface and concentrated loads, as well as the effects of the Winkler-Pasternak foundation. Moreover, non-conventional boundary conditions are introduced, and the numerical solution is assessed from the Generalized Differential Quadrature (GDQ) method. The proposed formulation is validated with respect to refined three-dimensional simulations, pointing out its accuracy and computational efficiency

Numerical study of the FRP-concrete bond behavior under thermal variations

In a context where daily and seasonal temperature changes or potential fire exposure can affect the mechanical response of structures strengthened with fiber-reinforced polymer (FRP) composites during their life cycle, the present work studies the bond behavior of FRP laminates glued to concrete substrates under a thermal variation. The problem is tackled computationally by means of a contact algorithm capable of handling both the normal and tangential cohesive responses, accounting for the effect of thermal variations on the interfacial strength and softening parameters, which defines the failure surface and post cracking response of the selected specimen. A parametric investigation is performed systematically to check for the effect of thermo-mechanical adhesive and geometrical properties on the debonding load of the FRP-to-concrete structural system. The computa- tional results are successfully validated against some theoretical predictions from literature, which could serve as potential benchmarks for developing further thermomechanical adhesive models, even in a coupled sense, for other reinforcement-to-substrate systems, useful for design purposes in many engineering applications

Thermal Buckling and Vibration Analysis of SMA Hybrid Composite Sandwich Beams

This work studies the buckling and free vibration behavior of Shape Memory Alloy Hybrid Composite (SMAHC) sandwich beams under a thermal environment. The sandwich beams consist of layers reinforced with SMAs and a FGM core, and they are simply supported at both ends. The higher order theory is combined with the Minimum Potential Energy principle or Hamilton principle to derive the governing equations of the thermal buckling and thermal vibration problems, respectively. The material properties of the beam are assumed as temperature-independent (TID) or temperature-dependent (TD). In the last case, two different types of thermal distribution are considered, namely a uniform and a linear distribution. The results based on the proposed formulation are verified against the reference literature, with a very good matching. A parametric study checks for the influence of different effective parameters such as thickness-to-length ratios, volume fraction powers, initial strain, volume fraction of SMA wires, and temperature distribution on the overall mechanical response of the selected structural member, with useful insights from a design standpoint

Thermo-Mechanical Buckling and Non-Linear Free Oscillation of Functionally Graded Fiber-Reinforced Composite Laminated (FG-FRCL) Beams

We investigated the thermal buckling temperature and nonlinear free vibration of functionally graded fiber-reinforced composite laminated (FG-FRCL) beams. The governing nonlinear partial differential equations were derived from the Euler-Bernoulli beam theory, accounting for the von Karman geometrical nonlinearity. Such equations were then reduced to a single equation by neglecting the axial inertia. Thus, the Galerkin method was applied to discretize the governing nonlinear partial differential equation in the form of a nonlinear ordinary differential equation, which was then solved analytically according to the He's variational method. Three different boundary conditions were selected, namely simply, clamped and clamped-free supports. We also investigated the effect of power-index, lay-ups, and uniform temperature rise on the nonlinear natural frequency, phase trajectory and thermal buckling of FG-FRCL beams. The results showed that FG-FRCL beams featured the highest fundamental frequency, whereas composite laminated beams were characterized by the lowest fundamental frequency. Such nonlinear frequencies increase for an increased power index and a decreased temperature. Finally, it was found that FG-FRCL beams with [0/0/0] lay-ups featured the highest nonlinear natural frequency and the highest thermal buckling temperature, followed by [0/90/0] and [90/0/90] lay-ups, while a [90/90/90] lay-up featured the lowest nonlinear natural frequency and critical buckling temperature

Thermomechanical buckling analysis of the e&p-fgm beams integrated by nanocomposite supports immersed in a hygrothermal environment

Due to the widespread use of sandwich structures in many industries and the importance of understanding their mechanical behavior, this paper studies the thermomechanical buckling behavior of sandwich beams with a functionally graded material (FGM) middle layer and two composite external layers. Both composite skins are made of Poly(methyl methacrylate) (PMMA) reinforced by carbon-nano-tubes (CNTs). The properties of the FGM core are predicted through an exponential-law and power-law theory (E&P), whereas an Eshelby–Mori–Tanaka (EMT) formulation is applied to capture the mechanical properties of the external layers. Moreover, different high-order displacement fields are combined with a virtual displacement approach to derive the governing equations of the problem, here solved analytically based on a Navier-type approximation. A parametric study is performed to check for the impact of different core materials and CNT concentrations inside the PMMA on the overall response of beams resting on a Pasternak substrate and subjected to a hygrothermal loading. This means that the sensitivity analysis accounts for different displacement fields, hygrothermal environments, and FGM theories, as a novel aspect of the present work. Our results could be replicated in a computational sense, and could be useful for design purposes in aerospace industries to increase the tolerance of target productions, such as aircraft bodies

Free Vibration Analysis of Thick Annular Functionally Graded Plate Integrated with Piezo-Magneto-Electro-Elastic Layers in a Hygrothermal Environment

The present work aims at investigating the hygrothermal effect on the natural frequencies of functionally graded (FG) annular plates integrated with piezo-magneto-electro-elastic layers resting on a Pasternak elastic foundation. The formulation is based on a layer-wise (LW) theory, where the Hamiltonian principle is used to obtain the governing equation of the problem involving temperature- and moisture-dependent material properties. The differential quadrature method (DQM) is applied here as a numerical strategy to solve the governing equations for different boundary conditions. The material properties of FG annular plates are varied along the thickness based on a power law function. The accuracy of the proposed method is, first, validated for a limit-case example. A sensitivity study of the free vibration response is, thus, performed for different input parameters, such as temperature and moisture variations, elastic foundation, boundary conditions, electric and magnetic potential of piezo-magneto-electro-elastic layers and geometrical ratios, with useful insights from a design standpoint

The Influence of GPL Reinforcements on the Post-Buckling Behavior of FG Porous Rings Subjected to an External Pressure

The work focuses on the post- buckling behavior of functionally graded graphene platelet (FG-GPL)-reinforced porous thick rings with open-cell internal cavities under a uniform external pressure. The generalized rule of mixture and the modified Halpin–Tsai model are here used to evaluate the effective mechanical properties of the ring. Three types of porosity patterns are assumed together with five different GPL distributions as reinforcement across the ring thickness. The theoretical formulation relies on a 2D-plane stress linear elasticity theory and Green strain field in conjunction a virtual work principle to derive the nonlinear governing equations of the postbuckling problem. Unlike the simple ring models, 2D elasticity considers the thickness stretching. The finite element model combined with an iterative Newton–Raphson algorithm is used to obtain the post-buckling path of the ring up to the collapse. A systematic investigation evaluates the effect of the weight fraction of nanofillers, the coefficient of porosity, porosity distribution, and the GPLs distribution on the deep post-buckling path of the ring. Based on the results, it is found that the buckling value and post-buckling strength increase considerably (by approximately 80%) by increasing the weight fraction of the nanofiller of about 1%

Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins

A novel quasi-3D hyperbolic shear deformation theory (QHSDT) with five unknowns is here employed, together with the Hamilton's principle and the modified couple stress theory (MCST) to analyze the vibrational behavior of rectangular micro-scale sandwich plates resting on a visco-Pasternak foundation. The sandwich structure features a Nomex or Glass phenolic honeycomb core, and two composite face sheets reinforced with graphene nanoplatelets (GPLs). The effective properties of both face sheets are evaluated by means of the Halpin-Tsai and extended rule of mixture (ERM) micromechanical schemes. The governing equations of the problem are derived by applying the Hamilton's principle, whose solutions are determined theoretically according to a classical Navier-type procedure. A parametric study checks for the effect of different material properties, length-scale parameters, foundation parameters and geometrical properties of the honeycomb cells, and the reinforcing GPLs, on the vibration response of the layered structure, which can be of great interest for many modern engineering applications and their optimization design