Search Results (6)

This study is concerned with the nonlinear free vibration of a cracked functionally graded porous cylindrical panel reinforced with graphene platelets by introducing a phase-field crack model. Conventional crack modeling by separating the grid nodes lying on the crack line is not only painstaking but also suffers from numerical instability. To overcome this problem, the internal crack is modeled by adopting the phase-field formulation and a virtual geometry rotation. The nonlinear numerical method is developed based on the first-order shear deformation theory incorporated with the von Kármán geometry nonlinearity in the framework of the 2-D extended natural element method, a recently introduced mesh-free method. The crack-induced singular field is represented by adopting the crack-tip singular functions, and the troublesome numerical locking is restrained by combining the MITC3+ shell concept and the shear stabilization factor. The curved shell surface is mapped to a 2-D rectangular NEM grid to avoid difficulty in defining the interpolation functions. The developed numerical method is verified through a comparison with the reference solutions, and the large-amplitude free vibration of porous cracked functionally graded grapheme platelet-reinforced cylindrical panels is profoundly examined by changing the major parameters. Full article

Large deflection nonlinear bending of functionally graded (FG) porous cylindrical panels reinforced with graphene platelets (GPLs) on a Pasternak-type elastic foundation is examined by developing a reliable and effective 2D meshfree-based nonlinear numerical method. The large displacement field is express by the first-order shear deformation theory (FSDT) and the von Kármán nonlinearity, and approximated by 2D natural element method (NEM) in conjunction with the stabilized MITC3+ shell concept and the shell surface–rectangular grid geometry transformation. The nonlinear simultaneous equations are solved by a load incremental Newton–Raphson scheme. The developed nonlinear numerical method is justified from by comparing with the reference solutions, and the load–deflection and bending moment of FG-GPLRC porous cylindrical panels on elastic foundation are scrutinizingly examined. Four different symmetric GPL distribution patters (except for FG-Λ) and three different symmetric porosity distributions are considered and their combined effects on the nonlinear bending behavior are investigated, as well as the effects of foundation stiffness and GPL amount. Also, the results are compared with those of FG CNT-reinforced porous cylindrical panels. Full article

The lightweight of structure is widely applied in industrial applications, and the conflict between both dynamic stability and structural lightweight is still prominent. In this paper, functionally graded porous (FGP) elliptic cylindrical shells and panels with general boundary conditions are analyzed to explore the effect of the FGP on dynamic performance. First, the FGP elliptic cylindrical shell and panel models are established. Therein, three kinds of porosity distribution are considered, including nonsymmetric, symmetric, and uniform distributions. The energy expressions of the FGP elliptic cylindrical shell and panel are established by the first-order shear deformation theory (FSDT). To simulate various boundary conditions, the artificial spring boundary technique is employed in this study. Then, the Jacobi orthogonal polynomials and Fourier series are adopted to express the admissible displacements. Finally, the accuracy of this model is verified by comparing it with open literature and ABAQUS software. Results show that the variations of the boundary conditions, linear springs, thickness ratio, and porosity have close relation with the dynamic performance of the structure by affecting the stiffness of the structure. Full article

The free vibration of functionally graded porous cylindrical shell panels reinforced with graphene platelets (GPLs) was numerically investigated. The free vibration problem was formulated using the first-order shear deformation shell theory in the framework of the 2-D natural element method (NEM). The effective material properties of the GPL-reinforced shell panel were evaluated by employing the Halpin–Tsai model and the rule of mixtures and were modified by considering the porosity distribution. The cylindrical shell surface was transformed into the 2-D planar NEM grid to avoid complex computation, and the concept of the MITC3+shell element was employed to suppress shear locking. The numerical method was validated through benchmark experiments, and the free vibration characteristics of FG-GPLRC porous cylindrical shell panels were investigated. The numerical results are presented for four GPL distribution patterns (FG-U, FG-X, FG-O, and FG-Λ) and three porosity distributions (center- and outer-biased and uniform). The effects of GPL weight, porosity amount, length–thickness and length–radius ratios, and the aspect ratio of the shell panel and boundary condition on the free vibration characteristics are discussed in detail. It is found from the numerical results that the proposed numerical method accurately predicts the natural frequencies of FG-GPLRC porous cylindrical shell panels. Moreover, the free vibration of FG-GPLRC porous cylindrical shell panels is significantly influenced by the distribution pattern as well as the amount of GPLs and the porosity. Full article

In this study, a novel, dynamic model of a graphene-platelet-reinforced, porous (GPLRP) double-cylindrical-panel system is proposed. The material properties of a graphene-platelet-reinforced, porous, double-cylindrical-panel system were determined by the Halpin–Tsai micromechanics model and the typical mechanical properties of open-cell metal foams. Different types of porosity distribution and graphene platelet (GPL) distribution patterns were considered. Love’s shell theory was utilized to derive the theoretical formulation, and the Rayleigh–Ritz method was used to calculate the natural frequencies of the system. The proposed model was validated by several comparison studies with the natural frequencies in the existing literature. Finally, the effects of stiffness of Winkler springs, boundary condition, porosity coefficient, porosity distribution, GPL distribution pattern, and GPL weight fraction on the free vibration characteristics of the system were evaluated. Full article

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability. Full article