Josephine Voigt Carstensen

arXiv2026

Minimum Carbon Trusses: Constructible Multi-Component Designs with Mixed-Integer Linear Programming

Truss optimization is a rich research field receiving renewed interest in limiting the carbon emissions of construction. However, a persistent challenge has been to construct highly optimized and often complex designs. This contribution formulates and solves new mixed-integer linear programs that enable consideration of the interplay between environmental impact and constructability. Specifically, the design engineer is enabled to design with multiple materials and/or structural components, apply separate minimum and maximum cross-sectional area bounds, and constrain the complexity of the structural connections. This is done while explicitly considering compatibility and constitutive laws. The results demonstrate that the lowest embodied carbon designs change significantly when constructability constraints are applied, highlighting the need for an integrated optimization approach. In one example, introducing a lower-carbon material option has almost no effect on the environmental performance, whereas another sees an improvement of nearly 29%. The extensibility of the formulation to design with three component types and additional constraints is demonstrated for a prestressed tensegrity example.

cs.CE↗

arXiv2020

Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection

We present a strategy grounded in the element removal idea of Bruns and Tortorelli [1] and aimed at reducing computational cost and circumventing potential numerical instabilities of density-based topology optimization. The design variables and the relative densities are both represented on a fixed, uniform finite element grid, and linked through filtering and Heaviside projection. The regions in the analysis domain where the relative density is below a specified threshold are removed from the forward analysis and replaced by fictitious nodal boundary conditions. This brings a progressive cut of the computational cost as the optimization proceeds and helps to mitigate numerical instabilities associated with low-density regions. Removed regions can be readily reintroduced since all the design variables remain active and are modeled in the formal sensitivity analysis. A key feature of the proposed approach is that the Heaviside functions promote material reintroduction along the structural boundaries by amplifying the magnitude of the sensitivities inside the filter reach. Several 2D and 3D structural topology optimization examples are presented, including linear and nonlinear compliance minimization, the design of a force inverter, and frequency and buckling load maximization. The approach is shown to be effective at producing optimized designs equivalent or nearly equivalent to those obtained without the element removal, while providing remarkable computational savings.

math.NA↗