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The purpose of this study is to evaluate the long-term vertical deformations of segmented pre-tensioned concrete bridges by a new approach. It provides a practical and reliable method for calculating the amount of long-term deformation based on creep and shrinkage in segmented prestress bridges. There are various relationships for estimating the creep and shrinkage of concrete. The analytical results of existing models can be very different, and the results are not reliable. In this paper, the different existing relationships are written in MATLAB software. After calculation, the values of the creep and shrinkage are stored. Then a sample bridge is simulated in the CSI-Bridge software, and different values of creep and shrinkage are allocated separately. Therefore, the data are analyzed, and its maximum deformation value is extracted at a critical span (D_v-max). Assigning different amount of creep and shrinkage to the model results in different values  of D_v-max. In the next step, all D_v-max values  resulting from the change in creep and shrinkage contents should be re-introduced to MATLAB code to perform the calculation of the failure curve, and extract the corresponding D_v-max values at 95% probability. In a new approach, fragility curves are used to obtain the corresponding creep and shrinkage values corresponding to the desired probability percentage. Thus, instead of simulating several models, only one model is simulated. The results of the analysis of a bridge sample in this study indicate acceptable accuracy of the proposed solution for the 95% probability.

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This study investigates the geometrical and material design aspects of functionally graded (FG) doubly-curved shells. The FG material system comprises a combination of metal and ceramic constituents, and the effective properties across the shell thickness are estimated using Voigt’s rule of mixtures. To analyze the structural behaviour, the finite element method is employed within the framework of third-order shear and normal deformation theories. The grey wolf optimization (GWO) algorithm is implemented to achieve design optimization. The objective function aims to minimize both the maximum displacement and the fundamental dimensionless natural frequency in each optimization process individually. The findings indicate that under highly constrained boundary conditions, the curvature parameters remain constant. Conversely, for less constrained conditions, the parameter R₂ assumes a value approximately ten times greater than R₁.