A Solution Method For Solving Inverse Mechanics Problems Based On ABAQUS And Complex Variable Differentiation Method

With the development of numerical methods and computer science technology,the research objects of solid mechanics are becoming more and more diverse,including many complex nonlinear problems.In many engineering fields,the research on the direct problem of solid mechanics has not been able to meet all demands.In some cases,the reasons for the change of the response of the known structure are to be explored,and inverse solid mechanics problem are to be solved.Based on the known deformation or displacement of the structure,the material properties of the structure,the boundary of the structure,or the unknown shape inside the structure can be obtained by solving inverse problems.Considering that existed methods for solving inverse problems are lack of adaptivity to large engineering structures,this thesis presents a new method for solving nonlinear inverse solid mechanics problems,which is based on commercial finite element software secondary development,and multiple parameters are inverted.First,for nonlinear power-hardening elasticoplasticity materials in this thesis,according to the characteristics of the material,the process of the finite element static analysis is given.Then,the corresponding UEL(user element subroutine)and UMAT(user material subroutine)programs of ABAQUS are developed based on the above theory,guaranteeing the static analysis of power-hardening elasticoplasticity material is with high accuracy.At the same time,in order to increase the inversion accuracy,based on real variable UEL,the complex variable derivation method(CVDM)is introduced to establish a kind of element which could not only effectively simulate elasticoplasticity materials,but also could accurately calculate the sensitivity coefficients providing the key parameters for gradient inversion algorithms.Then,the inverse plane strain problem is used as an example to verify the inversion method.After verifying the calculation accuracy of the complex variable element,the unknown material constitutive parameters and boundary conditions are simultaneously inverted by solving the inverse problem.The effects of initial values and measurement errors on the inversion process and results are explored.In order to verify the versatility,another calculation example with different structure and boundary conditions is selected.The results prove that the inversion algorithm still has good characteristics.Finally,a three-dimensional calculation example with an engineering background is used to verify the inversion algorithm.After verifying the accuracy of the complex variable element,multiple parameters of the three-dimensional structure ae inverted to validate the accuracy and efficiency of the algorithm.Meanwhile,the effects of initial values,the number of measurement points and the random errors are studied.Finally,the inversion of the boundary conditions with the functional form is also carried out.Research shows that the algorithm is still effective for parameter identification of such boundary conditions.