Study On Performance Of Variable Gradient Functionally Graded Plate Based On Fast Calculation Method

As one of the new materials,functionally gradient material has a wide range of application fields.With the deepening of application,the single functionally gradient material has gradually been unable to meet the actual needs in the complex and changeable environment.Therefore,it is of great significance to study the performance of functionally gradient plate with variable gradient parameters.In this paper,the heat transfer and dynamic properties of functionally graded plate with variable gradient parameters are studied and discussed by using a fast calculation method.In the second chapter,the three-dimensional model of the functional graded plate is simplified into the two-dimensional model,and the model is described.The variable gradient parameter model of power function type and exponential function type is compared.In order to satisfy the application under multiple conditions,the exponential model is selected to study the variable gradient parameters.Secondly,by changing the gradient parameters,the change of the material volume fraction in the functional graded plate is obtained.Finally,the physical model of the functional graded plate with variable gradient parameters was described,and the heat transfer model is established based on the mixed numerical method,and the dynamic model is established based on the strip element method.In the third chapter,the heat conduction problem of functionally graded plates with variable gradient parameters under H(t)heat source is studied based on the established model and the hybrid numerical method.The weighted residual value equation of heat conduction under thermal boundary conditions is considered,and the temperature distribution under the load of H(t)heat source is calculated by using Fourier transform and inverse transform,and the rationality and correctness of the mixed numerical method are verified by the finite element simulation experiment.The results show that the gradient parameter has a great influence on the temperature distribution,but with the increase of the gradient parameter,the influence of the parameter on the temperature distribution gradually decreases,when the gradient parameter reaches a certain critical value,the temperature does not change.By comparing the temperature distributions of the upper and lower surfaces,the temperature decreases gradually and approaches zero with the increase of the distance between the heat sources,which indicates that the influence of the heat sources on the plate is local and in accordance with Saint Venant's principle.The variation law of the temperature distribution on the lower surface of the functionally graded board with gradient parameters is discussed,and the gradient parameters with the best thermal insulation effect are obtained.In the fourth chapter,dynamical problem of functionally graded plates with variable gradient parameters under harmonic loading is studied by means of the strip element method.By establishing the dynamic theoretical model and the strip element method model of the functionally graded plate with variable gradient parameters,the displacement responses of the plate with different gradient parameters under non-fixed boundary conditions and fixed boundary conditions are calculated,and the rationality and accuracy of the theory of strip element method are verified by finite element simulation experiment.The results show that under the non-fixed boundary condition,the displacement of the functionally gradient plate decreases with time and gradually approaches zero,which is in accordance with the general law of Saint Venant's principle.With the increase of the gradient parameters,the displacement response increases first and then slows down.Under the fixed boundary condition,the displacement of the functionally graded plate along the thickness direction is in a harmonic form,and with the increase of the gradient parameters,the fluctuation period of the displacement increases with time,and the displacement peak also increases gradually.By comparing the relationship between the displacements of the upper,middle and lower surfaces and the gradient parameters at different positions,the peak displacement of the functional gradient plate increases with the increase of the gradient parameters,but the displacement trend decreases.The displacement perpendicular to the direction of load gradually approaches zero along the x-axis,and the peak displacement appears in the middle of the functionally graded plate.