| The inverse heat conduction problem is a typical ill-posed problem,which has been widely used in aerospace,nuclear power engineering,biological medicine,metallurgy,casting,and other fields.Because of its extensive application background,researchers have conducted indepth research on this kind of problems and a variety of methods have been proposed.The gradient methods have high precision and fast convergence speed,which have obvious advantages in engineering applications.In this kind of methods,it is very important to accurately determine the sensitivity matrix.However,for nonlinear inverse problems,it is difficult to accurately calculate the sensitivity matrix coefficients.The complex-variabledifferentiation-method has been applied to accurately calculate sensitivity coefficients.However,in the previous studies,this method needs in-house program codes to solve the direct problem,which can't be combined with commercial software.In this thesis,a complex variable finite element is constructed by ABAQUS user element subroutine(UEL),by which sensitivity coefficients could be accurately calculated during the process for solving the direct heat conduction problem.The transient nonlinear heat conduction problems are solved by using the complex variable finite element to verify the accuracy and effectiveness of the complex variable finite element.Then,the Levenberg-Marquardt algorithm is used to establish the inverse programs,and the two-dimensional and three-dimensional transient nonlinear inverse heat conduction problems are solved,respectively.Numerical examples are given to validate the accuracy and efficiency of the proposed method,and the influence of initial values and measurement errors on the inversion results is studied.Finally,the method is extended to solve the inverse heat conduction problem with phase change,and the accuracy,efficiency,stability and robustness of the method are verified,which further indicates that the method has good universality and expansibility. |
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