Hybrid Trefftz Finite Element Analysis Of Axisymmetric Coupled Thermal-Mechanical Problems

Thermomechanical coupling is one of important problems encountered in many model engineering fields.In these problems,thermal deformation,thermal stress and thermal strain due to the temperature change damages the devices.Generally,the thermoelasticity analysis is conducted by experimental determination,theoretical analysis and numerical simulation.For the cases of complicated geometry and boundary conditions,the numerical method has been become an indispensable research tool.In recent years,the hybrid Trefftz finite element method(HT-FEM)has attracted much attention due to the fact that it collects all the merits of conventional finite and boundary methods.Based on the particular method and under the framework of HT-FEM,this thesis investigates elasticity problems including body forces such as gravity and centrifugal force as well as the thermoelastic problems due to the thermal loading.The constructed element assumes two displacement interpolation modes: intra-element field and frame field.The intra-element field is approximated by using fundamental solutions as interpolation functions,so it is called the hybrid fundamental solution Trefftz finite element method(HFS-FEM).Mathematically speaking,like the body force,the thermal loading introduces the nonhomogeneous term into the governing equation.Due to the nonhomogeneous term,the domain integral involves in the finite element formulation.This will eliminate the inherent advantages of HFS-FEM.To overcome this difficulty,the full solution of the original problem is divided into a linear combination of homogeneous and particular solutions by means of the method of particular solution.The variational functional for the original problem is converted to that for an equivalent homogeneous problem by modifying boundary conditions.Therefore,the domain integral appeared in the finite element formulation is avoided.For thermoelastic problems,the nonhomogeneous terms in governing equations are derivatives for the temperature,so it is difficult in deriving the particular solution of displacement based on the governing equations.Therefore,we introduce a potential function for the thermoelastic displacement.In doing this,the original governing equation is converted to Poisson's equation in terms of the potential function and temperature.It becomes easier to obtain the particular solution.However,the potential function is sometimes unknown especially when the analytical solution of temperature is complicated or does not exist.The temperature field is first approximated in terms of polynomial function.And then,the potential function is obtained based on Poisson's equation.Several classical examples are provided for the validation of HFS-FEM.Compared to the commercial software ABAQUS,the proposed method exhibits stronger immunity to mesh distortion.For the above analysis,some solving models are selected as numerical examples to evaluate the effectiveness of the proposed hybrid fundamental solution Trefftz finite element method.Then,the numerical results are given and compared with other solution to demonstrate the accuracy,higher efficiency.Comparing the solution obtained by the finite element method with the analytical solution or the calculation result of ABAQUS,the accuracy and efficiency of the method are shown.In addition,for the mesh is adjusted to the distortion mesh that cannot be processed by the conventional finite element,the results of hybrid fundamental solution Trefftz finite element method show a good mesh distortion immunity...