A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularit...A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.展开更多
A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of outof-plane（SH） waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space ...A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of outof-plane（SH） waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space is proposed by applying the discrete Fourier series expansions of sine and cosine functions. The semi-circular hill problem is discussed as a special case for the new formulated equation.Compared with the previous semi-circular cases solutions, the present method can give surface displacement amplitudes which agrees well with previous results. Although the proposed equation can only solve the problem of SH-waves diffracted by almost semi-circular shallow hills, the stress and displacement residual amplitudes are numerical insignificantly everywhere. Moreover, the influences of the depth-towidth ratio（a parameter defined in this paper to evaluate the shallowness of the topography of hills） on ground motions are presented and summarized. The limitations and errors of truncation from Graf’s addition theorem and Fourier series equations in the present paper are also discussed.展开更多
基金The project is supported by National Natural Science Foundation of China(No.59975025).
文摘A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
文摘A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of outof-plane（SH） waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space is proposed by applying the discrete Fourier series expansions of sine and cosine functions. The semi-circular hill problem is discussed as a special case for the new formulated equation.Compared with the previous semi-circular cases solutions, the present method can give surface displacement amplitudes which agrees well with previous results. Although the proposed equation can only solve the problem of SH-waves diffracted by almost semi-circular shallow hills, the stress and displacement residual amplitudes are numerical insignificantly everywhere. Moreover, the influences of the depth-towidth ratio（a parameter defined in this paper to evaluate the shallowness of the topography of hills） on ground motions are presented and summarized. The limitations and errors of truncation from Graf’s addition theorem and Fourier series equations in the present paper are also discussed.
