Search Results (67)

An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated. Full article

In the field of crack mechanics, predicting the direction of a crack is important because this will evaluate whether, when the crack propagates, it penetrates into important areas and whether the structure is dangerous or not. This paper will refer to three theories that predict the propagation direction of cracks: a theory of maximum tangential normal stress, a theory of maximum energy release, and a theory of minimum strain energy density. At the same time, the finite element method (FEM)–ANSYS program will be used to calculate stress intensity factors (SIFs), strain energy release rate (J-integral), stress field, displacement near a crack tip, and crack propagation phenomenon based on the above theories. The calculated results were compared with the results in other scientific papers and experimental results. This research used ANSYS program, an experimental method combined with FEM based on the above energy theories to simulate the J-integral, the SIFs, and the crack propagation. The errors of the SIFs of the FGM rectangular plate has a through-thickness center crack of 1.77%, J-integral of 4.49%, and crack propagation angle ${\theta }_c$ of 0.15%. The FEM gave good errors compared to experimental and exact methods. Full article

The thick-walled thickness effect in layered-symmetrical structure is very important for considering the external thermal heating on the surface of functionally graded material (FGM) plates. Dynamic thermal vibration with advanced shear correction on the FGM plates are presented. The third-order shear deformation theory (TSDT) is included to calculate the values of advanced shear correction for the thick plates based on the displacement assumed in the middle symmetry plane. The values of advanced shear correction coefficient are in nonlinear variation with respect to the power-law index value for FGM. The dynamic stresses are calculated when the displacements and shear rotations are obtained for the given natural frequency of displacements, frequency of applied heat flux and time. The natural frequencies of sinusoidal displacements and shear rotations are obtained by using the determinant of the coefficient matrix in the fully homogeneous equation. Only the numerical dynamic results of displacements and stresses subjected to sinusoidal applied heat loads are investigated. The heating study in symmetry structure of FGMs to induce thermal vibration is interesting in the field of engineering and materials. The center displacements can withstand a higher temperature of 1000 K and a power-law index of 5, for which the length-to-thickness ratio 5 is better than that for 10. Full article

A nonlinear finite element model for circular and annular micro-plates under thermal and mechanical loading was developed using a third-order shear deformation theory. In the kinematic assumptions, a change in plate thickness is allowed, and no transverse shear strains are considered on the top and bottom surfaces. A power-law distribution was utilized to account for variations in two constituents through the thickness of the plate. Three different types of porosity distributions are considered. The strain gradient effect in micro-scale structures is accounted for by using the modified couple stress theory. Hamilton’s principle is used to obtain the equations of motion, and conforming plate elements are used in the development of the finite element model. The developed finite element model was verified against the available literature and analytical solutions. The effects of the material and porosity distribution, microstructure-dependency, geometric nonlinearity, and various boundary conditions on the bending response of functionally graded and porous circular and annular micro-plates were studied using the developed nonlinear finite element model. Full article

This study is based on typical thermal studies on thick, functionally graded material (FGM)-coupled plates and circular shells. Numerical studies have been previously published by researchers on the linear first-order shear deformation theory (FSDT) model for thin-thickness and two-layer materials. The present relationship was further studied by the author on the nonlinear third-order shear deformation theory (TSDT) model for thick-thickness and four-layer FGMs. The material properties of FGM layers deal with the effect of temperature. The novelty of this study is in its further consideration of four layers of FGMs and the non-dimensional shear coefficient. The stiffness and stiffness integrals of the four layers are studied. The material properties in the power law expression of the functions of the four layers are assumed for the first time. Under the conditions of a time sinusoidal, varied thermal loads and simply supported conditions for four layers are studied. Parametric case studies involving temperature, the standard power law form of the index, and the nonlinear term of the displacement theory and shear coefficient for the dynamic stresses and displacements are obtained and presented. Full article

The study of the mechanical behavior of functionally graded material (FGM) sandwich plates under thermo-mechanical loading is of great significance for advanced structural design. This study systematically verifies the applicability of the shear strain functions proposed by Reddy and Touratier in the nonlinear bending analysis of porous FGM sandwich plates. Using the existing four-variable shear deformation theory framework, the governing equations are derived through the principle of minimum potential energy, and the Navier method is applied for a numerical solution. For the first time, the study systematically compared the effects of three different porosity distribution patterns on dimensionless deflection, and verified the reliability of the model by comparing it with literature data. The results demonstrate that the adopted shear strain functions can accurately predict the influence of key parameters, including layer thickness ratio, aspect ratio, side-to-thickness ratio, volume fraction index, and porosity, on the deflection performance of sandwich plates. This research provides an important verification basis for the theoretical analysis and engineering application of FGM sandwich plates, particularly offering quantitative evidence for assessing the influence of porosity effects on theoretical prediction accuracy. Full article

This paper explores and discusses how wing structures vibrate by using the Mindlin–Reissner plate theory, which takes into consideration the effects of transverse shear deformation and rotary inertia. This theory works well for thicker structures, like aircraft wings, where it gives accuracy by detecting shear and rotation effects. FGMs, or functionally graded materials, are used in aviation to enhance structural patterns and reduce stress points by gradually changing material properties along the wing thickness based on the volume fraction index. Finite element method (FEM) simulations were conducted to compare the natural frequencies and mode shapes of tapered and interpolated wing geometries. The results indicate that interpolated meshes exhibit higher natural frequencies due to increased stiffness, whereas tapered meshes show lower frequencies due to their flexibility. Validation through ANSYS simulations confirms the accuracy of the FEM results, highlighting the influence of geometry and material gradation on vibrational behavior. The findings offer valuable insights for aerospace applications, supporting the development of lightweight and efficient wing designs. Full article

The thermal vibration of thick Terfenol-D control law on functionally graded material (FGM) plates/cylindrical shells in nonlinear unsteady supersonic flow with third-order shear deformation theory (TSDT) is investigated by using the generalized differential quadrature (GDQ) method. The effects of the coefficient term of TSDT displacement models on the thermal stress and center displacement of Terfenol-D control law on FGM plates/cylindrical shells in nonlinear unsteady supersonic flow are investigated. The coefficient term of TSDT models of thick Terfenol-D control law on FGM plates/cylindrical shells provide an additional effect on the values of displacements and stresses. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. Full article

A numerical, generalized differential quadrature (GDQ) method is presented on applied heat vibration for a thick-thickness magnetostrictive functionally graded material (FGM) plate coupled with a cylindrical shell. A nonlinear c₁ term in the z axis direction of a third-order shear deformation theory (TSDT) displacement model is applied into an advanced shear factor and equation of motions, respectively. The equilibrium partial differential equation used for the thick-thickness magnetostrictive FGM layer plate coupled with the cylindrical shell under thermal and magnetostrictive loads can be implemented into the dynamic GDQ discrete equations. Parametric effects including nonlinear term coefficient of TSDT displacement field, advanced nonlinear varied shear coefficient, environment temperature, index of FGM power law and control gain on displacement, and stress of the thick magnetostrictive FGM plate coupled with cylindrical shell are studied. The vibrations of displacement and stress can be controlled by the control gain algorithms in velocity feedback control law. Full article

The presented problem considers the static temperature analysis of a three-layered, annular plate with heterogeneous facings made of material with radially variable parameters. They are defined by the accepted exponent functions. The plate is composed of thin metal facings and a thicker foam core. The plate is loaded with a flat temperature field with a gradient directed across the plate radius. Using the approximation finite-difference method, the eigen-value problem is solved in order to calculate the temperature differences between plate edges, which cause a loss of plate stability. Taking into account the different material and geometrical parameters, the critical temperature state parameters are evaluated. The meaning of the mixed system of parameters connected with the plate shape geometry, dimensions of the plate-transversal structure, and with the gradation of the material in the radial direction on the thermal response of the composite plate have been found. Numerous results of numerical calculations show the responses of the examined composite plate with facings made of the heterogeneously directed material. Full article

Functionally graded materials (FGMs) are heterogeneous composites characterized by outstanding properties. They are built from two or more components with a gradient distribution of chemical composition along a given direction. A promising graded material for biomedical engineering as an implant could be a FGM made of titanium (Ti) and hydroxyapatite (HAP). It would allow us to counteract the difference between the stiffness modulus of pure titanium and bone tissue. Moreover, it can be a good solution to the problem of stress shielding for bone fixation plates made of conventional titanium or steel. The presented paper aims to perform micromechanical modeling and optimization of a functionally Ti-HAP graded plate, followed by numerical analysis of a fractured tibia stabilization system under specific boundary conditions. Finite element analysis was performed using ANSYS Workbench 2021 software. The models of the FGM plate and tibial fixation system were made using the Space Claim tool. The ANSYS software allowed the optimization of the model considered and the selection of the appropriate structural parameters of the FGM Ti-HAP material. In general, the results proved that the osteosynthesis plate built of graded Ti-HAP material resulted in lower bone stress compared to titanium and steel plates. The results obtained confirmed the validity of the design and the possibility to use functionally graded Ti-HAP bone fixation plates. Full article

Although metallic materials have been used as load-bearing materials in dental and biomedical fields since they have good mechanical properties such as good ductility and strength, their aesthetic properties are inferior to those of ceramic or resin. To obtain aesthetically improved Ti dental devices, the formation of white titanium oxide on pure Ti dental devices was studied. Direct atmospheric pressure plasma (APP) treatment using alternating current was carried out on pure a Ti plate and wire. It was found that a titanium oxide layer with enough whiteness can be obtained on pure Ti wire using direct APP treatment. Although delamination of the titanium oxide layer was found after a bending test, the concept of functionally graded materials (FGMs) can overcome the shortcoming. Full article

The shear effect is usually considered in the numerical calculation of thick composited FGM plates. The characteristics that have the greatest effect on thickness are displacement type, shear correction coefficient, material property and temperature. For the advanced frequency study of thick composited functionally graded material (FGM) plates, it is interesting to consider the extra effects of the nonlinear coefficient c₁ term of the third-order shear deformation theory (TSDT) of displacement on the calculation of varied shear correction coefficients. The values of nonlinear shear correction coefficients are usually functions of c₁, the power-law exponent parameter and environment temperature. Numerical frequency computations are calculated using a simple homogeneous equation, and are investigated using TSDT and the nonlinear shear correction coefficient for thick composited FGM plates. Results for natural frequencies are found via the functions of length-to-thickness ratio, the power-law exponent parameter, c₁ and environment temperature. This novel study in advanced frequency aims to determine the effects of the TSDT and nonlinear shear correction on thick FGM plates under free vibration. Full article

Functionally graded materials (FGMs) are revolutionizing various industries with their customizable properties, a key advantage over traditional composites. The rise of voxel-based 3D printing has furthered the development of FGMs with complex microstructures. Despite these advances, current design methods for FGMs often use abstract mathematical functions with limited relevance to actual performance. Furthermore, conventional micromechanics models for the analysis of FGMs tend to oversimplify, leading to inaccuracies in effective property predictions. To address these fundamental deficiencies, this paper introduces new gradation functions for functionally graded beams (FGBs) based on bending strain energy density, coupled with a voxel-based design and analysis approach. For the first time, these new gradation functions directly relate to structural performance and have proven to be more effective than conventional ones in improving beam performance, particularly under complex bending moments influenced by various loading and boundary conditions. This study reveals the significant role of primary and secondary gradation indices in material composition and distribution, both along the beam axis and across sections. It identifies optimal combinations of these indices for enhanced FGB performance. This research not only fills gaps in FGB design and analysis but also opens possibilities for applying these concepts to other strain energy density types, like shearing and torsion, and to different structural components such as plates and shells. Full article