Potential And Elasticity Inverse Problems Based On Cuckoo Search Algorithm

The inverse problem of mechanics has extensive engineering background and academic value.The inverse problems mainly include physical parameter identification,geometric recognition,boundary condition identification and defect detection.These problems are generally ill-posed.Therefore,it is necessary to propose a stable and effective numerical methods to solve such problems.For boundary condition inverse problems in 2-D isotropic potential,I take the steady state inverse heat conduction problem into consideration.Introducing polynomial function to approximate the unknown temperature on the inaccessible boundary,then the inverse problem of boundary condition identification is transformed into the problem of unknown polynomial coefficient recognition.The unknown temperature is retrieved by minimizing the least square error between the calculated and the measured temperature at the measured point by the cuckoo search algorithm.Introducing temperature boundary condition into the direct problem,then the unknown gradient boundary condition is obtained by using the boundary element method.The influences of element number,nest number,measurement point number,polynomial degree and measurement error are discussed.For Cauchy boundary condition inverse problems in 2-D elasticity,I apply polynomial function to approximate the unknown traction boundary conditions.The unknown tractions on the inaccessible part of the boundary are identified by minimizing the calculated and the given values of the tractions on the accessible part of the boundary through the cuckoo search algorithm.Based on the boundary element method,the unknown boundary displacements are obtained by solving the direct problem with the inversed tractions and the other known conditions.The influences of nest number,polynomial order,measurement noise and element number are discussed.The numerical results show that the accuracy of inversion results is improved by increasing the number of nests.The calculation results with and without using polynomial approximation are compared,it is proved that polynomial approximation is a more accurate and effective method to solve unknown boundary conditions.The numerical results show that increasing the number of nest,the inversion results will improve.The degree of polynomials also has a great influence on the calculation results.Choosing the right degree of polynomials can improve the accuracy and efficiency of the results.With the increase of measurement error,the accuracy of inversion results gradually decreases.With the increase of the element number,the accuracy of numerical results increases.For the parameter identification problem in 2-D elasticity,the cuckoo search algorithm is used to minimize the objective function and to realize the inversion of unknown parameters such as shear modulus,poisson's ratio,the position and size of the cavity.The influence of the number of parameters to be identified and the measurement error is discussed.It can be seen that the number of iterations increases with the increase of the number of parameters to be identified,and the accuracy of parameter identification results decreases with the increase of measurement error.