PhD Final Defense – Sebastian Pozo Ocampo

Topology Optimization of Building-Type Structures Under Seismic Excitation

Advisor: Professor Billie F. Spencer Jr.

Abstract 

This dissertation advances topology optimization toward the seismic design of building-type structures. While topology optimization has become a powerful tool for generating efficient structural layouts, its direct use in building design remains limited by three major challenges: simplified structural representations, the computational cost of stochastic dynamic analysis, and the need to evaluate performance under realistic seismic demands. This work addresses these challenges through a sequence of computational developments that progressively increase the physical relevance of optimized structural layouts while preserving the efficiency required for large-scale design studies.

The first part of the dissertation focuses on structural representation. A minimum-thickness, or 2.5D, topology optimization formulation is developed to bridge the gap between conventional two-dimensional density-based optimization and full three-dimensional topology optimization. By treating element thickness as a design variable, the method captures meaningful out-of-plane material variation while retaining the computational cost of a two-dimensional model. This provides layouts that are easier to interpret as building components and establishes an efficient modeling basis for the more demanding stochastic formulations that follow.

The second part introduces covariance-based topology optimization for structures subjected to seismic excitation. Building on stochastic response analysis, stationary ground motion is modeled through filtered white noise and response statistics are computed using Lyapunov equations. Efficient adjoint sensitivities and dynamic reduction make the approach feasible for building-scale problems. The framework is then extended to nonstationary excitation, allowing the time-varying nature of earthquake intensity to be included directly in the optimization process. These developments shift the design objective from static stiffness toward seismic performance measures such as inter-story drift.

The final part incorporates nonlinear energy-dissipation devices and multi-intensity performance constraints. Equivalent linearization enables the simultaneous optimization of the primary structural topology and supplemental protective components, while the performance-based extension evaluates designs across multiple seismic demand levels.

Overall, this dissertation shows that seismic topology optimization can evolve from an idealized layout-generation tool into a computational framework for performance-oriented conceptual design. By combining efficient structural modeling, stochastic response analysis, nonlinear protective systems, and multi-intensity constraints, the work provides a foundation for optimized building layouts that better reflect the demands of earthquake-resistant design.