Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 797-810.

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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

Tianjiao Kou1(), Eburilitu1,*(), Alatancang2()   

  1. 1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
    2 Inner Mongolia Normal University, Hohhot 010022
  • Received:2020-05-14 Online:2021-06-26 Published:2021-06-09
  • Contact: Eburilitu;;
  • Supported by:
    the NSFC(11862019);the NSFC(11761029);the NSF of Inner Mongolia(2020ZD01)


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