Research has focused on creating new methodologies such as supervised machine learning algorithms that can easily calculate the mechanical properties of fiber-reinforced concrete. This research aims to forecast the flexural strength (FS) of steel fiber-reinforced concrete (SFRC) using computational approaches essential for quick and cost-effective analysis. For this purpose, the SFRC flexural data were collected from literature reviews to create a database. Three ensembled models, i.e., Gradient Boosting (GB), Random Forest (RF), and Extreme Gradient Boosting (XGB) of machine learning techniques, were considered to predict the 28-day flexural strength of steel fiber-reinforced concrete. The efficiency of each method was assessed using the coefficient of determination (R²), statistical evaluation, and k-fold cross-validation. A sensitivity approach was also used to analyze the impact of factors on predicting results. The analysis showed that the GB and RF models performed well, and the XGB approach was in the acceptable range. Gradient Boosting showed the highest precision with an R² of 0.96, compared to Random Forest (RF) and Extreme Gradient Boosting (XGB), which had R² values of 0.94 and 0.86, respectively. Moreover, statistical and k-fold cross-validation studies confirmed that Gradient Boosting was the best performer, followed by Random Forest (RF), based on reduced error levels. The Extreme Gradient Boosting model performance was satisfactory. These ensemble machine learning algorithms can benefit the construction sector by providing fast and better analysis of material properties, especially for fiber-reinforced concrete.

An extension has been made to the popular Galerkin method by integrating the weighted equation of motion over the time of one period of vibrations to eliminate the harmonics from thee deformation function. A set of successive equations of coupled higher-order vibration amplitudes is resulted, and a nonlinear eigenvalue problem is obtained for the frequency-amplitude dependence of nonlinear vibrations with successive displacements. The subsequent solutions of vibration frequencies and deformation are consistent with other successive approximate methods, such as the harmonics balance method. This is an extension of the Galerkin method which has broad applications for asymptotic solutions, particularly for problems in solid mechanics. This extended Galerkin method can also be utilized for the analysis of free and forced nonlinear vibrations of structures as a new technique with significant advantages in calculations.

For the optimal design and accurate prediction of structural behavior, the nonlinear analysis of large deformation of elastic beams has broad applications in various engineering fields. In this study, the nonlinear equation of flexure of an elastic beam, also known as an elastica, was solved by the Galerkin method for a highly accurate solution. The numerical results showed that the third-order solution of the rotation angle at the free end of the beam is more accurate and efficient in comparison with results of other approximate methods, and is perfectly consistent with the exact solution in elliptic functions. A general procedure with the Galerkin method is demonstrated for efficient solutions of nonlinear differential equations with the potential for adoption and implementation in more applications.

This paper proposed a new method for modelling joints, using anisotropic plate elements and elastic bar elements to address the issue that joints between panels are usually disregarded in numerical modelling. For small-scale deep excavations, which are frequently performed in the construction of various working shafts but have not been sufficiently studied, two numerical models were developed, using the No.1 Shaft of Tongtu Road Utility Tunnel in Ningbo, China, as a research object. One model considered the joints between the panels as proposed, while the other disregarded the joints as conventional. In comparison to the conventional method, the proposed method was validated due to yielding wall displacements that closely matched the results of the field monitoring, with a notable reduction in the error observed in the calculated displacements for the short side of the excavation. Furthermore, 34 numerical models were developed in order to investigate the influence of excavation length, depth, and diaphragm wall thickness on the relative differences between the calculated displacements obtained by the two models. The results of this study can provide references for the development of finite element models for designing small-scale deep excavation.

Piezoelectric crystals are widely used for acoustic wave resonators of different functioning modes and types including BAW and SAW. It is well-known that only some special orientations of crystals will exhibit desirable properties such as mode couplings, thermal stability, acceleration sensitivity, and others that are important in design and applications of resonators. With extensive studies on physical properties in last decades and increasing industrial needs of novel products, it is necessary to comb the known knowledge of quartz crystal material for novel orientations and better products. With known elastic, piezoelectric, dielectric, and thermal constants, we can establish the relationships between vibrations and bias fields such as temperature to ensure a resonator immunizing from excessive response to changes causing significant degradation of resonator properties and performances. Since the theoretical framework of wave propagation in piezoelectric solids is known, we need to use the existing data and results for the validation of current orientations in actual products. Through rotations, we calculated physical properties as functions of angles and bias fields, enabling the calculation of resonator properties for the identification of optimal cuts.