• Smart Structures and Systems
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• v.19 no.1
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• pp.33-38
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• 2017

This research tries to present a nonlinear thermo-elastic solution for a functionally graded spherical shell subjected to mechanical and thermal loads. Geometric nonlinearity is considered using the Lagrange or finite strain tensor. Non-homogeneous material properties are considered based on a power function. Adomian's decomposition method is used for calculation of nonlinear results. Nonlinear results such as displacement can be evaluated for sphere in terms of different indexes of non-homogeneity. A comprehensive comparison between linear and nonlinear results and evaluation of the percentage of difference between them can be performed in this paper. The obtained results indicate that the improvement of the results due to usage of nonlinear analysis is depending on the non-homogeneous index.

• Steel and Composite Structures
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• v.17 no.5
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• pp.753-776
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• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.

• Structural Engineering and Mechanics
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• v.47 no.1
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• pp.27-44
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• 2013

A finite element computational procedure for the accurate analysis of quasistatic thermorheological complex structures response is developed. The geometrical nonlinearity, arising from large displacements and rotations (but small strains), is accounted for by the total Lagrangian description of motion. The Schapery's nonlinear single-integral viscoelastic constitutive model is modified for a time-stress-temperature-dependent behavior. The nonlinear thermo-viscoelastic constitutive equations are incrementalized leading to a recursive relationship and thereby the resulting finite element equations necessitate data storage from the previous time step only, and not the entire deformation history. The Newton-Raphson iterative scheme is employed to obtain a converged solution for the non-linear finite element equations. The developed numerical model is verified with the previously published works and a good agreement with them is found. The applicability of the developed model is demonstrated by analyzing two examples with different thermal/mechanical loading histories.

• Steel and Composite Structures
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• v.19 no.4
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• pp.1011-1033
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• 2015

In this article, large amplitude bending behaviour of laminated composite flat panel under combined effect of moisture, temperature and mechanical loading is investigated. The laminated composite panel model has been developed mathematically by introducing the geometrical nonlinearity in Green-Lagrange sense in the framework of higher-order shear deformation theory. The present study includes the degraded composite material properties at elevated temperature and moisture concentration. In order to achieve any general case, all the nonlinear higher order terms have been included in the present formulation and the material property variations are introduced through the micromechanical model. The nonlinear governing equation is obtained using the variational principle and discretised using finite element steps. The convergence behaviour of the present numerical model has been checked. The present proposed model has been validated by comparing the responses with those available published results. Some new numerical examples have been solved to show the effect of various parameters on the bending behaviour of laminated composite flat panel under hygro-thermo-mechanical loading.

• International journal of steel structures
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• v.18 no.4
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• pp.1177-1190
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• 2018

This study presents an analytical framework for estimating the thermo-mechanical behavior of a composite beam exposed to fire. The framework involves: a fire simulation from which the evolution of temperature on the structure surface is obtained; data transfer by an interface model, whereby the surface temperature is assigned to the finite element model of the structure for thermo-mechanical analysis; and nonlinear thermo-mechanical analysis for predicting the structural response under high temperatures. We use a plastic-damage model for calculating the response of concrete slabs, and propose a method to determine the stiffness degradation parameter of the plastic-damage model by a nonlinear regression of concrete cylinder test data. To validate simulation results, structural fire experiments have been performed on a real-scale steel-concrete composite beam using the fire load prescribed by ASTM E119 standard fire curve. The calculated evolution of deflection at the center of the beam shows good agreement with experimental results. The local test results as well as the effective plastic strain distribution and section rotation of the composite beam at elevated temperatures are also investigated.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.565-584
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• 2020

The nonlinear thermo-electro-elastic buckling behavior of viscoelastic nanoplates under magnetic field is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory considers the effect of small size, which enables the present model to become effective in the analysis and design of nano-sensors and nano actuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the buckling analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small scale effects, elastomeric medium, magnetic field, temperature effects, the viscidity and aspect ratio of the nanoplate on its nonlinear buckling characteristics. It is explicitly shown that the thermo-electro-elastic nonlinear buckling behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates as fundamental elements in nanoelectromechanical systems.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1061-1064
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• 2006

Optimal design of functionally graded plates is investigated considering stress and critical temperature. Material properties are assumed to be temperature dependent and varied continuously in the thickness direction. The effective material properties are obtained by applying linear rule of mixtures. The 3-D finite element model is adopted using an 18-node solid element to analyze more accurately the variation of material properties and temperature field in the thickness direction. For stress analysis, the tensile stress ratio and compressive stress ratio of the structure under mechanical load are investigated. In the thermo-mechanical buckling analysis, temperature at each node is obtained by solving the steady-state heat transfer problem and Newton-Raphson method is used for material nonlinear analysis. Finally, the optimal design of FGM plates is studied for stress reduction and improving thermo-mechanical buckling behavior, simultaneously.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.4
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• pp.369-376
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• 2016

In this study, a numerical analysis framework for investigating the nonlinear behavior of structures under fire conditions is presented. In particular, analysis procedure combining fire-driven flow simulation and thermo-mechanical analysis is discussed to investigate the mechanical behavior of fire-exposed representative volume structures made of steel and concrete, respectively. First of all, fire-driven flow analysis is conducted using Fire Dynamics Simulator(FDS) in a rectangular parallelepiped domain containing the structure. The FDS simulation yields the time history of temperature on the surface of the structure under fire conditions. Second, mechanical responses of the fire-exposed structure with respect to prescribed uniformly distributed loads are calculated by a coupled thermo-mechanical analysis using the time-varying surface temperature as boundary conditions. Material nonlinearities of steel and concrete have been considered in the thermo-mechanical analysis. A series of numerical results are presented to demonstrate the feasibility of the multiphysics structural fire analysis for investigating the structural behavior under fire conditions.

• Journal of the Microelectronics and Packaging Society
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• v.20 no.2
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• pp.33-38
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• 2013

In this study, both a finite element analysis and an experimental analysis are executed to investigate the mechanical characteristics of dielectric material effects on warpage. Also, viscoelastic material properties are measured by DMA and are considered in warpage simulation. A finite element analysis is done by using both thermal elastic analysis and a thermo-viscoelastic analysis to predict the nonlinear effects. For experimental study, specimens warpage of non-symmetric structure with body size of $22.5{\times}22.5$ mm, $37.5{\times}37.5$ mm and $42.5{\times}42.5$ mm are measured under the reflow temperature condition. From the analysis results, experimental warpage is not similar to FEA results using thermal elastic analysis but similar to FEA results using thermo-viscoelastic analysis. Also, its effect on substrate warpage is increased as core thickness is decreased and body size is getting larger. These FEA and the experimental results show that the nonlinear characteristics of dielectric material play an important role on substrate warpage. Therefore, it is strongly recommended that non-linear behavior characteristics of a dielectric material should be considered to control warpage of FCBGA substrate under conditions of geometry, structure and manufacturing process and so on.