• Steel and Composite Structures
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• v.16 no.4
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Steel and Composite Structures
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• v.35 no.1
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• pp.129-145
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• 2020

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.1875-1882
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• 1993

Variable thickness plates are commonly used as structural members in the majority of industrial sectors. Previous fracture mechanics researches on variable thickness plates were limited to mode I loading cases. In practice, however, cracks are usually located inclined to the loading direction. In this respect, combined mode(mode I/II) stress intensity factors $K_{I}$ and $K_{II}$ at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a slant edge crack were chosen. The parameters used in this study were dimensionless crack $length{\lambda}$, slant $angle{\alpha}$, thickness $ratio{\beta}$ and width ratio{\omega}$. Stress intensity factors were calculated by crack opening displacement(COD) and crack sliding displacement(CSD)method proposed by Ingraffea and Manu.

• Steel and Composite Structures
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• v.19 no.3
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• pp.679-695
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• 2015

A numerical solution using finite difference method to evaluate the thermal buckling of simply supported FGM plate with variable thickness is presented in this research. First, the governing differential equation of thermal stability under uniform temperature through the plate thickness is derived. Then, the governing equation has been solved using finite difference method. After validating the presented numerical method with the analytical solution, the finite difference formulation has been extended in order to include variable thickness. The accuracy of the finite difference method for variable thickness plate has been also compared with the literature where a good agreement has been found. Furthermore, a parametric study has been conducted to analyze the effect of material and geometric parameters on the thermal buckling resistance of the FGM plates. It was found that the thickness variation affects isotropic plates a bit more than FGM plates.

• Smart Structures and Systems
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• v.18 no.4
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• pp.755-786
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• 2016

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.1-7
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• 1993

Most of wall or plate structures subjected to nonuniform earth or water pressure has variable thickness. These problems were generally solved by models with uniform thickness and pressure. To obtain more accurate and economic solution for this type of problem. efficient isoparametric plate element considering variable thickness and nonuniform pressure were developed. Some example problems demonstrated efficiency of the proposed element.

• Journal of the korean Society of Automotive Engineers
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• v.15 no.2
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• pp.112-120
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• 1993

Variable thickness plates are commonly encountered in the majority of mechanical/structural components of industrial applications. And, as a result of the unsymmetry of the structure or the load and the anisoptropy of the materials, the cracks in engineering structures are generally subjected to combined stresses. In spite of considerable practical interest, however, a few fracture mechanics study on combined mode crack in a variable thickness plate have carried out. In this respect, combined mode 1/3 stress intensity factors $K_{1}$ and $K_{3}$ at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a central slant crack were chosen. the parameters used in this study were dimensionless crack length .lambda. crack slant angle .alpha, thickness ratio .betha. and width ratio .omega. Stress intensity factors were calculated by crack opening displacement(COD) and crack tearing displacement(CTD) method proposed by Ingraffea and Manu. The effect of thickness ratio .betha. on $K_{1}$ is relatively great in comparison to $K_{3}$.

• Journal of the Korean Society of Safety
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• v.13 no.3
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• pp.24-31
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• 1998

Variable thickness plates are commonly encountered in the majority of mechanical/structural components of industrial applications. And, as a result of the unsymmetry of the structure or the load and the anisoptropy of the materials, the cracks in engineering structures are generally subjected to combined stresses. In spite of considerable practical interest, however, a few fracture mechanics study on combined mode crack in a variable thickness plate have carried out. In this respect, combined mode I/III stress intensity factors $K_I$ and $K_III$ at the crack tip for a variable thickness plate were obtained by 3-dimensional finite element analysis. Variable thickness plates containing a central slant crack were chosen. The parameters used in this study were dimensionless crack length $\lamda$, crack slant angle $\alpha$, thickness ratio $\beta$ and width ratio $\omega$. Stress intensity factors were calculated by crack opening displacement(COD) and crack tearing displacement(CTD) method.

• Coupled systems mechanics
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• v.11 no.4
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• pp.357-371
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• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Magazine of the Korean Society of Agricultural Engineers
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• v.31 no.4
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• pp.58-71
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• 1989

This study aims to develop a computerized program for analysis of the ground-supported cylindrical shell structure with step varied section and to find out its mechanical characteri- stics through application of the developed program to the analysis of a ensiled farm silo as a model structure. The thickness of wall and bottom-plate of farm silo is assumed to be step-varied and its detailed structural dimensions are presented in Tab. 1 and 2. Several numerical case studies show that sectional stresses of the sample structures are largely reduced by adopting "varied section" design technique. And, other major results ob- tained from this study are summarize4 as follows ; 1. The variation of wall-thickness has a great influence on bending stresses of wall. Ho- wever, the larger the relative thickness of bottom-plate is, the smaller the influence is. 2. The magnitude of thickness of projecting toe of bottom-plate has negligible effect on sectional stresses 3. The conventional design methodology, which assumes the bottom edge of wall as clam- ped on ground, is proved to be discarded through the numerical analysis. 4. It is found that the "varied section" design technique should get similar effects as in the case of thick bott6m-plate having uniform thickness. 5. The variation of wall-thickness has a considerable effect on the bending stresses of bo- ttom-plate. Especially, this phenomenon is very remarkable in its projecting toe. In some cases. the negative bending moment may be acted on.