CivilAche

Reliability-Based Structural Design Optimization (RBSDO) evaluates the performance and safety of structural systems under inherent uncertainties in material properties, geometric dimensions, and applied operational loads. Unlike conventional deterministic design approaches that rely on empirical safety factors, RBSDO quantifies failure probabilities through probabilistic limit state functions, ensuring structural efficiency and cost minimization while satisfying target reliability index thresholds. The structural performance is governed by a Limit State Function $g(\mathbf{X})$, where $\mathbf{X} = \{X_1, X_2, \dots, X_n\}^T$ is a vector of random resistance ($R$) and load ($S$) variables: $$g(\mathbf{X}) = R(\mathbf{X}) - S(\mathbf{X})$$ The structural safe domain is defined by $g(\mathbf{X}) > 0$, the failure domain by $g(\mathbf{X}) $$P_f = \iint \dots \int_{g(\mathbf{X}) \le 0} f_{\mathbf{X}}(x_1, x_2, \dots, x_n) \, dx_1 \, dx_2 \dots dx_n$$ Under the First-Order R...