• Steel and Composite Structures
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• 제33권5호
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• pp.663-679
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• 2019

In this work, a simple four-variable trigonometric shear deformation model with undetermined integral terms to consider the influences of transverse shear deformation is applied for the dynamic analysis of anti-symmetric laminated composite and soft core sandwich plates. Unlike the existing higher order theories, the current one contains only four unknowns. The equations of motion are obtained using the principle of virtual work. The analytical solution is determined by solving the eigenvalue problem. The influences of geometric ratio, modular ratio and fibre angle are critically evaluated for different problems of laminated composite and sandwich plates. The eigenfrequencies obtained using the current theory are verified by comparing the results with those of other theories and with the exact elasticity solution, if any.

• Steel and Composite Structures
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• 제25권2호
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.

• 한국항공우주학회지
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• 제47권7호
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• pp.535-540
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• 2019

MDO(Multi-disciplinary Optimization)를 위한 서로 다른 모델 간의 결합은 계산 프레임 워크의 복잡성을 크게 증가시키는 동시에 CPU 시간과 메모리 사용을 증가시킨다. 이러한 어려움을 극복하기 위해 POD(Proper Orthogonal Decomposition)와 RBF(Radial Basis Function)를 사용하여 복합 샌드위치 구조가 항공기 날개 스킨 재료로 사용될 때 복합재와 샌드위치 코어의 두께를 결정하는 최적화 문제의 해를 구했다. POD와 RBF를 사용하여 날개 형상과 하중 데이터에 대한 대리 모델을 만들었으며 대리 모델에 의해 얻어진 목적 함수 및 제약 함수 값을 사용하여 최적해를 구하였다.

• Steel and Composite Structures
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• 제43권1호
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• pp.117-127
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• 2022

This study investigates the wave propagation in porous functionally graded (FG) sandwich plates subjected to hygrothermal environments. A new simple three-unknown first-ordershear deformation theory (FSDT) incorporating an integral term is utilized in this paper. Only three unknowns are used to formulate the governing differential equation by applying the Hamilton principle. The FG layer of the sandwich plate is modeled using the power-law function with evenly distributed porosities to represent the defects of the manufacturing process. The plate is subjected to nonlinear hygrothermal changes across the thickness. The effects of the power-law exponent, core to thickness ratios, porosity volume, and the relations between volume fraction and wave properties of porous FG plate under the hygrothermal environment are investigated. The results showed that the waves' phase velocities increase linearly with the waves number in the FGM plate. The porosity of the FG materials plate has a noticeable impact on the phase velocity when considering the high ratios of the core layer. It has a negligible effect on small core layers. Finally, it is observed that changing temperatures and moistures do not influence the relationship between the power law and the phase velocity.

• Steel and Composite Structures
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• 제41권6호
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Smart Structures and Systems
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• 제20권3호
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• pp.329-342
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• 2017

In this paper, the dispersion characteristics of elastic waves propagation in sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) is investigated based on various high order shear deformation beam theories (HOSDBTs) as well as nonlocal strain gradient theory (NSGT). In order to align CNTs as symmetric and asymmetric in top and bottom face-sheets with respect to neutral geometric axis of the sandwich nano-beam, various patterns are employed in this analysis. The sandwich nano-beam resting on Pasternak foundation is subjected to thermal, magnetic and electrical fields. In order to involve small scale parameter in governing equations, the NSGT is employed for this analysis. The governing equations of motion are derived using Hamilton's principle based on various HSDBTs. Then the governing equations are solved using analytical method. A detailed parametric study is conducted to study the effects of length scale parameter, different HSDBTs, the nonlocal parameter, various aligning of CNTs in thickness direction of face-sheets, different volume fraction of CNTs, foundation stiffness, applied voltage, magnetic intensity field and temperature change on the wave propagation characteristics of sandwich nano-beam. Also cut-off frequency and phase velocity are investigated in detail. According to results obtained, UU and VA patterns have the same cut-off frequency value but AV pattern has the lower value with respect to them.

• Steel and Composite Structures
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• 제36권3호
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• pp.355-367
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• 2020

The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton's principle and solved by Galerkin's approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.

• Steel and Composite Structures
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• 제7권6호
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• pp.457-468
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• 2007

Analytical and experimental investigation on dynamic properties of extra lightweight concrete sandwich beams reinforced with various lay ups of carbon reinforced epoxy polymer composites (CFRP) are discussed. The lightweight concrete used in the core of the sandwich beams was made up of extra lightweight aggregate, Lica. The density of concrete was half of that of the ordinary concrete and its compressive strength was about $100Kg/cm^2$. Two extra lightweight unreinforced (control) beams and six extra lightweight sandwich beams with various lay ups of CFRP were clamped in one end and tested under an impact load. The dimension of the beams without considering any reinforcement was 20 cm ${\times}$ 10 cm ${\times}$ 1.4 m. These were selected to ensure that the effect of shear during the bending test would be minimized. Three other beams, made up of ordinary concrete reinforced with steel bars, were tested in the same conditions. For measuring the damping capacity of sandwich beams three methods, Logarithmic Decrement Analysis (LDA), Hilbert Transform Analysis (HTA) and Moving Block Analysis (MBA) were applied. The first two methods are in time domain and the last one is in frequency domain. A comparison between the damping capacity of the beams obtained from all three methods, shows that the damping capacity of the extra lightweight concrete decreases by adding the composite reinforced layers to the upper and lower sides of the beams, and becomes most similar to the damping of the ordinary beams. Also the results show that the stiffness of the extra lightweight concrete beams increases by adding the composite reinforced layer to their both sides and become similar to the ordinary beams.

• Steel and Composite Structures
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• 제39권5호
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• pp.615-630
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• 2021

The main purpose of the present work was to study the dynamic instability of a three-layered, thick composite sandwich beam with the functionally graded (FG) flexible core subjected to an axial compressive follower force. Flutter instability of a sandwich cantilever beam was analyzed using the high-order theory of sandwich beams, for the first time. The governing equations in general for sandwich beams with an FG core were extracted and could be used for all types of sandwich beams with any types of face sheets and cores. A polynomial function is considered for the vertical distribution of the displacement field in the core layer along the thickness, based on the results of the first Frosting's higher order model. The governing partial differential equations and the equations of boundary conditions of the dynamic system are derived using Hamilton's principle. By applying the boundary conditions and numerical solution methods of squares quadrature, the beam flutter phenomenon is studied. In addition, the effects of different geometrical and material parameters on the flutter threshold were investigated. The results showed that the responses of the dynamic instability of the system were influenced by the follower force, the coefficients of FGs and the geometrical parameters like the core thickness. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory. The results showed that the follower force of the flutter phenomenon threshold for long beams tends to the corresponding results in the Timoshenko beam.

• Geomechanics and Engineering
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• 제32권2호
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.