Multi-hazard stochastic time-dependent tropical cyclone fragilities for coastal structures

This paper presents a reliability-based multilattice topology optimization framework for structural design under uncertainty in material properties.Many natural and engineered materials-such as bone, wood, and polymers-possess hierarchical microstructures and spatially varying mechanical properties, enabling multifunctionality and adaptability.Inspired by these systems, architected lattice materials (also known as metamaterials) are engineered to achieve tunable mechanical performance through controlled porosity and microstructural orientation.These attributes enable the design of heterogeneous, high-performance systems that surpass the capabilities of their individual constituents.Topology optimization (TO) serves as a powerful tool for designing structures with spatially tailored material distributions and hierarchical configurations.However, computing the effective properties of lattice unit cells via homogenization at every optimization step is computationally intensive.To address this challenge, we propose a density-based TO framework that incorporates multiple lattice structures while accounting for material uncertainty.A Kriging-based surrogate modeling approach is employed to efficiently estimate the effective behavior of lattice structures across a range of relative densities, significantly reducing computational effort.Numerical examples involving multiscale lattice configurations demonstrate the feasibility and effectiveness of the proposed framework in generating lightweight, structurally robust designs under probabilistic constraints.The approach provides a scalable solution for engineering applications demanding high performance, adaptability, and resilience under uncertainty. INTRODUCTIONTopology optimization (TO) is a computational method used to determine the optimal material distribution within a given design domain, typically by minimizing structural compliance subject to constraints such as material volume, stress, or stability [1].TO has been widely applied across engineering fields, including mechanical [2], aerospace [3], biomedical [4], and civil engineering [5,6].Recent developments have extended TO to multi-material and lattice-based designs, enabling optimized spatial allocation of materials for multifunctional performance such as stiffness, energy absorption, or negative Poisson's ratio [7,8].Lattice structures, in particular, offer high stiffness-to-weight ratios and are well-suited for additive manufacturing.Their integration into TO has been explored through homogenization-based modeling [9] and more recently, through data-driven and surrogate