Papers by Minh-Chien Trinh
Aerospace Science and Technology, 2019
This study develops a three variable refined shear deformation theory to analyze the free vibrati... more This study develops a three variable refined shear deformation theory to analyze the free vibration and bending behavior of porous functionally graded doubly curved shallow shells subjected to uniform and sinusoidal pressure. Shell displacements are assumed to be caused by extensional, bending, and shear effects. The in-plane displacements produced by bending effects are considered taking the form of the classical plate theory. The in-plane displacements produced by shear effects satisfy the stress-free and strain-free condition at the top and bottom surfaces, eliminating the usage of the shear correction factor in the present study. Two porosity types influence material properties and structure behaviors in different aspects. Hamilton's principle is used to derive Euler-Lagrange equations. Spatial solutions for the differential equation are assumed satisfying boundary conditions and their time-dependent amplitude equations are obtained by applying the Bubnov-Galerkin technique. Natural frequencies and transverse deflections of the shell in different geometry configurations and different porosity types and degrees are obtained and compared. The proposed theory is proved feasible to be applied in the analysis of functionally graded plates and shells with porosity.
Aerospace Science and Technology, 2019
The fundamental frequencies and nonlinear dynamic responses of functionally graded sandwich shell... more The fundamental frequencies and nonlinear dynamic responses of functionally graded sandwich shells with double curvature under the influence of thermomechanical loadings and porosities are investigated in this study. Two material models are considered. The continuity requirement of material properties throughout layers are fulfilled by newly introducing refined effects of two porosity types regarding the average of constituent properties weighted by the porosity volume fraction. The first-order shear deformation theory taking the out-of-plane shear deformation into account is employed to obtain the Lagrange equation of motions. The number of primary variables reduces from five to three after introducing the Airy stress function. The system of dynamic governing equations is obtained by utilizing the Bubnov-Galerkin procedure. The natural frequencies are analytically computed by solving eigenvalue problems, and the fundamental frequencies are acquired by further assumptions about the inertial force caused by the shell rotation variables. The nonlinear dynamic responses of the functionally graded spherical, cylindrical, and hyperbolic paraboloid shells under the influence of different geometry configurations, loading conditions, and porosity types and degrees are obtained by applying the fourth-order Runge-Kutta method. The numerical results are presented and verified with available studies in the literature. Although porosities are usually considered material defects weakening the structure performance, this study has proved clearly that porosities stiffen the shell structures to some extent.
Aerospace Science and Technology, 2019
Theoretical closed-form solutions and numerical results for nonlinear stability of the moderately... more Theoretical closed-form solutions and numerical results for nonlinear stability of the moderately thick functionally graded sandwich shells subjected to thermomechanical loadings are presented in this study. Two proposed material distribution models supported by elastic foundations are examined. The nonlinear strain field is deduced from the first-order shear deformation theory taking the stretching, bending and shear effects into consideration. The Bubnov-Galerkin procedure and harmonic balance principle are utilized to bring about the explicit algebraic expression for the shell static behaviors from governing equations derived from Hamilton's principle. Mechanical buckling loads and critical thermal rises for the shells in spherical, cylindrical, and hyperbolic paraboloid forms are obtained. The effect of geometry, elastic foundations, volume fraction index, material distribution models, buckling modes, and imperfections on the shell stability behaviors are considered in parametric studies. The yielding plateau in the thermal analysis of the spherical shells in case of temperature dependent characteristics is recognized for the first time. Verification studies are also conducted.
Composite Structures, 2018
Analytical closed-form solutions for thermos-mechanical stability and explicit expressions for fr... more Analytical closed-form solutions for thermos-mechanical stability and explicit expressions for free-and forced-vibration of thin functionally graded sandwich shells with double curvature resting on elastic bases are investigated for the first time in this study. A core layer of ceramic and two cover layers of functionally graded materials constitute the shell structure. Governing equations are derived from the classical shell theory using Hamilton's principle admitting Volmir assumption and von Karman nonlinear displacement fields. Theoretical solutions are achieved by using the Bubnov-Galerkin procedure in solving differential equations. Parametric studies showing the effects of temperature-dependent features, material constituents, initial geometry imperfections , external thermos-mechanical loadings, elastic bases, and geometry configuration on static and dynamic behaviors of the shells are performed. Thin functionally graded sandwich spherical, cylindrical, and hyperbolic paraboloid shells are studied. Snap-through phenomena under load-control conditions are recognized in thin functionally graded sandwich cylindrical shells. The fourth-order Runge-Kutta method is employed to numerically solve dynamic problems and four analogies are drawn to validate theoretical formulations.
Aerospace Science and Technology, 2018
This work presents an analytical approach to investigate buckling and post-buckling behavior of F... more This work presents an analytical approach to investigate buckling and post-buckling behavior of FGM plate with porosities resting on elastic foundations and subjected to mechanical, thermal and thermomechanical loads. The formulations are based on Reddy's higher-order shear deformation plate theory taking into consideration Von Karman nonlinearity, initial geometrical imperfections, and Pasternak type of elastic foundations. By applying Galerkin method, closed-form relations of buckling loads and post-buckling equilibrium paths for simply supported plates are determined. Numerical results are carried out to show the effects of porosity distribution characteristics (Porosity-I and Porosity-II), geometrical parameters, material properties and elastic foundations on the mechanical, thermal and thermomechanical buckling loads and post-buckling resistance capacity of the porous FGM plates.
Journal of Applied and Computational Mechanics, 2018
In this paper, the first-order shear deformation theory is used to derive theoretical formulation... more In this paper, the first-order shear deformation theory is used to derive theoretical formulations illustrating the nonlinear dynamic response of functionally graded porous plates under thermal and mechanical loadings supported by Pasternak's model of the elastic foundation. Two types of porosity including evenly distributed porosities (Porosity-I) and unevenly distributed porosities (Porosity-II) are assumed as effective properties of FGM plates such as Young's modulus, the coefficient of thermal expansion, and density. The strain-displacement formulations using Von Karman geometrical nonlinearity and general Hooke's law are used to obtain constitutive relations. Airy stress functions with full motion equations which is employed to shorten the number of governing equations along with the boundary and initial conditions lead to a system of differential equations of the nonlinear dynamic response of porous FGM plates. Considering linear parts of these equations, natural frequencies of porous FGM plates are determined. By employing Runge-Kutta method, the numerical results illustrate the influence of geometrical configurations, volume faction index, porosity, elastic foundations, and mechanical as well as thermal loads on the nonlinear dynamic response of the plates. Good agreements are obtained in comparison with other results in the literature.
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Papers by Minh-Chien Trinh