Numerical study of a geometrically nonlinear transverse bending problem three-layer plate with transversally soft filler

The review of recent literature shows that the bending performances of transversely loaded laminated composite singly curved stiffened surfaces are not studied in detail using the geometrically nonlinear strains. The present paper aims to fill that void and proposes an isoparametric C° finite element formulation combining von-Karman nonlinearity and Sanders’ first approximation theory. The curved surfaces are simulated using nonlinear strains. The stiffeners are formulated using geometrically linear and nonlinear strains. The correctness of the proposed approach is confirmed through solution of benchmark problems. The relative performances of stiffened curved surfaces in terms of maximum transverse displacements are studied for industrially important parametric variations like boundary conditions, laminations, stacking sequences, and number, orientations, eccentricities, and depth of stiffeners. The results are critically discussed and it is concluded that the clamped 0°/90°/0° shell with curved stiffeners ( y-stiffener) located below the mid-surface shows the greatest bending stiffness. The nonlinear approach is essential for both shell and stiffener for correct prediction of the transverse displacements. The relatively simpler linear approach can be considered for single x-stiffener only.

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Geometrically nonlinear dynamic analysis of functionally graded porous partially fluid-filled cylindrical shells subjected to exponential loads

Journal of Vibration and Control ◽

10.1177/1077546320982462 ◽

2020 ◽

pp. 107754632098246

Author(s):

Majid Khayat ◽

Abdolhossein Baghlani ◽

Seyed Mehdi Dehghan ◽

Mohammad Amir Najafgholipour

Keyword(s):

Material Properties ◽

Nonlinear Dynamic ◽

Numerical Study ◽

Equations Of Motion ◽

Cylindrical Shells ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Geometrically Nonlinear ◽

Graphene Platelet ◽

Graphene Platelets

This article investigates the influence of graphene platelet reinforcements and nonlinear elastic foundations on geometrically nonlinear dynamic response of a partially fluid-filled functionally graded porous cylindrical shell under exponential loading. Material properties are assumed to be varied continuously in the thickness in terms of porosity and graphene platelet reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin–Tsai equations are used to find the effective material properties of the graphene platelet–reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’s theory. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. An incremental–iterative approach is used to solve the nonlinear equations of motion of partially fluid-filled cylindrical shells based on the Newmark direct integration and Newton–Raphson methods. The governing equations of liquid motion are derived using a finite strip formulation of incompressible inviscid potential flow. The effects of various parameters on dynamic responses are investigated. A detailed numerical study is carried out to bring out the effects of some influential parameters, such as fluid depth, porosity distribution, and graphene platelet dispersion parameters on nonlinear dynamic behavior of functionally graded porous nanocomposite partially fluid-filled cylindrical shells reinforced with graphene platelets.

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Geometrically Nonlinear Problem of Longitudinal and Transverse Bending of a Sandwich Plate with Transversally Soft Core

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080218030046 ◽

2018 ◽

Vol 39 (3) ◽

pp. 448-457 ◽

Cited By ~ 30

Author(s):

I. B. Badriev ◽

M. V. Makarov ◽

V. N. Paimushin

Keyword(s):

Nonlinear Problem ◽

Sandwich Plate ◽

Soft Core ◽

Geometrically Nonlinear ◽

Transverse Bending ◽

Transversally Soft Core

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MATHEMATICAL MODELING OF STRESS-STRAIN STATE OF LOADED RODS WITH ACCOUNT OF TRANSVERSE BENDING

Bulletin of TUIT: Management and Communication Technologies ◽

10.51348/tuitmct117 ◽

2018 ◽

pp. 11-21

Keyword(s):

Mathematical Model ◽

Research Work ◽

Dynamic Processes ◽

Variation Principle ◽

Refined Theory ◽

Geometrically Nonlinear ◽

Science Centers ◽

Transverse Bending ◽

Non Linear ◽

Statics And Dynamics

Mathematical simulation of static and dynamic processes of strain taking into account of transverse bending under loading is presented in the paper in linear and geometrically nonlinear statements. An extensive analysis of research work carried out in universities and science centers all over the world is given, the relevance of the problem and the areas of solution application are emphasized. The mathematical correctness of the problem statement is shown. Variations of kinetic, potential energy, volume and surface forces are determined for mathematical models of static and dynamic processes of strain with taking into account of transverse bending of loaded rods in linear and geometrically nonlinear statements. Based on the theory of elastic strains and the refined theory of Vlasov-Dzhanelidze-Kabulov, and using the Ostrogradsky-Hamilton variation principle, a mathematical model of the statics and dynamics of the process of rod points displacement is developed for transverse bending in linear and geometrically nonlinear statements. Equations of a mathematical model with natural initial and boundary conditions in a vector form are given. A computational algorithm is developed for calculating the statics and dynamics of rods under loading in linear and geometrically non-linear statements using the central finite differences of the second order of accuracy. The strain processes when the rod is rigidly fixed at two edges are considered in linear and geometrically nonlinear statements. The calculation results obtained are given in the form of graphs. The propagation of longitudinal, transverse vibrations and the angle of inclination along the length of the rod was studied at different points of times. Linear and geometrically non-linear vibration results are analyzed and compared.

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