Browsing by Author "Leissa, AW"

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Vibrations of mindlin sectorial plates using the ritz method considering stress singularities
(2006-06-01)
Huang, CS
;
Chang, MJ
;
Leissa, AW
;
土木工程學系
;
Department of Civil Engineering
This paper reports very accurate vibration frequencies of moderately thick sectorial plates with various boundary conditions and vertex angles (alpha = 90 degrees, 180 degrees, 270 degrees, 300 degrees, 330 degrees, and 355 degrees) based on Mindlin plate theory, and provides the nodal patterns of their vibration modes for the first time in the published literature. Most of the extensive frequencies presented are exact to the four digits shown. The classical Ritz method is employed, using corner functions and algebraic trigonometric functions as the admissible functions. Because the corner functions properly describe the singularity behaviors of moments and shear forces in the vicinity of the vertex of a sectorial plate, they substantially enhance the convergence and accuracy of the numerical results, which is shown by convergence studies.
Vibrations of skewed cantilevered triangular, trapezoidal and parallelogram Mindlin plates with considering corner stress singularities
(2005-04-07)
Huang, CS
;
Leissa, AW
;
Chang, MJ
;
土木工程學系
;
Department of Civil Engineering
Based on the Mindlin shear deformation plate theory, a method is presented for determining natural frequencies of skewed cantilevered triangular, trapezoidal and parallelograrn plates using the Ritz method, considering the effects of stress singularities at the clamped re-entrant corner. The admissible displacement functions include polynomials and corner functions. The admissible polynomials form a mathematically complete set and guarantee the solution convergent to the exact frequencies when Sufficient terms are used. The corner functions properly account for the singularities of moments and shear forces at the re-entrant corner and accelerate the convergence of the solution. Detailed convergence Studies are carried out for plates of various shapes to elucidate the positive effects of corner functions Oil the accuracy of the solution. The results obtained herein are compared with those obtained by other investigators to demonstrate the validity and accuracy of the solution. Copyright (c) 2005 John Wiley B Sons, Ltd.