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This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

Fragility and the presence of a poisonous substance (lead) are the two major issues with traditional piezoceramics and structures that include them. This work suggests an active structure that is lightweight, flexible, and eco-friendly such that a polymeric foam plate is sandwiched between two piezoelectrically activated nanocomposite layers. A combination of a polymer and piezoelectric nanowires (NWs) of zinc oxide (ZnO) is used in the nanocomposite layers. For the proposed active structure, two types of void distributions and functionally graded (FG) distributions of the NWs have been assumed in each corresponding layer. The buckling characterization of the proposed eco-friendly active sandwich plate (EFASP) under biaxial mechanical loads has been conducted using an extended meshless solution based on a third-order theory. An in-depth parametric study on the EFASPs' biaxial buckling resistance revealed that increasing NW content considerably enhances buckling resistance, with this enhancement strongly reliant on the distribution profile of the NWs. Moreover, it was observed that embedding voids in the substrate layer can lead to a large structural weight reduction while only marginally lowering the buckling performance of suggested EFASPs. [ABSTRACT FROM AUTHOR]

An analytical investigation on buckling behavior of thick functionally graded shells with nearly cylindrical shapes and porosities under mechanical loads is presented in this paper. Loading conditions considered are that axial compressive load, lateral pressure and combined mechanical loads in thermal environments. Porosities are evenly or unevenly distributed within the shell. Governing equations are established based on a higher order shear deformation theory taking into account interaction between the shell and surrounding elastic medium. Two-term form of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive closed-form results of buckling loads. [ABSTRACT FROM AUTHOR]

Thermo-mechanical buckling analysis of laminated spherical shells bounded with the piezoelectric actuator layers has been presented in this article. Applied loads are a combination of thermal, mechanical and electrical loads. Derivations of equilibrium and stability equations are based on the classical laminated shell theory and Sanders's nonlinear kinematic relations. The analysis employs the Galerkin method to achieve closed-form formulas for the buckling loads of the piezo-laminated spherical shell. Effects of applied actuator voltage, voltage sign, geometrical parameters of the shell (length, diameter, and thickness), material properties, and layout of composite layers on the buckling strength are investigated. Analytical solutions are obtained for three types of thermal loading, and one thermo-mechanical loading condition. The results are validated by the known data in the literature. [ABSTRACT FROM AUTHOR]

The high temperature environment makes the buckling of composite laminated plate happen earlier. Further weight savings can be achieved once the plate has a favorable postbuckling stiffness. This study aims to address this issue by developing a ROM-driven lamination optimization to maximize the buckling and postbuckling performance of compressed plates under initial temperature field. The reduced-order model(ROM) constructed using the improved Koiter theory is reformulated to be suitable for thermal-mechanical buckling problems. A linear subspace of the force space is represented to be the span of the mechanical load, the thermal load and a set of predefined perturbation loads. The thermal load related to the initial temperature field is constant during the increase of in-plane compressive load. An independently additional degree of freedom corresponding to the thermal load is implemented into the construction of the reduced-order model. The buckling and postbuckling performance can be extracted from the solution of reduced-order model, and then subsequently selected as inputs to achieve the optimal laminate. The main novelty of this work is to achieve the thermal-mechanical buckling and postbuckling optimization, benefitting from the highly efficient single run of thermoelastic geometrically nonlinear analysis. Various numerical examples have been selected to validate the performance of the proposed method, considering the influences of length-to-width ratio, α1/α2, ply number and nonuniform temperature field. [ABSTRACT FROM AUTHOR]

This article presents the axial buckling analysis of polymer-CNT-fiber nanocomposite annular system (PCFCAS) resting on Winkler-Pasternak substrates under various temperature gradients. With the aid of Hamilton's principle and the higher-order shear deformation theory (HSDT), the governing equations are derived. For developing an accurate solution approach, a generalized differential quadrature method (GDQM) is finally employed. Various geometrically parameters are taken into account to investigate the axial buckling analysis of the PCFCAS subjected to a high-temperature environment. Finally, the presented results demonstrate that different parameters such as outer to inner radius ratio (Ro/Ri), patterns of temperature increase, volume fraction and orientation angle of the carbon fibers (CFs), weight fraction and distribution patterns of carbon-nanotubes (CNTs), and other geometrical and physical parameters have an important role in the axial buckling load of the current structure. The fundamental and golden results of this paper could be that when the PCFCAS is in an environment with sinusoidal, and uniform temperature change, the structure encounters with the highest axial buckling load. In contrast, the lowest buckling load occurs for the uniform temperature change. Also, when the effect of the Winkler and Pasternak foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the axial buckling load of the disk, and this matter is true for all boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear time history response and dynamic-buckling of functionally graded material (FGM) shell structures in thermal environments with temperature-dependent material properties is studied. An implicit conservative/decaying time integration scheme and a curved 8-node degenerated shell element are used for time and spatial discretization respectively. Numerical results show that the developed shell element formulation with the implicit time integration scheme is capable of solving nonlinear dynamic-buckling and large displacement dynamic problems of FGM shells in severe thermal environments. Th influence of material constituents, power-law indexes and thermo-mechanical loadings on the transient dynamic response and dynamic-buckling phenomena are considered. [ABSTRACT FROM AUTHOR]

This article aims to investigate the post-buckling behavior of plates and cylindrical panels made of functionally graded materials (FGM) and carbon-nanotubes reinforced composites (FG-CNTRC) under mechanical loads. Unlike the other high order shear deformation theories, the proposed formulation is elaborated within a double directors finite shell element which allows a parabolic distribution of the transverse shear strains, guarantee the zero condition of the transverse shear stresses on the extreme surfaces of the shell and introduces large deformations and finite rotations through a non-linear framework. Newton-Raphson with arc length control solution strategy is used to resolve the equilibrium paths. A power-law distribution and the extended rule of mixture are used to determine the effective material properties of functionally graded materials and carbon-nanotubes reinforced composites. The effectiveness and the accuracy of the formulation is checked via several comparisons with published results in the literature. Especially, some complex post-buckling curves of FGM and FG-CNTRC curved panels and plates with different mechanical loadings are provided that could be useful for future references. The effects of various parameters are also reported. [ABSTRACT FROM AUTHOR]

In this paper, the mechanics of shear deformable micro beams is investigated via finite element analysis, and a machine learning technique (Deep Learning Neural Network (DLNN)). DLNN is provided for the first time to accurately model and predict this behavior. Using the Finite Element Method (FEM), the obtained coupled equations of motion for shear deformable micro-scale beams are solved using a combination of Timoshenko beam theory and the modified couple stress theory (MCST). The results are compared with literature for each analysis to show the accuracy and the proposed finite element model. After presenting the mechanical model, by using Finite Element Analysis (FEA), a deep learning neural network model is developed for small-scale structures and the capability of this model in predicting different mechanical behavior under thermo-mechanical loading is investigated. It is shown that the presented model has great accuracy in predicting both static and dynamic behavior of small-scale structures with a significant reduction in the computational cost. The application of DLNN for modeling the machines of small- scale structures is a step forward for predicting the behavior of Nano/Micro Electro Mechanical Systems (NEMS/MEMS). [ABSTRACT FROM AUTHOR]

Present investigation deals with the snap-through phenomenon in a thermally pre-buckled or post-buckled reinforced composites beam. Composite laminated beam is reinforced with graphene platelets (GPLs) where the weight fraction of GPLs may vary in each layer. The governing equations of the beam are obtained by means of the first order shear deformation beam theory and the von-Kármán type of kinematic assumptions. The conventional Ritz method with Chebyshev polynomials is used to discretize the governing equations and establish a set of non-linear equations dealing with the response of a beam under the action of thermal and mechanical loads. Furthermore, the case of uniform temperature elevation in the beam and uniform lateral pressure is considered. At first, the response of the beam under uniform temperature elevation is obtained. Depending on the magnitude of temperature rise, beam may remain flat or undergo thermal post-buckling. Using the displacement control strategy, the non-linear eigenvalue problem is solved. After that the response of the pre-buckled or post-buckled beam subjected to uniform lateral pressure in large deflection is evaluated. Due to the possibility of snap-through phenomenon, the cylindrical arch-length technique is employed. At first, two comparison studies are provided to assure the validity and efficiency of the developed formulation. After that, novel numerical results are given to discuss the effects of temperature change, weight fraction of GPLs, distribution pattern of GPLs and boundary conditions. It is shown that the limit loads of the snapping phenomenon and the intensity of the snap-through phenomenon are highly dependent to the mentioned factors. [ABSTRACT FROM AUTHOR]