Nonlinear eigenvalue topology optimization for structures with frequency-dependent material properties

Eigenvalue topology optimization problem has been a hot topic in recent years for its wide applications in many engineering areas. In the previous studies, the applied materials are usually assumed as elastic, and the resulting structural eigenfrequencies are obtained by solving a linear or quadratic eigenvalue problem. However, many engineering materials, such as viscoelastic materials, have frequency-dependent modulus, which results in a more complicated nonlinear eigenvalue problem. This paper presents a systematic study on the nonlinear eigenvalue topology optimization problem with frequency-dependent material properties. The nonlinear eigenvalue problem is solved by a continuous asymptotic numerical method based on the homotopy algorithm and perturbation expansion technique, which involves higher-order differentiation of the nonlinear term and shows a fast convergence. Several schemes are proposed to improve the computational accuracy, applicability, and robustness of the method for the application in topology optimization, including Faà di Bruno's theorem, bisection method, and inverse iteration based eigenvector modification method. Three optimization problems are solved to demonstrate the effectiveness of the developed methods, including the maximization of the fundamental frequency, the eigenfrequency separation interval between two adjacent eigenfrequencies of given orders, and the eigenfrequency separation interval at a given frequency. Numerical examples show the large influence of the frequency-dependent material properties on the optimized results and validate the effectiveness of the developed method

Application of high-precision 3D seismic technology to shale gas exploration: A case study of the large Jiaoshiba shale gas field in the Sichuan Basin

The accumulation pattern of the marine shale gas in South China is different from that in North America. The former has generally thin reservoirs and complex preservation conditions, so it is difficult to make a fine description of the structural features of shale formations and to reflect accurately the distribution pattern of high-quality shale by using the conventional 2D and 3D seismic exploration technology, which has an adverse effect on the successful deployment of horizontal wells. In view of this, high-precision 3D seismic prospecting focusing on lithological survey was implemented to make an accurate description of the distribution of shale gas sweet spots so that commercial shale gas production can be obtained. Therefore, due to the complex seismic geological condition of Jiaoshiba area in Fuling, SE Sichuan Basin, the observation system of high-precision 3D seismic acquisition should have such features as wide-azimuth angles, small trace intervals, high folds, uniform vertical and horizontal coverage and long spread to meet the needs of the shale gas exploration in terms of structural interpretation, lithological interpretation and fracture prediction. Based on this idea, the first implemented high-precision 3D seismic exploration project in Jiaoshiba area played an important role in the discovery of the large Jiaoshiba shale gas field. Considering that the high-quality marine shale in the Sichuan Basin shows the characteristics of multi-layer development from the Silurian system to the Cambrian system, the strategy of shale gas stereoscopic exploration should be implemented to fully obtain the oil and gas information of the shallow, medium and deep strata from the high-precision 3D seismic data, and ultimately to expand the prospecting achievements in an all-round way to balance the high upstream exploration cost, and to continue to push the efficient shale gas exploration and development process in China