<p>Beyond static topology optimization for stiffness performance, considering strength constraints, dynamic issues, and inherent uncertainties is crucial for structural design. This study proposes a novel interval sequential optimization and time-variant reliability assessment (ISOTRA) framework for topology design with dynamic stress constraints and uncertainty inputs. Within this framework, the interactive completion of time-invariant interval reliability-based topology optimization (IRBTO) and non-probabilistic time-variant reliability (NTR) evaluation is pursued. To address the stress singularity and huge constrain problems during topological updating, we first employ P-norm stress aggregation and q-p relaxation methods. To appropriately characterize the transient uncertainty accumulation, we develop an interval process model and determine the time-varying boundary rules for aggregated stress functions using the set-theoretical Kriging surrogate method (SKSM). Additionally, a novel NTR index based on the set intersection principle and the second-order narrow bounds theory is defined for stress safety monitoring within the ISOTRA strategy. Furthermore, the design sensitivity analysis of the time-invariant reliability measure is discussed. Finally, numerical examples are provided to illustrate the reasonability and validity of the proposed methodology. Our findings suggest that different design concepts will yield different optimized structures, and the proposed design framework can achieve more robust topological configurations without stress concentration effects.</p>