Using the"symplectic superposition"method in the Hamiltonian system and based on the theory of elastic thin plates,an analytically study was carried out for the static problem of rectangular thin plates with mixed boundary conditions of constraint on two opposite sides and middle-constraint ends-simplely-supported on the other two sides.Firstly,based on the Hamiltonian system,the symplectic geometry method was used to analytically solve the problem of classical boundary condition of simply supported edges.Then,based on this solution as the basic system,the superposition method was used to solve the case of complex mixed boundary condition of constraint on two opposite sides and middle-constraint ends-simplely-supported on the other two sides.Finally,the correctness and convergence of the proposed method were verified using the finite element numerical simulations.The method presented in this paper has both advantages of the rationality of symplectic geometry and the regularity of superposition method.During the solving process,there is no need to assume the form of the solution in advance,and the analytical solution is obtained directly from the basic equations of elasticity through strict step-by-step derivation.This method has strong generality and can be used in some rectangular plate problems that are difficult to solve analytically using the traditional methods.
关键词
混合边界/弹性薄板理论/Hamilton体系/辛-叠加方法/静力弯曲
Key words
mixed boundary/theory of elastic thin plate/Hamilton system/symplectic superposition method/static bending
维普
万方数据