Analysis Of Edge Effect Of Composite Laminates Plate Based On Symplectic System

The damage and destroy of the composite plate and shell is controlled by the interlaminarstresses in composite laminates, which is also one of important topics in the composite field.According to the results of experiments and researches, there is a phenomena of stressesconcentration at the free boundary of composite laminates under uniform axial strain, even thesingularity also existing. Different kinds of models and solutions have been proposed since1960s, most of which are approximate solutions based on classical methods. But the solutionsbased on traditional elasticity system are always got with the field of one kind of variables,belonging to the Lagrange system, which is hard to satisfysynchronously the given boundariesand the interface continuity conditions. Prof Zhong introduced the Hamiltonian system theoryinto the theory of elasticity by the dual variables, especially for composite laminates, whichcan satisfy synchronously the the interface continuity conditions and the boundary conditions.In this paper, the Pipes-Pagano model is researched. The Hamilton mixed energyvariational principle is also derived from Hellinger-Rainssner variational principle. Then theHamilton canonical equation form is got, and the direct solution method of separation ofvariables and the symplectic eigen-solution expansion method can be applied to find thesolution. The results show that there is stress singularity at the boundary of the section and thetensile stress also exists. For the multi-layered laminates with hundreds of layers used in thesociety, the traditional numerical methods need mass memory, so the practicability is notgratifying. Based on the second chapter of this paper, a new numerical method is proposed.Compared with the traditional method, it is more simple. The step is that: firstly, by thediscretion is performed along z axis and the elements is plotted out, then a series of equationsare derived from the variational principle, then the precise integration method is used to getsolution..The results are important for the research of the mechanics of damage of compositelaminates and also is a reference for the research of sigularity of open pore, cut, gap and thediscontinuation of load. The availability of this method prove that the symplectic system canbe introduced to the research of composite laminates.