• Advances in Computational Design
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• v.2 no.3
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.691-729
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• 2018

In this paper the hygro-thermo-mechanical vibration and buckling behavior of embedded FG nano-plates are investigated. The Eringen's and Gurtin-Murdoch theories are applied to study the small scale and surface effects on frequencies and critical buckling loads. The effective material properties are modeled using Mori-Tanaka homogenization scheme. On the base of RPT and HSDPT plate theories, the Hamilton's principle is employed to derive governing equations. Using iterative and GDQ methods the governing equations are solved and the influence of different parameters on natural frequencies and critical buckling loads are studied.

• Coupled systems mechanics
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• v.9 no.2
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• pp.163-182
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• 2020

Coupled thermo-mechanical analysis of reinforced concrete slab at elevated temperatures from a fire accounting for nonlinear thermal parameters is carried out. The main focus of the paper is put on a one-way continuous reinforced concrete slab exposed to fire from the single (bottom) side as the most typical working condition under fire loading. Although contemporary techniques alongside the fire protection measures are in constant development, in most cases it is not possible to avoid the material deterioration particularly nearby the exposed surface from a fire. Thereby the structural fire resistance of reinforced concrete slabs is mostly influenced by a relative distance between reinforcement and the exposed surface. A parametric study with variable concrete cover ranging from 15 mm to 35 mm is performed. As the first part of a one-way coupled thermo-mechanical analysis, transient nonlinear heat transfer analysis is performed by applying the net heat flux on the exposed surface. The solution of proposed heat analysis is obtained at certain time steps of interest by α-method using the explicit Euler time-integration scheme. Spatial discretization is done by the finite element method using a 1D 2-noded truss element with the temperature nodal values as unknowns. The obtained results in terms of temperature field inside the element are compared with available numerical and experimental results. A high level of agreement can be observed, implying the proposed model capable of describing the temperature field during a fire. Accompanying thermal analysis, mechanical analysis is performed in two ways. Firstly, using the guidelines given in Eurocode 2 - Part 1-2 resulting in the fire resistance rating for the aforementioned concrete cover values. The second way is a fully numerical coupled analysis carried out in general-purpose finite element software DIANA FEA. Both approaches indicate structural fire behavior similar to those observed in large-scale fire tests.

• Advances in nano research
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• v.6 no.4
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• pp.377-397
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• 2018

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.746-755
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• 1997

This paper addresses the systematic procedure using sequential approach for the analysis of the coupled thermo-mechanical behavior of a steady rolling tire. Not only the knowledge of mechanical stresses but also of the temperature loading in a rolling tire are very important because material damage and material properties are significantly affected by the temperature. In general, the thermo-mechanical behavior of a pneumatic tire is highly complex transient phenomenon that requires the solution of a dynamic nonlinear coupled themoviscoelasticity problem with heat source resulting from internal dissipation and friction. In this paper, a sequential approach, with effective calculation schemes, to modeling this system is presented in order to predict the temperature distribution with reasonable sccuracies in a steady state rolling tire. This approach has the three major analysis modules-deformation, dissipation, and thermal modules. In the dissipation module, an analytic method for the calculation of the heat source in a rolling tire is established using viscoelastic theory. For the verification of the calculated temperature profiles and rolling resistance at different velocities, they were compared with the measured ones.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.617-639
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• 2016

In this work, an analytical formulation based on both hyperbolic shear deformation theory and stress function, is presented to study the nonlinear post-buckling response of symmetric functionally graded plates supported by elastic foundations and subjected to in-plane compressive, thermal and thermo-mechanical loads. Elastic properties of material are based on sigmoid power law and varying across the thickness of the plate (S-FGM). In the present formulation, Von Karman nonlinearity and initial geometrical imperfection of plate are also taken into account. By utilizing Galerkin procedure, closed-form expressions of buckling loads and post-buckling equilibrium paths for simply supported plates are obtained. The effects of different parameters such as material and geometrical characteristics, temperature, boundary conditions, foundation stiffness and imperfection on the mechanical and thermal buckling and post-buckling loading capacity of the S-FGM plates are investigated.

• Smart Structures and Systems
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• v.9 no.6
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• pp.505-534
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• 2012

The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.45-65
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• 2002

A constitutive model on oorthotropic thermo-elasto-viscoplasticity for fiber-reinforced composite materials Is illustrated, and their thermomechanical responses are predicted with the fully-coupled finite element formulation. The unmixing-mixing scheme can be adopted with the multipartite matrix method as the constitutive model. Basic assumptions based upon the composite micromechanics are postulated, and the strain components of thermal expansion due to temperature change are included In the formulation. Also. more than two sets of mechanical variables, which represent the deformation states of multipartite matrix can be introduced arbitrarily. In particular, the unmixing-mixing scheme can be used with any well-known isotropic viscoplastic theory of the matrix material. The scheme unnecessitates the complex processes for developing an orthotropic viscoplastic theory. The governing equations based on fully-coupled thermomechanics are derived with constitutive arrangement by the unmixing-mixing concept. By considering some auxiliary conditions, the Initial-boundary value problem Is completely set up. As a tool of numerical analyses, the finite element method Is used with isoparametric Interpolation fer the displacement and the temperature fields. The equation of mutton and the energy conservation equation are spatially discretized, and then the time marching techniques such as the Newmark method and the Crank-Nicolson technique are applied. To solve the ultimate nonlinear simultaneous equations, a successive iteration algorithm is constructed with subincrementing technique. As a numerical study, a series of analyses are performed with the main focus on the thermomechanical coupling effect in composite materials. The progress of viscoplastic deformation, the stress-strain relation, and the temperature History are careful1y examined when composite laminates are subjected to repeated cyclic loading.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.131-157
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• 2018

In this study, Eringen nonlocal elasticity theory in conjunction with surface elasticity theory is employed to study nonlinear free vibration behavior of FG nano-plate lying on elastic foundation, on the base of Reddy's plate theory. The material distribution is assumed as a power-law function and effective material properties are modeled using Mori-Tanaka homogenization scheme. Hamilton's principle is implemented to derive the governing equations which solved using DQ method. Finally, the effects of different factors on natural frequencies of the nano-plate under hygrothermal situation and various boundary conditions are studied.