Weak Formulation Study For Thermoelastic Buckling Analysis Of Thick Laminated Cylindrical Shells

Weak formulations of mixed state equations of closed laminated cylindrical shells are presented in the Hamilton System. The Hamilton canonical equation of closed cylindrical shell is established. By means of applying the transfer matrix method and taking the advantage of Hamiltonian matrix in the calculation, a unified approach and three-dimensional thermoelastic solutions are obtained for the buckling analysis of closed thick laminated cylindrical shells. All equations of elasticity can be satisfied and all elastic constants can be taken into account. Numerical results are given to compare with those of FEM calculated using SAP5. The principle and method suggested here have clear physical concepts. The equations and boundary conditions proposed in this paper are weakened. The solutions and results given here may serve as a benchmark for other numerical procedures.

A Wavelet Collocation Precise Integration Method for Laminated Rectangular Plates with Four Sides Clamped

By using Quasi-Shannon wavelet, we develop a wavelet collocation method for the Hamilton canonical equation of elastic bodies, and get the Hamilton canonical equation which is discrete in the plane of the rectangular laminated plate and continuum along its thickness. The approximate solution expressed by Quasi-Shannon wavelet satisfies the clamped boundary conditions of the plate easily. Hence, it is convenient to establish the wavelet collocation precise integration method for the static problem of the rectangular laminated plate with four sides clamped. Numerical results show that the current approach offers excellent predictive capability for rectangular composite laminated plate with clamped boundary conditions.

Meshless Method with Radial Basis Functions for Hamilton Canonical Equation

Meshless element of Hamilton canonical equation was established in this paper by combining the modified Hellinger-Reissner variational principle for elastic material and radial point interpolation functions. Using Multiquadric (MQ), Gaussian (EXP) and thin plane spine (TPS), the astringency of meshless methods and the effects of the dimensionless shape parameters on the maximum displacement were investigated by the numerical examples of the single or the cross-lay laminated plates. And all of the numerical results of displacement w were compared with that of MSC. Nastran This study introduced the advantages of meshless finite element method into semi-analytic solution of Hamilton canonical equation, and a new semi-analytic method was presented for Hamilton canonical equation.