Study On Semi-analytical Solution For Thermoelastic Composite Laminated Plate

With the increasing application of composite materials in the fields of aerospace,automobile industry,transportation,chemical and textile,the thermoelastic problem of composite laminated plate has become a research emphasis on materials and mechanics.Based on the semi-analytical method of Hamilton canonical equation for thermoelastic problems of laminated plate,a semi-analytical mixed element is developed by using the displacement method,which can be used for the static thermoelastic response analysis of composite laminated plate.The main contents of this thesis include:First,the Hamilton canonical equation theory of elastic mechanics is introduced,then the merit and demerit of the semi-analytical solution based on Hamilton canonical equation in solving plate and shell problems are analyzed.This solution has a certain oscillation in solving the displacement and stress of the plate.That is,the correlate result is not stable enough.In addition,with the increasing of mesh density,high-dimensional exponential computing requires a lot of computer time,internal storage and running speed.So it is not suitable for large-scale finite element problems.Then,based on the semi-analytical method of the Hamilton system and combined with the displacement solution which based on the principle of minimum potential energy,a novel semi-analytical solution for solving the thermoelastic problem of laminated plate is deduced.In particular,based on the principle of minimum potential energy of elastic mechanics,a functional of the principle of the minimum potential energy of the thermoelasticity is deduced.Combining the finite element which based on the principle of the minimum potential energy of the thermoelasticity and the relationship between the stress and the displacement in the Hamilton semi-analytical solution for the thermoelasticity.Then a novel semi-analytic mixed element was constructed.This novel mixed element combines the advantages of the displacement solution with semi-analytical solution of Hamilton canonical equation.At last,according to different lamination angles,boundary conditions and temperature loading forms,examples is carried out to verify the correctness of the novel semi-analytical solution in solving thermoelastic problems.The numerical examples show that this novel semi-analytical solution can effectively reduce the calculation and ensure the accuracy of displacement and stress when solving the thermoelastic problems.And it can guarantee the continuity of out-of-plane stress like the Hamilton semi-analytical method.