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A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates.

Li R, Wang P, Tian Y, Wang B, Li G - Sci Rep (2015)

Bottom Line: A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates.The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation.The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates. The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation. The main advantage of the developed approach is its wide applicability since no trial solutions are needed in the analysis, which is completely different from the other methods. Numerical examples for both static bending and free vibration plates are presented to validate the developed analytic solutions and to offer new numerical results. The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

No MeSH data available.


Related in: MedlinePlus

Distribution of (a) nondimensional deflections and (b) nondimensional bending moments along the diagonal of a square thin foundation plate with four corners point-supported, with Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104, respectively.
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f2: Distribution of (a) nondimensional deflections and (b) nondimensional bending moments along the diagonal of a square thin foundation plate with four corners point-supported, with Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104, respectively.

Mentions: The second example is a square thin foundation plate with four corners point-supported under a central concentrated load, with the nondimensional foundation modulus Ka4/D = 102. The analytic results are tabulated in Table 2 by comparison with those by FEM only since we did not find any such solutions in the literature. Excellent agreement is also observed for all the results. It is convenient to use the above analytic solutions to investigate the effect of K on the plate solutions. As shown in Fig. 2, nondimensional deflections (Fig. 2a) and bending moments (Fig. 2b) along the diagonal of a square thin foundation plate are plotted for Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104. Again, excellent agreement with FEM is observed.


A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates.

Li R, Wang P, Tian Y, Wang B, Li G - Sci Rep (2015)

Distribution of (a) nondimensional deflections and (b) nondimensional bending moments along the diagonal of a square thin foundation plate with four corners point-supported, with Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4660308&req=5

f2: Distribution of (a) nondimensional deflections and (b) nondimensional bending moments along the diagonal of a square thin foundation plate with four corners point-supported, with Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104, respectively.
Mentions: The second example is a square thin foundation plate with four corners point-supported under a central concentrated load, with the nondimensional foundation modulus Ka4/D = 102. The analytic results are tabulated in Table 2 by comparison with those by FEM only since we did not find any such solutions in the literature. Excellent agreement is also observed for all the results. It is convenient to use the above analytic solutions to investigate the effect of K on the plate solutions. As shown in Fig. 2, nondimensional deflections (Fig. 2a) and bending moments (Fig. 2b) along the diagonal of a square thin foundation plate are plotted for Ka4/D = 102, 5 × 102, 103, 5 × 103, and 104. Again, excellent agreement with FEM is observed.

Bottom Line: A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates.The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation.The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China.

ABSTRACT
A unified analytic solution approach to both static bending and free vibration problems of rectangular thin plates is demonstrated in this paper, with focus on the application to corner-supported plates. The solution procedure is based on a novel symplectic superposition method, which transforms the problems into the Hamiltonian system and yields accurate enough results via step-by-step rigorous derivation. The main advantage of the developed approach is its wide applicability since no trial solutions are needed in the analysis, which is completely different from the other methods. Numerical examples for both static bending and free vibration plates are presented to validate the developed analytic solutions and to offer new numerical results. The approach is expected to serve as a benchmark analytic approach due to its effectiveness and accuracy.

No MeSH data available.


Related in: MedlinePlus