• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.553-561
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• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.1
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• pp.1-8
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• 2010

The dynamic instability analysis of delaminated composite structures subjected to in-plane pulsating forces is carried out based on the higher order shell theory of Sanders. In the finite element (FE) formulation, the seven degrees of freedom per each node are used with transformations in order to fit the displacement continuity conditions at the delamination region. The boundaries of the instability regions are determined using the method proposed by Bolotin. The numerical results obtained for skew plates and shells are in good agreement with those reported by other investigators. The new results for delaminated skew plate and shell structures in this study mainly show the effect of the interactions between the radius-length ratio and other various parameters, for example, skew angles, delamination size, the fiber angle of layer and location of delamination in the layer direction. The effect of the magnitude of the periodic in-plane load on the instability regions is also investigated.

• Advances in aircraft and spacecraft science
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• v.4 no.5
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

• Advances in nano research
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• v.13 no.1
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• pp.29-45
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• 2022

The optimization for dynamic response associated with a cylindrical shell which is made of laminated composites embedded in a piezoelectric layer which is subjected to temperature rises and is resting on an elastic foundation is investigated for the first time. The first shear order theory (FSDT) is utilized in order to obtain the strain relations of the shell. Then, using the energy method, the equations of motions as well as boundary condition of the problem are attained. The formulation of this study together with the solution procedure which is a numerical solution method, differential quadrature method (DQM) is validated using other researches. This paper presents a thorough study on the parameters which impacts the vibration frequency of the laminated shell. The results of this paper shows that any type of laminated composite shell can reduce the vibration frequency providing that the angle related to layer are higher than 85 degrees. Also, in order to reduce the effect of temperature rises, the laminated composites instead of orthotropic one can be used.

• Steel and Composite Structures
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• v.18 no.1
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Computers and Concrete
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• v.32 no.1
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• pp.61-74
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• 2023

This article investigates the wave propagation analysis of the imperfect functionally graded (FG) sandwich plates based on a novel simple four-variable integral quasi-3D higher-order shear deformation theory (HSDT). The thickness stretching effect is considered in the transverse displacement component. The presented formulation ensures a parabolic variation of the transverse shear stresses with zero-stresses at the top and the bottom surfaces without requiring any shear correction factors. The studied sandwich plates can be used in several sectors as areas of aircraft, construction, naval/marine, aerospace and wind energy systems, the sandwich structure is composed from three layers (two FG face sheets and isotropic core). The material properties in the FG faces sheet are computed according to a modified power law function with considering the porosity which may appear during the manufacturing process in the form of micro-voids in the layer body. The Hamilton principle is utilized to determine the four governing differential equations for wave propagation in FG plates which is reduced in terms of computation time and cost compared to the other conventional quasi-3D models. An eigenvalue equation is formulated for the analytical solution using a generalized displacements' solution form for wave propagation. The effects of porosity, temperature, moisture concentration, core thickness, and the material exponent on the plates' dispersion relations are examined by considering the thickness stretching influence.

• Structural Monitoring and Maintenance
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• v.10 no.4
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• pp.315-337
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• 2023

During the design phase, it is crucial to determine the interface stresses between the reinforcing plate and the concrete base in order to predict plate end separation failures. In this work, a simple theoretical study of interface shear stresses in beams reinforced with P-FGM and E-FGM plates subjected to an arbitrarily positioned point load, or two symmetrical point loads, was presented using the linear elastic theory. The presence of pores in the reinforcing plate distributed in several forms was also taken into account. For this purpose, we analyze the effects of porosity and its distribution shape on the interracial normal and shear stresses of an FGM beam reinforced with an FRP plate under different types of load. Comparisons of the proposed model with existing analytical solutions in the literature confirm the feasibility and accuracy of this new approach. The influence of different parameters on the interfacial behavior of reinforced concrete beams reinforced with functionally graded porous plates is further examined in this parametric study using the proposed model. From the results obtained in this study, we can say that interface stress is significantly affected by several factors, including the pores present in the reinforcing plate and their distribution shape. Additionally, we can conclude from this study that reinforcement systems with composite plates are very effective in improving the flexural response of reinforced RC beams.

• Advances in concrete construction
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• v.9 no.3
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• pp.327-335
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• 2020

Concrete pipes are considered important structures playing integral role in spread of cities besides transportation of gas as well as oil for far distances. Further, concrete structures under seismic load, show behaviors which require to be investigated and improved. Therefore, present research concerns dynamic stress and strain alongside deflection assessment of a concrete pipe carrying water-based nanofluid subjected to seismic loads. This pipe placed in soil is modeled through spring as well as damper. Navier-Stokes equation is utilized in order to gain force created via fluid and, moreover, mixture rule is applied to regard the influences related to nanoparticles. So as to model the structure mathematically, higher order refined shear deformation theory is exercised and with respect to energy method, the motion equations are obtained eventually. The obtained motion equations will be solved with Galerkin and Newmark procedures and consequently, the concrete pipe's dynamic stress, strain as well as deflection can be evaluated. Further, various parameters containing volume percent of nanoparticles, internal fluid, soil foundation, damping and length to diameter proportion of the pipe and their influences upon dynamic stress and strain besides displacement will be analyzed. According to conclusions, increase in volume percent of nanoparticles leads to decrease in dynamic stress, strain as well as displacement of structure.