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This paper explores the application of structural tessellation in architectural and structural design, where surfaces or spaces are divided into smaller repeating shapes or units to create aesthetic and functional structures. Structural tessellation offers various advantages, including improved stability, increased load-bearing capacity, and enhanced aesthetic appeal. The growing use of digital tools and advanced numerical algorithms has facilitated the creation of complex and intricate tessellations that can be tailored to suit specific project requirements. This research focuses on algorithmic methods for generating tessellations and their utilization in structural engineering and design optimization. Diverse patterns and configurations of tessellation are investigated through mesh generation algorithms, parametric approaches, and pattern gradation and repetitions, with data visualization accomplished using computing scripts and Grasshopper. The tessellation elements are employed to discretize the design domain in structural optimization and create initial patterns. The paper demonstrates the feasibility of proposed frameworks for structural design and application through the examination of various numerical examples. In conclusion, the strategic use of structural tessellation proves to be effective in producing unique and functional structures that seamlessly combine visual appeal with material and resource efficiency.

The recent advancements in theories and numerical methods of engineering optimization have paved the way for the widespread application of computational techniques in architectural and structural design, as well as software development. This paper is focused on exploring the practical implementation of various optimization strategies within architectural and structural design contexts. By utilizing mesh generation algorithms, intricate geometries inherent to architectural and structural design can be systematically constructed and discretized, facilitating analysis, design, and optimization processes. In the domain of grid-shell design, achieving optimal and aesthetic forms while adhering to engineering constraints is essential. This research explores grid-shell form finding and optimization, using a potential energy-based algorithm to reach equilibrium in grid-shell structures. Subsequent size optimization addresses stress and buckling concerns to ensure structural robustness. For long-span structures, often desired for their creation of expansive spaces and incorporation of architectural design principles, structural performance optimization is achieved using topology optimization. This study explores multiple manufacturing constraints embedded within topology optimization to enhance the feasibility of realizing topologically optimized material configurations. Another area of engineering optimization is in roof truss and frame design, aimed at creating distinctive and aesthetically pleasing configurations beyond traditional forms while meeting engineering load combinations and design criteria. To generate unique forms for roof truss structures, the genetic algorithm is employed in this study. This algorithmic approach facilitates diverse geometrical configurations while maintaining required strength and serviceability criteria. Through these studies, the paper highlights the transformative potential of optimization methodologies in shaping innovative architectural and structural designs with enhanced efficiency and functionality. [ABSTRACT FROM AUTHOR]