Three dimensional shear buckling of FG plates with various boundary conditions

2013 ◽  
Vol 96 ◽  
pp. 670-682 ◽  
Author(s):  
B. Uymaz ◽  
M. Aydogdu
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Shear Buckling

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

scholarly journals Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

2016 ◽  
Vol 68 (5) ◽  
Author(s):  
Saba Saeb ◽  
Paul Steinmann ◽  
Ali Javili
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Linear Displacement ◽  
Computational Homogenization ◽  
Finite Strains ◽  
Underlying Assumption ◽  
Numerical Examples ◽  
Various Boundary Conditions ◽  
Computational Aspects

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill–Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

Flutter of Rectangular Plates in Three Dimensional Incompressible Flow With Various Boundary Conditions: Theory and Experiment

2012 ◽  
Author(s):  
Ivan Wang ◽  
Samuel C. Gibbs ◽  
Earl H. Dowell
Keyword(s):  
Boundary Conditions ◽  
Structural Model ◽  
Three Dimensional ◽  
Flexible Plate ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Test Bed ◽  
Trailing Edge ◽  
Various Boundary Conditions ◽  
Trailing Edge Flap

The aeroelastic stability of rectangular plates are well-documented in literature for certain sets of boundary conditions. Specifically, wing flutter, panel flutter, and divergence of a plate that is clamped on all sides are well-understood. However, the ongoing push for lighter structures and novel designs have led to a need to understand the aeroelastic behavior of elastic plates for other boundary conditions. One example is NASA’s continuous mold-line link project for reducing the noise generated by commercial transport aircraft during landing; in order to reduce the noise generated by vortex shedding from the trailing edge flap during landing, the project proposes to connect the gap between the trailing edge flap and the rest of the wing with a flexible plate. This paper summarizes the aeroelastic theory, numerical results, and experimental results of a study on the flutter and/or divergence mechanisms of a rectangular plate for different sets of structural boundary conditions. The theory combines a three-dimensional vortex lattice aerodynamic model with a plate structural model to create a high-fidelity frequency domain aeroelastic model. A modular experimental test bed is designed for this study in order to test the different boundary conditions. The test bed is also designed to test different plate thicknesses and sizes with only a small number of modifications. The well-understood boundary conditions are used as test cases to validate the analysis results, and then results of additional configurations that have not been extensively explored are presented. The results of this paper can be used to support the design efforts of projects involving plates or plate-membranes. In addition, the paper adds to the fundamental understanding of plate aeroelasticity and provides a wealth of experimental data for comparison and future validation.

Stress analysis in transverse loading of soft core sandwich plates with various boundary conditions

2018 ◽  
Vol 22 (8) ◽  
pp. 2692-2734 ◽  
Author(s):  
Isa Ahmadi
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Sandwich Plates ◽  
Local Concentration ◽  
Governing Equations ◽  
Transverse Loading ◽  
Weak Formulation ◽  
Various Boundary Conditions ◽  
Out Of Plane

In this paper, the transverse loading of sandwich plate is formulated to study the three-dimensional stress field in the sandwich plates for various edge conditions. The formulation is based on the weak formulation approach. A complete three-dimensional displacement field is considered and the weak formulation approach is employed to obtain the governing equations of the plate using the three dimensional equilibrium equations of elasticity. An analytical solution is presented for governing equations when two opposite edges of plate are simply supported. A one-step stress recovery scheme is used to compute the out-of-plane stresses in the sandwich plates. A comparison is made with the predictions of exact elasticity solutions in the open literature and very good agreements are achieved. The distribution of stresses is investigated for various boundary conditions and the log-linear procedure is employed to study the order of stress singularity at free and clamped edge of the plate. It is seen that the present approach accurately predicts the distribution of out-of-plane stresses and local concentration of stresses in the vicinity of free and clamped edges of sandwich structures.

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