International Journal of Computational Methods

Employing various mathematical tools in machine learning is crucial since it may enhance the learning problem’s efficiency. Dynamic systems are among the most effective tools. In this study, an effort is made to examine a kind of machine learning from the perspective of a dynamic system, i.e., we apply it to learning problems whose input data is a time series. Using the discretization approach and radial basis functions, a new data set is created to adapt the data to a dynamic system framework. A discrete dynamic system is modeled as a matrix that, when multiplied by the data of each time, yields the data of the next time, or, in other words, can be used to predict the future value based on the present data, and the gradient descent technique was used to train this matrix. Eventually, using Python software, the efficacy of this approach relative to other machine learning techniques, such as neural networks, was analyzed.

Dynamic load identification is a commonly used and quite important approach to obtain the excitation loads of structures in engineering practice. In this paper, a novel dynamic load identification method combining the least squares time element method (LSTEM), wavelet scaling function and regularization method is proposed, which performs a better accuracy and a stronger anti-noise ability. It decomposes the time history of dynamic load into a series of time elements, and approximates the load profile at each time element using wavelet scaling functions. In order to balance the accuracy and efficiency for load identification, an optimal wavelet resolution is then determined. Simultaneously, the least squares time element model is derived which establishes the forward model for computing the wavelet coefficient. Finally, the wavelet coefficients for dynamic load identification are accurately and stably solved by implementing regularization. By this method, on the one hand, the wavelet scaling function and LSTEM improve the identification accuracy, and on the other hand, the integral process in the least squares operation gains the anti-noise ability for the load identification. A numerical example of a roof structure and an experiment of a composite laminate are studied and verify the effectiveness of the proposed method.

The slender circle submarine pipeline possesses both shell and beam characteristics, which are widely used in practical engineering. Unfortunately, for some reason, there will be some geometric defects in the cross-section of the pipeline (such as machining errors and seawater corrosion, etc.), resulting in the stiffness of the circular submarine pipeline being different. The cracked variable stiffness pipeline is actually a typical three-dimensional complex crack problem. In this paper, taking the outer circle and inner ellipse submarine pipeline as an example, a method based on elementary mechanics and the concept of the conservation law is proposed to determine the stress intensity factors (SIFs) of variable stiffness pipeline, and a series of closed-form expressions of SIF are derived for the cracked pipeline. The results from the present method are shown to agree well with available solutions and FEM. In particular, the present method can also be easily applied to other similar variable stiffness submarine pipelines.

The efficiency and accuracy of the cell-based smoothed discrete shear gap (CS-DSG3) are improved in simplifying the application process of the cell-based strain smoothing technique and redefining the stabilized parameter of Stenberg’s stabilization method, respectively. In the original CS-DSG3, both the smoothed bending strain and the smoothed shear strain are derived by the cell-based strain smoothing technique. This study proves that the smoothed bending strain matrix in the original CS-DSG3 is equal to the unsmoothed bending strain matrix. Theoretically, abandoning the bending strain smoothing operation can improve the efficiency while maintaining the accuracy of the original CS-DSG3. The introduction of Stenberg’s stabilization method can boost the accuracy of shear strain in the original CS-DSG3, whereas the relationships of the stabilized parameter in Stenberg’s stabilization method with the mesh density, the thickness–span ratio, and the boundary condition are still unclear. In this study, the range of the optimal stabilized parameter for different analyses and boundary conditions is determined through the static and dynamic analysis of the plate. The new stabilized parameter is applied to static analyses, free vibration analyses, and frequency response analyses for verification and comparison, which demonstrates that it can significantly improve the accuracy of the CS-DSG3.

Finite element (FE) analysis of hybrid fiber reinforced engineered cementitious composite (hybrid-ECC) link slabs is conducted under static loading. First, the material model of hybrid-ECC is developed and validated with standard material test results. Numerical analyses are then conductedto investigate the materials’ effects on the structural performances of link slabs built by using hybrid-ECCs with different volume fractions of polyethylene (PE) and steel (ST) fibers. The FE model of the link slab is validated against test results. Analysis results suggest the hybrid-ECC with volume fractions of 1.25% PE and 0.75% ST fiber is suitable for link slab applications.

This work proposes a hybrid block numerical method of tenth order for the direct solution of fifth-order initial value problems. The formulas that constitute the block method are derived from a continuous approximation obtained through interpolation and collocation techniques. In order to obtain better accuracy, sixth-order derivatives are incorporated to develop the formulas. The main characteristics of the method are analyzed, namely, the order, local truncation errors, zero-stability, consistency and convergence. The proposed strategy performs well, as shown by some numerical examples and the corresponding efficiency curves. Compared to existing numerical methods in the literature, the proposed method is competitive and the numerical approximations it provides are significantly close to the precise solutions.