Browsing by Author "Chang, M. J."

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Accurate frequencies and mode shapes for moderately thick, cantilevered, skew plates
(2007-09-01)
Leissa, A. W.
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Huang, C. S.
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
Accurate free vibration frequencies and mode shapes are presented for complete sets of moderately thick, cantilevered skew plates of triangular, trapezoidal and parallelogram shape. These accurate results are obtained by using the Ritz method applied to the Mindlin plate theory. Two sets of functions are employed simultaneously for each of the three dependent variables: transverse displacement (w) and bending rotations (phi(x) and phi(y)). One set is the widely used algebraic polynomials. The other is the set of corner functions which provide the proper stress singularities in the reentrant clamped-free corner, and accelerates the convergence of the solutions. The extensive frequencies presented are exact to the four digits shown. Corresponding mode shapes are also shown, by means of nodal patterns, most of which are novel in the published literature.
Corner stress singularities in an FGM thin plate
(2007-05-01)
Huang, C. S.
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
Describing the behaviors of stress singularities correctly is essential for obtaining accurate numerical solutions of complicated problems with stress singularities. This analysis derives asymptotic solutions for functionally graded material (FGM) thin plates with geometrically induced stress singularities. The classical thin plate theory is used to establish the equilibrium equations for FGM thin plates. It is assumed that the Young's modulus varies along the thickness and Poisson's ratio is constant. The eigenfunction expansion method is employed to the equilibrium equations in terms of displacement components for an asymptotic analysis in the vicinity of a sharp corner. The characteristic equations for determining the stress singularity order at the corner vertex and the corresponding corner functions are explicitly given for different combinations of boundary conditions along the radial edges forming the sharp corner. The non-homogeneous elasticity properties are present only in the characteristic equations corresponding to boundary conditions involving simple support. Finally, the effects of material non-homogeneity following a power law on the stress singularity orders are thoroughly examined by showing the minimum real values of the roots of the characteristic equations varying with the material properties and vertex angle. (c) 2006 Elsevier Ltd. All rights reserved.
Geometrically Induced Stress Singularities of a Thick FGM Plate Based on the Third-Order Shear Deformation Theory
(2009)
Huang, C. S.
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
Asymptotic solutions for a functionally graded material (FGM) plate are developed to elucidate stress singularities at a plate corner, using a third-order shear deformation theory. The characteristic equations are given explicitly for determining the order of stress singularity at the vertex of a corner with two radial edges having various boundary conditions. The non-homogeneous elasticity properties are present only in the characteristic equations for a corner with one of its two edges simply supported. The effects of material non-homogeneity on the stress singularities are extensively examined. The present results are very useful for developing accurate numerical solutions for an FGM plate under static or dynamic loading when the plate involves stress singularities, such as a V-notch or crack.
Stress singularities in an anisotropic body of revolution
(2014-05-15)
Huang, C. S.
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Hu, C. N.
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Lee, C. C.
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Chang, M. J.
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土木工程學系
To fill the gap in the literature on the application of three-dimensional elasticity theory to geometrically induced stress singularities, this work develops asymptotic solutions for Williams-type stress singularities in bodies of revolution that are made of rectilinearly anisotropic materials. The Cartesian coordinate system used to describe the material properties differs from the coordinate system used to describe the geometry of a body of revolution, so the problems under consideration are very complicated. The eigenfunction expansion approach is combined with a power series solution technique to find the asymptotic solutions by directly solving the three-dimensional equilibrium equations in terms of the displacement components. The correctness of the proposed solution is verified by convergence studies and by comparisons with results obtained using closed-form characteristic equations for an isotropic body of revolution and using the commercial finite element program ABAQUS for orthotropic bodies of revolution. Thereafter, the solution is employed to comprehensively examine the singularities of bodies of revolution with different geometries, made of a single material or bi-materials, under different boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.
Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method
(2019-01-01)
Huang, C. S.
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Lee, H. T.
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Li, P. Y.
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Hu, K. C.
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Lan, C. W.
This study presents a novel three-dimensional elasticity-based numerical solution for buckling analysis of a functionally grated material (FGM) plate with a side crack or an internal crack, which is first shown in literature. The distributions of material properties are assumed to follow a power law through plate thickness. The buckling loads of cracked plates are found by the Ritz method with admissible functions constructed by the moving least squares (MLS) technique. The admissible functions are formed by multiplying a set of regular polynomials in the z coordinate with shape functions in x-y coordinates, established by MLS along with a set of basis functions consisting of regular polynomials and proposed crack functions. The proposed crack functions yields the correct singularity order for stresses at a crack front and shows the displacement and slope discontinuities across the crack, which enhances the ability of the Ritz method to handle problems with cracks. In order to validate the proposed solutions, convergence studies for buckling loads of cracked homogeneous plates are performed and a comparison is presented between the present results, previously published ones, and those obtained from commercial finite element software. The proposed approach is further applied to analyze the buckling of All Al2O3 FGM rectangular plates with side cracks and skewed rhombic plates with central internal cracks while considering the effects of material distributions, plate thickness, skew angles, crack lengths, inclination angles and positions, boundary conditions, and loading conditions on the buckling loads of these plates.
Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks
(2012-09-01)
Huang, C. S.
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Yang, P. J.
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
The free vibrations of rectangular FGM plates with through internal cracks are investigated using the Ritz method. Three-dimensional elasticity theory is employed, and new sets of admissible functions for the displacement fields are proposed to enhance the effectiveness of the Ritz method in modeling the behaviors of cracked plates. The proposed admissible functions accurately describe the stress singularities at the fronts of the crack and display displacement discontinuities across the crack. The correctness and validity of the present approach are established through comprehensive convergence studies and comparisons with published results for homogeneous cracked plates, based on various plate theories. The locally effective material properties of FGM in the thickness direction are estimated by a simple power law. The effects of the volume fraction of the constituents of FGM and the thickness-to-length ratio on the frequencies are investigated. Frequency data for FGM square plates with three types of boundary conditions along the four side faces and with internal cracks of various crack lengths, positions and orientations are tabulated for the first time. (c) 2012 Elsevier Ltd. All rights reserved.
Vibration and Buckling Analysis of Internally Cracked Square Plates by the MLS-Ritz Approach
(2018-09-01)
Huang, C. S.
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Lee, M. C.
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
Based on the classical thin plate theory, this paper proposes new sets of enriched basis functions for in-plane and out-of-plane displacements of square plates that can yield admissible functions for the Ritz method using the moving least-squares (MLS) approach. These admissible functions display the discontinuities of displacement and slope across a crack; give the correct singularity order for the stress resultants at the crack tips; and enhance the Ritz method's ability to recognize the existence of an internal crack in a plate. To confirm the validity of the proposed approach, convergence studies were performed on the buckling loads and vibration frequencies of plates with central horizontal cracks, and the results obtained agree closely with the published ones as well as those generated by the commercial finite element software. To demonstrate the importance of including all the in-plane stress resultant components in the analysis, the effects of different in-plane stress resultant components on the buckling loads and vibration frequencies of simply supported center-cracked square plates under uniaxial uniform loading were investigated. The present approach was further employed to study the effects of cracks' lengths, orientations, and locations on the buckling loads and frequencies of cracked square plates under different boundary conditions and in-plane loading conditions.
Vibrations and stability of a loaded side-cracked rectangular plate via the MLS-Ritz method
(2016-09)
Zeng, H. C.
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Huang, C. S.
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Leissa, A. W.
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Chang, M. J.
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土木工程學系
This study deals with vibration and stability analyses of a rectangular plate with a side crack based on classical thin plate theory using the famous Ritz method with admissible functions that are constructed by the moving least square (MLS) method with enriched basis functions. The enriched basis functions consist of regular polynomial functions along with crack functions that appropriately describe the stress singularities at the crack tip and show the discontinuities of displacement or slope crossing the crack. Comprehensive convergence studies on the stress intensity factor, buckling loads and vibration frequencies of a cracked rectangular plate under uniform loading at its two opposite edges are carried out and demonstrate the accuracy and efficiency of the presented approach by comparing the present results with previously published ones. Finally, the present approach is applied to investigate the effects of location, length and orientation of side cracks on the buckling loads, vibration frequencies and mode shapes of cracked rectangular plates. The in-plane boundary conditions are normal traction prescribed along two opposite edges and free along the other edges. Two out-of-plane boundary condition combinations are considered. One is simply supported along all the edges, and the other is simply supported along the two loaded edges and free along the other edges. (C) 2016 Elsevier Ltd. All rights reserved.
Vibrations of cracked rectangular FGM thick plates
(2011-06-01)
Huang, C. S.
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McGee, O. G., III
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Chang, M. J.
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土木工程學系
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Department of Civil Engineering
Accurate first-of-its-kind solutions of the free vibration characteristics of side-cracked rectangular functionally graded material (FGM) thick plates are reported. From a brief review summary of available shear deformable plate theories, the well-established Reddy third-order plate theory apropos to cracked FGM thick plates is utilized. A novel Ritz procedure is developed incorporating special admissible functions appropriately named in this study as crack functions - that properly account for the stress singularity behaviors in the neighborhood of a crack tip, and that properly account for the discontinuities of displacements and slops across a crack. Material properties of the FGM plates are assumed to vary continuously in the thickness direction according to the Mori-Tanaka scheme or a simple power law. The proposed special admissible functions accelerate the convergence of the extensive non-dimensional frequency solutions summarized. The first known non-dimensional frequencies of simply-supported and cantilevered cracked aluminum (Al) and ceramic (zirconia (ZrO(2))) or alumina (Al(2)O(3)) FGM thick plates of moderate thickness ratio (side-length to plate thickness, b/h = 10) are accurately determined. The effects of the volume fraction in the modeling of material distribution in the thickness direction and of cracks with different lengths, locations and orientations on the non-dimensional frequencies are investigated. (C) 2011 Elsevier Ltd All rights reserved.