• Steel and Composite Structures
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• v.45 no.3
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• pp.305-330
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• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

• Steel and Composite Structures
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• v.44 no.5
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Steel and Composite Structures
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• v.49 no.4
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• pp.431-440
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• 2023

The functionally graded (FG) porous plates are usually characterized by the non-symmetric elastic modulus distribution through the thickness so that the plate neutral surface does not coincide with the mid-surface. Nevertheless, the conventional analysis models were mostly based on the plate mid-surface so that the accuracy of resulting numerical results is questionable. In this context, this paper presents the neutral surface-based static and free vibration analysis of FG porous plates and investigates the differences between the mid- and neutral surface-based analysis models. The neutral surface-based numerical method is formulated using the (3,3,2) hierarchical model and approximated by the last introduced natural element method (NEM). The volume fractions of metal and ceramic are expressed by the power-law function and the cosine-type porosity distributions are considered. The proposed numerical method is demonstrated through the benchmark experiment, and the differences between two analysis models are parametrically investigated with respect to the thickness-wise material and porosity distributions. It is found from the numerical results that the difference cannot be negligible when the material and porosity distributions are remarkably biased in the thickness direction.

• Tribology and Lubricants
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• v.39 no.5
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• pp.173-182
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• 2023

The composite planetary gear reducer, a power transmission component of armored vehicles, operates at a high torque and is used in severe environments such as mountain, gravel or unpaved roads. Therefore, they must be designed and manufactured to have high durability. To design such a planetary gear reducer, there are numerous specifications to validate, such as selecting the module and the number of teeth of each gear satisfied the requirements, and calculating gear specifications and durability strength. Because planetary gears constitute a combination of several gears, there are many restrictions and interferences in selecting the number of teeth and addendum modification coefficients, and designing the tooth shape. Developing an auto design program is necessary to design various planetary gears more conveniently and quickly. In this study, a planetary gear reducer design software, widely used in various machines and armored vehicles, was developed. This design software can automatically select the number of teeth and modules of the gears, calculate specifications and quickly evaluate its fatigue durability strength and scoring failure according to the planetary gear reducer design theory.

• Steel and Composite Structures
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• v.49 no.3
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• Steel and Composite Structures
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• v.49 no.6
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• pp.603-614
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• 2023

In this paper, frequency analysis of curved functionally graded (FG) nanobeam by consideration of deepness effect has been studied. Differential transform method (DTM) has been used to obtain frequency responses. The nonlocal theory of Eringen has been applied to consider nanoscales. Material properties are supposed to vary in radial direction according to power-law distribution. Differential equations and related boundary conditions have been derived using Hamilton's principle. Finally, by consideration of nonlocal theory, the governing equations have been derived. Natural frequencies have been obtained using semi analytical method (DTM) for different boundary conditions. In order to study the effect of deepness, the deepness term is considered in strain field. The effects of the gradient index, radius of curvature, the aspect ratio, the nonlocal parameter and interaction of aforementioned parameters on frequency value for different boundary conditions such as clamped-clamped (C-C), clamped-hinged (C-H), and clamped-free (C-F) have been investigated. In addition, the obtained results are compared with the results in previous literature in order to validate present study, a good agreement was observed in the present results.

• Steel and Composite Structures
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• v.49 no.6
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• pp.667-684
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• 2023

In the context of finite element method, a computational simulation is presented to study and analyze the dynamic behavior of regularly perforated functionally graded rotating beam for the first time. To investigate the effect of perforation configurations, both regular circular and squared perforation patterns are studied. To explore impacts of graded material distributions, both axial and transverse gradation profiles are considered. The material characteristics of graded materials are assumed to be smoothly and continuously varied through the axial or the thickness direction according the nonlinear power gradation law. A computational finite elements procedure is presented. The accuracy of the numerical procedure is verified and compared. Resonant frequencies, axial displacements as well as internal stress distributions throughout the perforated graded rotating cantilever beam are studied. Effects of material distributions, perforation patterns, as well as the rotating beam speed are investigated. Obtained results proved that the graded material distribution has remarkable effects on the dynamic performance. Additionally, circular perforation pattern produces more softening effect compared with squared perforation configuration thus larger values of axial displacements and maximum principal stresses are detected. Moreover, squared perforation provides smaller values of nondimensional frequency parameters at most of vibration modes compared with circular pattern.

• Steel and Composite Structures
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• v.50 no.1
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• pp.15-24
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• 2024

This research presents dynamical reaction investigation of pore-dependent and nano-thickness beams having functional gradation (FG) constituents exposed to a movable particle. The nano-thickness beam formulation has been appointed with the benefits of refined high orders beam paradigm and nonlocal strain gradient theory (NSGT) comprising two scale moduli entitled nonlocality and strains gradient modulus. The graded pore-dependent constituents have been designed through pore factor based power-law relations comprising pore volumes pursuant to even or uneven pore scattering. Therewith, variable scale modulus has been thought-out until process a more accurate designing of scale effects on graded nano-thickness beams. The motion equations have been appointed to be solved via Ritz method with the benefits of Chebyshev polynomials in cosine form. Also, Laplace transform techniques help Ritz-Chebyshev method to obtain the dynamical response in time domain. All factors such as particle speed, pores and variable scale modulus affect the dynamical response.

• Steel and Composite Structures
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• v.50 no.2
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Advances in Computational Design
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• v.9 no.1
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• pp.39-52
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• 2024

If the governing differential equation arising from engineering problems is treated as an analytic, continuous and derivable function, it can be expanded by one point as a series of finite numbers. For the function to be zero for each value of its domain, the coefficients of each term of the same power must be zero. This results in a recursive relationship which, after applying the natural conditions or the boundary conditions, makes it possible to obtain the values of the derivatives of the function with acceptable accuracy. The elastoplastic analysis of an inhomogeneous thick sphere of metallic materials with linear variation of the modulus of elasticity, yield stress and Poisson's ratio as a function of radius subjected to internal pressure is presented. The Beltrami-Michell equation is established by combining equilibrium, compatibility and constitutive equations. Assuming axisymmetric conditions, the spherical coordinate parameters can be used as principal stress axes. Since there is no analytical solution, the natural boundary conditions are applied and the governing equations are solved using a proposed new method. The maximum effective stress of the von Mises yield criterion occurs at the inner surface; therefore, the negative sign of the linear yield stress gradation parameter should be considered to calculate the optimal yield pressure. The numerical examples are performed and the plots of the numerical results are presented. The validation of the numerical results is observed by modeling the elastoplastic heterogeneous thick sphere as a pressurized multilayer composite reservoir in Abaqus software. The subroutine USDFLD was additionally written to model the continuous gradation of the material.