Researches On The Complex Variable Reproducing Kernel Particle Methods For Several Kinds Of Inverse Problems

The inverse problem is an important topic in the fields of science and engineering.Comparing with the direct problems,the inverse problems are much more complicated.The reproducing kernel particle method(RKPM)is one of the most widely used meshless methods.The complex variable reproducing kernel particle method(CVRKPM)has higher computational accuracy and efficiency than the RKPM because that the approximation function of a two-dimensional problem is obtained using the one-dimensional basis function.In this paper,the CVRKPM is used to form the approximation function,and the CVRKPM for variable coefficient advection-diffusion problems,the inverse heat conduction problems,the inverse elasticity problems and the inverse elastoplasticity problems is presented.The detail research work is as follows.Based on the approximation function of the CVRKPM,the CVRKPM for the variable coefficient advection-diffusion problems is presented,and the corresponding formulae are obtained.The advantage of the method is that the number of nodes is fewer,then the computational cost is fewer than that of the traditional RKPM under the same computational precision,and the computational precision is higher under the same node distributiom.On the basis of the direct heat conduction problems,the CVRKPM is applied to solve the inverse heat conduction problems with source parameters.Combining with the Galerkin weak form of transient heat conduction problems,the CVRKPM for inverse heat conduction problems is investigated,and the corresponding formulae are obtained.Based on the approximation function of the CVRKPM,the CVRKPM for inverse elasticity problems is presented on the basis of the CVRKPM for elasticity problems,and the corresponding formulae are obtained.The advantages of the method are of higher precision compared with RKPM.The CVRKPM for inverse elasticity problems has greater precision than the contraditional RKPM.Based on the approximation function of the CVRKPM,the CVRKPM for inverse elastoplasticity problems is presented,and the corresponding formulae are obtained.The CVRKPM for inverse elastoplasticity problems has greater precision than the contraditional RKPM.In order to show the efficiency of the CVRKPM in the dissertation,the MATLAB codes of the methods above have been written.Some numerical examples are provided,and the validity and efficiency of these methods are demonstrated.