Navier solution for the elastic equilibrium problems of rectangular thin plates with variable thickness in linear and nonlinear theories

1985 ◽  
Vol 6 (6) ◽  
pp. 545-558 ◽  
Author(s):  
Yin Si-ming ◽  
Ruan Sheng-huang
Keyword(s):  
Variable Thickness ◽  
Equilibrium Problems ◽  
Elastic Equilibrium ◽  
Thin Plates ◽  
Navier Solution ◽  
Linear And Nonlinear

Buckling Analysis of Circular FGM Plate Having Variable Thickness Under Uniform Compression by Finite Element Method

2005 ◽  
Author(s):  
Abazar Shamekhi ◽  
Mohammad H. Naei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Thin Plates ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

Nonlinear Bending of Rectangular Magnetoelectroelastic Thin Plates with Linearly Varying Thickness

2018 ◽  
Vol 19 (3-4) ◽  
pp. 351-356
Author(s):  
Feng Wang ◽  
Yu-fang Zheng ◽  
Chang-ping Chen
Keyword(s):  
Differential Equations ◽  
Variable Thickness ◽  
Plate Theory ◽  
Nonlinear Differential Equations ◽  
Thin Plates ◽  
Thickness Variation ◽  
Algebraic Equations ◽  
Nonlinear Bending ◽  
Nonlinear Load ◽  
Magnetic Potentials

AbstractWith employing the von Karman plate theory, and considering the linearly thickness variation in one direction, the bending problem of a rectangular magnetoelectroelastic plates with linear variable thickness is investigated. According to the Maxwell’s equations, when applying the magnetoelectric load on the plate’s surfaces and neglecting the in-plane electric and magnetic fields in thin plates, the electric and magnetic potentials varying along the thickness direction for the magnetoelectroelastic plates are determined. The nonlinear differential equations for magnetoelectroelastic plates with linear variable thickness are established based on the Hamilton’s principle. The Galerkin procedure is taken to translate a set of differential equations into algebraic equations. The numerical examples are presented to discuss the influences of the aspect ratio and span–thickness ratio on the nonlinear load–deflection curves for magnetoelectroelastic plates with linear variable thickness. In addition, the induced electric and magnetic potentials are also presented with the various values of the taper constants.

scholarly journals Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Pham Van Vinh
Keyword(s):  
Functionally Graded Material ◽  
Variable Thickness ◽  
Mixed Finite Element ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Thin Plates ◽  
Quadrilateral Element ◽  
Graded Material ◽  
Element Technique ◽  
Power Law Index

A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

Symmetrical Bending of Circular Plates of Constant Radial Bending Stress

1962 ◽  
Vol 29 (4) ◽  
pp. 696-700 ◽  
Author(s):  
J. P. Lee
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Integrodifferential Equation ◽  
Thin Plates ◽  
Bending Stress ◽  
Circular Plates ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Equation Boundary ◽  
Plates Of Variable Thickness

Bending of simply supported circular plates of constant radial bending stress subjected to uniformly distributed loading is investigated by solving a nonlinear integrodifferential equation. Boundary conditions are satisfied by joining the central portion of the plates of variable thickness to an annular rim along the boundary with uniform thickness. Usual assumptions for bending of thin plates of small deflections are assumed valid.

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