Innovative load-bearing designs depend on a careful balance between creative shape and structural performance. While existing preference-based topology optimization methods let designers add subjective preference, they pose high design experience barriers and suffer from inefficient interactions due to reliance on skilled manual sketching. In this study, we propose the bidirectional evolutionary structural optimization with skeleton control (SC-BESO) method. This method begins with extracting the skeleton graph of an existing design, where users can subjectively drag its skeletal nodes to deform the design. The deformed design is then used to guide the generation of its optimized structural design. A design parameter allows users to adjust the optimized result toward either performance-driven or preference-driven outcomes. Based on the proposed method, a cross-platform digital design tool, TouchBESO, is developed for 2D structural designs. Parametric studies show that, even after user interaction that results in stiffness reduction, the SC-BESO method can regain most of the lost performance with only small shape changes. Furthermore, a 3D cantilever example illustrates the scalability of the method, and two potential integrations with drawing systems and the similarity constraint are discussed for future interactive design frameworks.

Innovative load-bearing structures often emerge from a fine balance between creative forms and engineering principles. While preference-based topology optimization methods have advanced structural design by considering designers’ geometric preferences, they struggle with visualizing and editing complex 3D details crucial for diverse design options. To overcome this bottleneck, here we propose the improved bidirectional evolutionary structural optimization considering subjective preferences (ISP-BESO) method. This method introduces a similarity constraint that enables precise control over subjective preferences in optimized structures. Then, a design exploration strategy is proposed by integrating virtual reality (VR) with topology optimization for the interactive creation of desirable 3D structures. The strategy employs VR sculpting to offer immersive visualization and real-time feedback, guiding material redistribution during optimization. This workflow can iteratively produce innovative and efficient structures. Adjusting target similarity in ISP-BESO steers designs toward performance-driven or preference-driven outcomes. A museum design example demonstrates the practical potential of this strategy. • A novel preference-based topology optimization method is proposed. • The proposed method can control the influence of preferences on optimized structures. • A design exploration strategy is proposed by combining VR with topology optimization. • The strategy can iteratively perform sculpting and optimization to design structures. • A VR-based digital design tool integrating the proposed strategy is developed.

We present a method to approximate free-form surfaces using assemblies of rotational patches for architectural rationalization. Rotational surface patches inherently allow for the simultaneous repetition of multiple building elements along the arc direction. By assembling multiple patches, we can create diverse free-form-like geometries to satisfy broad design intents, while preserving local symmetry to enable cost-effective element fabrication. The main challenge lies in the strict constraint of maintaining local rotational symmetry, while ensuring the final tessellated form is seamless, smooth, and closely resembles the target surface. To address this, we propose a patch layout creation approach that segments the input surface into patches, resembling untrimmed rotational patches within a prescribed error threshold. Additionally, we develop a B-spline-based optimization framework to refine the fitted rotational patches for smooth connections and faithful surface approximation. To facilitate practical architectural applications, we provide a post-processing tool that converts the discrete patch assembly into a seamless, smooth quad mesh composed of locally repeated elements. We demonstrate that our approach is applicable to a variety of free-form surfaces, including those that mimic iconic architectural designs, and can address various practical requirements for a wide range of application scenarios.

Free-form structures are highly valued for their aesthetic appeal in architecture, but they typically comprise panels of many different shapes, which can pose great challenges for building construction. In this study, we aim to address this issue by proposing a novel clustering-optimization method to reduce the number of different n-gonal faces in free-form surface approximations. The method partitions the faces into several groups of similar shapes through clustering and transforms the ones within each group toward congruent forms through optimization. By utilizing this approach, the number of geometrically different panels can be reduced while also satisfying a user-specified error threshold. The potential practical application of this method is demonstrated by redesigning the façade of a real architectural project to achieve cost-effective solutions.