The Effect of Nodal Deviation on the Reliability Performance of the Optimized Free-Form Single-Layer Reticulated Shell

The free-form single-layer reticulated shell structure has the characteristics of complex shape, a high degree of static indeterminacy, and difficult node positioning in the construction process, and the nodal deviations that may occur in the construction stage have a significant impact on the reliability performance of the structure. In order to evaluate the influence of the nodal deviation on the reliability performance of the structure in the process of shape optimization, this paper takes the free-form surface of the rectangular plane as the initial structure. Shape optimization is carried out with the objective function of minimizing the strain energy under the uniform vertical load, and the influence of the nodal deviation on the reliability performance of the optimized structure is performed by analyzing changes in the structural response’s probability density function (PDF). The elastic modulus, yield strength, and nodal deviation of the material were selected as the basic random variables, and the PDF of the structural response was calculated using the probability density evolution method. In the case of considering and ignoring the nodal deviation, respectively, the PDF of the maximum displacement response of the structure under the same iteration step is calculated and compared. The results indicate that compared with the initial structure, the reliability performance of the optimized structure is significantly less sensitive to node deviations.