• Steel and Composite Structures
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• 제41권6호
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• pp.899-910
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• 2021

A 4-unknown shear deformation theory is applied to investigate the vibration of functionally graded plates under thermal environment. The plate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the plate thickness. Three types of thermal loadings, uniform, linear and nonlinear temperature rises along the plate thickness are taken into account. The present theory contains four unknown functions as against five or more in other higher order shear deformation theories. The through-the-thickness distributions of transverse shear stresses of the plate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem dependent shear correction factor. Analytical solutions for the free vibration analysis are derived based on Fourier series that satisfy the boundary conditions (Navier's method). Benchmark solutions are firstly considered to evaluate the accuracy of the proposed model. Comparisons with the solutions available in literature revealed the good capabilities of the present model for the simulations of vibration responses of FG plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.

• Steel and Composite Structures
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• 제43권6호
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

• 한국소프트웨어감정평가학회 논문지
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• 제16권2호
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• pp.135-142
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• 2020

본 논문에서는 RGB 영상에서 홍채 검출 방법에 관하여 기술하였다. 기존의 홍채 검출 방법은 대부분 적외선 영상을 대상으로 하고 있어, 다양한 응용을 위해서는 RGB 영상의 홍채 검출 기술이 요구된다. 제안된 홍채 검출 방법은 i) 입력 영상에서 원형 허프 변환을 사용한 홍채 후보 영역 검출, ii) 딥러닝 기반의 동공 중심점 검출, iii) 동공 중심점을 이용한 홍채 영역 선택, iv) 선택된 홍채 영역 보정 과정으로 구성된다. 홍채 후보 영역은 허프 공간을 생성한 후 중심점 후보의 교차 개수가 많은 순으로 검출하며, 후보 영역 중 홍채는 검출된 동공의 중심점을 기준으로 선택한다. 그리고, 홍채의 모양이 왜곡되어 오차가 발생하는 것을 보완하기 위해 검출된 홍채 중심을 기준으로 새로운 경계점을 찾아 보정하는 방법을 사용하였다. 또한, 실험을 통하여 제안된 방법이 기존 원형 허프 변환 방법 대비 약 27.4% 향상된 정확도를 갖는 것을 확인하였다.

• Steel and Composite Structures
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• 제46권4호
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• pp.471-483
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• 2023

This paper presents an analytical hyperbolic theory based on the refined shear deformation theory for mechanical stability analysis of the simply supported advanced composites plates (exponentially, sigmoidal and power-law graded) under triangular, trapezoidal and uniform uniaxial and biaxial loading. The developed model ensures the boundary condition of the zero transverse stresses at the top and bottom surfaces without using the correction factor as first order shear deformation theory. The mathematical formulation of displacement contains only four unknowns in which the transverse deflection is divided to shear and bending components. The current study includes the effect of the geometric imperfection of the material. The modeling of the micro-void presence in the structure is based on the both true and apparent density formulas in which the porosity will be dense in the mid-plane and zero in the upper and lower surfaces (free surface) according to a logarithmic function. The analytical solutions of the uniaxial and biaxial critical buckling load are determined by solving the differential equilibrium equations of the system with the help of the Navier's method. The correctness and the effectiveness of the proposed HyRPT is confirmed by comparing the results with those found in the open literature which shows the high performance of this model to predict the stability characteristics of the FG structures employed in various fields. Several parametric analyses are performed to extract the most influenced parameters on the mechanical stability of this type of advanced composites plates.

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.291-309
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• 2023

This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C⁰ and C¹ continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.

• Steel and Composite Structures
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• 제46권3호
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• pp.367-383
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• 2023

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

• Geomechanics and Engineering
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• 제34권3호
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• pp.233-250
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• 2023

This paper investigates the flexural analysis of isotropic, transversely isotropic, and laminated composite plates using a new higher-order normal and shear deformation theory. In the present theory, only five unknown functions are involved compared to six or more unknowns used in the other similar theories. The developed theory does not need a shear correction factor. It can satisfy the zero traction boundary conditions on the top and the bottom surfaces of the plate as well as account for sufficient distribution of the transverse shear strains. The thickness stretching effect is considered in the computation. A simply supported was considered on all edges of the plate. The plate is subjected to uniform and sinusoidal distributed load in the static analysis. Laminated composite, isotropic, and transversely isotropic plates are considered. The governing equations are obtained utilizing the virtual work principle. The differential equations are solved via Navier's procedure. The results obtained from the developed theory are compared with other higher-order theories considered in the previous studies and 3D elasticity solutions. The results showed that the proposed theory accurately and effectively predicts the bidirectional bending responses of laminated composite plates. Several parametric studies are presented to illustrate the various parameters influencing the static response of the laminated composite plates.

• Steel and Composite Structures
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• 제44권5호
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• pp.721-740
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• 2022

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton's principle and solved by means of the Navier's technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

• Structural Engineering and Mechanics
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• 제90권1호
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• pp.83-96
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• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• Structural Engineering and Mechanics
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• 제91권1호
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• pp.1-23
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• 2024

This paper formulates a new integral shear deformation shell theory to investigate the free vibration response of carbon nanotube (CNT) reinforced structures with only four independent variables, unlike existing shell theories, which invariably and implicitly induce a host of unknowns. This approach guarantees traction-free boundary conditions without shear correction factors, using a non-polynomial hyperbolic warping function for transverse shear deformation and stress. By introducing undetermined integral terms, it will be possible to derive the motion equations with a low order of differentiation, which can facilitate a closed-form solution in conjunction with Navier's procedure. The mechanical properties of the CNT reinforcements are modeled to vary smoothly and gradually through the thickness coordinate, exhibiting different distribution patterns. A comparison study is performed to prove the efficacy of the formulated shell theory via obtained results from existing literature. Further numerical investigations are current and comprehensive in detailing the effects of CNT distribution patterns, volume fractions, and geometrical configurations on the fundamental frequencies of CNT-reinforced nanocomposite shells present here. The current shell theory is assumed to serve as a potent conceptual framework for designing reinforced structures and assessing their mechanical behavior.