A reliability-based robust design for structural components with a variable cross section under limited probabilistic information

In engineering design, structural components with variable cross sections are extensively employed due to their excellent mechanical properties. From a strength and stiffness perspective, structural components with a uniform cross section are not always ideal. Therefore, to effectively utilize material, variable cross section structural components with excellent properties such as high strength and stiffness are employed in many practical engineering applications. As a multi-dimensional function is required to describe the state of a variable cross section structural component, determining the locations of its dangerous cross sections is very difficult. As a result, the development of a reliability-based design for a variable cross section structural component is a complex process. Therefore, strict theoretical derivations and reasonable quantitative research are required to understand the variation pattern of the reliability of the variable cross section structural component with the coordinates to determine the locations of its dangerous cross sections. This article presents a reliability sensitivity analysis with limited probabilistic information and a reliability-based robust design variable cross section structural component. Mathematical models for reliability sensitivity analysis and reliability-based robust design of variable cross section structural components with incomplete probabilistic information are established. Reliability sensitivity analysis and reliability-based robust design methods for variable cross section structural components with non-normally distributed parameters are proposed. The article provides the changing condition of the reliability with respect to the variable cross section, describes the change rule of reliability with respect to design parameters, and provides the multi-objective optimal design model based on reliability sensitivity. The reliability index obtained using the presented method is insensitive and therefore robust. Using a numerical example, the variation curves of the reliability index and reliability of a variable cross section structural component with coordinates of variable cross section are obtained. A reliability-based robust optimal design approach for variable cross section structural components for given design reliability index conditions is provided.