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a b s t r a c tIn this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method (BEM). The existing fullplane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.

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The first step in Structures Health Monitoring (SHM), are determining the location, intensity and type of damage in structures. Crack is a damage that often occurs in structural elements and may cause serious ruptures in the structure. One of the important approaches is the wavelet analysis of vibration modes structures. In this study, it has been performed the crack detection method in steel cantilever beam structure, using an optimized wavelet-based model. The wavelet analysis has been performed based on the higher orders of the structure's mode shapes. The results show that the proposed method is able to accurately detect all kinds of cracks, in which the cracks location are variable. In this study also, cracks with length of 20%, 10%, 5% and 2% of the beam's depth have been considered and one of the most prominent results is introducing a method for detecting robust and environmental noisy cracks. The proposed method is capable of accurately detecting crack in the cantilever beams in noisy conditions about 20 dB of SNR.

Geometrically nonlinear analysis is required for resolving issues such as loading causes failure and structure buckling analysis. Although numerical methods are recommended for estimating the exact solution, they lack the necessary convergence in the presence of bifurcation points, making it challenging to find the equilibrium path using these methods. Thus, the modified energy method is employed instead of the numerical method, frequently used to solve quasi-static problems with nonlinear nature and bifurcation points. The ultimate goal of this study is to determine the critical load of structures through the modified energy method rather than other methods in which the relationship between force, displacement, and constraint is used to solve the problem. This study first describes the energy method for this type of problem and then details its computational steps progressively. This method yields numerical results when applied to numerical examples such as truss and frame structures and coded in MATLAB software. These findings are compared to the analytical results. The energy method is more precise than the alternative methods and superior to the Newton–Raphson method at crossing the load–displacement curve’s bifurcation points.

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