一角点支撑另一对边固支正交各向异性矩形薄板弯曲的辛叠加解

Abstract

Abstract:

The bending problem of a uniformly loaded orthotropic rectangular thin plate with a corner point-supported and the other opposite edge clamped is studied. First, we divide the bending problem into two sub-problems with two opposite edges slidingly clamped and another sub-problem with one edge slidingly clamped and its opposite edge simply supported. Then we obtain the eigenvalues and eigenfunctions of the Hamiltonian operator corresponding to the three sub-problems, respectively. Then the solutions of the above three sub-problems are solved by the method of symplectic eigenfunction expansion respectively. Finally, we obtain the symplectic superposition solution of the original bending problem by superposition of the solutions of the three sub-problems. In addition, we calculate the deflection and bending moment values at some points of the bending problems of isotropic rectangular plate and orthotropic rectangular plate by using the symplectic superposition solution obtained in this paper.

Key words: Orthotropic rectangular thin plate, Hamiltonian operator, Eigenfunction, Corner point-supported, Symplectic superposition solution

CLC Number:

O302

Tianjiao Kou, Eburilitu, Alatancang. Symplectic Superposition Solution for the Bending of a Corner Point-Supported and the Other Opposite Edge Clamped Orthotropic Rectangular Thin Plate[J].Acta mathematica scientia,Series A, 2021, 41(3): 797-810.

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Figures/Tables 3

References 18

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				$y = b/2$
$b/a$			$x = 0$	$x = a/4$	$x = a/2$	$x = 3a/4$	$x = a$
$1.0$	$Dw/(qa^{4})$	present	0.02943	0.02436	0.01842	0.01115	0.002789
		Ref.[10]	0.02949	0.02442	0.01847	0.01118	0.002783
	$M_y/(qa^{2})$	present	-0.01137	-0.008667	0.002233	0.01683	0.03146
		Ref.[10]	-0.01161	-0.008872	0.002031	0.01663	0.03130
$1.2$	$Dw/(qa^{4})$	present	0.05251	0.04247	0.03168	0.01956	0.006469
	$M_y/(qa^{2})$	present	0.01263	0.013099	0.022244	0.03556	0.05058
$1.4$	$Dw/(qa^{4})$	present	0.08433	0.06754	0.05032	0.03202	0.013093
	$M_y/(qa^{2})$	present	0.04384	0.041989	0.048879	0.06048	0.07534
$1.6$	$Dw/(qa^{4})$	present	0.12619	0.10093	0.07574	0.04992	0.023990
	$M_y/(qa^{2})$	present	0.08095	0.076966	0.081643	0.09153	0.10597
$1.8$	$Dw/(qa^{4})$	present	0.17962	0.14421	0.10954	0.07485	0.040737
	$M_y/(qa^{2})$	present	0.12328	0.117456	0.120189	0.12860	0.14255

				$y = b/2$
$b/a$			$x = 0$	$x = a/4$	$x = a/2$	$x = 3a/4$	$x = a$
$1.0$	$100E_{T}h^{3}Dw/(qa^{4})$	present	4.50209	4.33322	3.83644	2.59816	0.53881
	$M_y/(qa^{2})$	present	-0.269027	-0.247932	-0.206159	-0.101362	0.121649
$1.2$	$100E_{T}h^{3}Dw/(qa^{4})$	present	9.67375	8.79869	7.35414	4.77077	1.11120
	$M_y/(qa^{2})$	present	-0.382724	-0.341621	-0.264498	-0.106729	0.173482
$1.4$	$100E_{T}h^{3}Dw/(qa^{4})$	present	18.21916	15.81380	12.62913	7.97018	2.02218
	$M_y/(qa^{2})$	present	-0.499650	-0.437193	-0.320878	-0.104608	0.231455
$1.6$	$100E_{T}h^{3}Dw/(qa^{4})$	present	31.03660	26.01927	20.08335	12.44326	3.35009
	$M_y/(qa^{2})$	present	-0.612517	-0.528390	-0.372671	-0.096795	0.293216
$1.8$	$100E_{T}h^{3}Dw/(qa^{4})$	present	48.96215	40.04606	30.15277	18.44113	5.16290
	$M_y/(qa^{2})$	present	-0.716491	-0.609928	-0.416522	-0.084249	0.356611

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Symplectic Superposition Solution for the Bending of a Corner Point-Supported and the Other Opposite Edge Clamped Orthotropic Rectangular Thin Plate

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