arXiv subjects

Barbara Gronostajska

Publications and source records attributed to Barbara Gronostajska.

3 recordsLinked to original sources

arXiv2026

Optimizing the Geometry of an L-Shaped Building to Enhance Energy Efficiency and Sustainability

The geometric form of a building strongly influences its material use, heat losses, and energy efficiency. This paper presents an analytical optimization of L-shaped residential buildings aimed at minimizing the external surface area for a prescribed volume. Both symmetric and asymmetric configurations are examined under realistic design constraints, including fixed or bounded wing aspect ratios and fixed building height. Using explicit optimization methods and Karush-Kuhn-Tucker conditions, closed-form expressions for the optimal geometric parameters and minimal envelope area are derived. The results show that unconstrained optimization leads to degenerate cuboid shapes, highlighting the importance of geometric constraints to preserve the L-shaped form. The obtained results provide practical design guidelines for architects and engineers, supporting informed early stage decisions that balance functional requirements, regulatory constraints, architectural intent, and energy performance. Case studies of existing houses demonstrate that the proposed approach can reduce external surface area or confirm near-optimality of practical designs, supporting energy-efficient early-stage architectural decisions.

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arXiv2026

From geometry to sustainability: Optimal shapes of hip roof houses

In this paper, we develop a rigorous mathematical framework for the optimization of hip roof house geometry, with the primary goal of minimizing the external surface of the building envelope for a given set of design constraints. Five optimization scenarios are systematically analyzed: fixed volume, fixed footprint ratio, fixed slenderness ratio, fixed floor area, and constrained height. For each case, explicit formulas for the optimal dimensions are derived, offering architects and engineers practical guidelines for improving material efficiency, reducing construction costs, and enhancing energy performance. To illustrate the practical relevance of the theoretical results, case studies of real-world hip roof houses are presented, revealing both inefficiencies in common practice and near-optimal examples. Furthermore, a freely available software application has been developed to support designers in applying the optimization methods directly to architectural projects. The findings confirm that square-based footprints combined with balanced slenderness ratios yield the most efficient forms, while deviations toward elongated or flattened proportions significantly increase energy and material demands. This work demonstrates how mathematical modeling and architectural design can be integrated to support sustainable architecture, providing both theoretical insight and practical tools for shaping energy-efficient, cost-effective, and aesthetically coherent residential buildings.

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arXiv2026

Designing sustainable barn-type houses: Optimal shapes for minimal envelope and energy use

Barn-type houses have become one of the most popular single-family housing typologies in Poland and across Europe due to their simplicity, functionality, and potential for energy efficiency. Despite their widespread use, systematic methods for optimizing their geometry in terms of envelope area and energy performance remain limited. This paper develops a rigorous mathematical framework for determining the optimal proportions of barn-type houses with respect to minimizing the external surface area while satisfying constraints of either fixed volume or fixed floor area. Closed-form solutions for the optimal width, length, and height are derived as explicit functions of the roof slope, together with formulas for the minimal achievable surface. A recently introduced dimensionless compactness measure is also calculated, allowing quantitative assessment of how far a given design deviates from the theoretical optimum. The methodology is applied to case studies of three existing houses, showing that while some designs deviate significantly from optimal compactness, others already closely approximate it. The results confirm that theoretical optimization can lead to meaningful reductions in construction costs and energy demand. To support practical implementation, two original freely available software tools were developed, enabling architects and engineers to perform optimization analyses.

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