# A Computational Sketch-Based Approach Towards Optimal Product Design Solutions
###### Abstract  
This paper presents a numerical sketch-based methodology to achieve optimal product design solutions, bridging the gap between initial conceptual sketches and advanced engineering analyses. The proposed approach enables the transformation of simple hand-drawn sketches into digital models suitable for complex computational simulations and design optimization. Using computer vision algorithms, sketches are processed to generate digital design components that serve as inputs for Finite Element Analysis (FEA). In order to further enhance the overall design process, topology optimization (TO) is also performed, iteratively refining the geometry to achieve optimal material distribution for improved structural performance. Additionally, Adaptive Mesh Refinement (AMR) techniques are applied to ensure computational efficiency and accuracy by dynamically refining the mesh in regions of high complexity or stress concentration. The synergy of sketch-based modeling, FEA, TO, and AMR demonstrates significant potential in reducing design cycles while maintaining high-performance standards. Finally, it should be noted that the proposed pipeline consists of a fully automated procedure, hence it could reduce the learning curve for the designers, enabling companies to onboard employees faster and integrate advanced design techniques into their workflows without extensive training. The above-mentioned modules render the introduced approach particularly suitable for applications in product design development that can be utilized in several industries like mechanical, manufacturing, and furniture. s 2025 15 202  
stresses. This process often results in organic, complex shapes that may not be intuitive through traditional design methods, enabling the creation of lightweight components without compromising structural integrity [3]. By leveraging algorithms and Finite Element Analysis (FEA), TO ensures that the final design model is both functionally optimal and material efficient. During the upcoming detailed design phase, the optimized geometry will be refined and validated to certify manufacturability and accommodate the generated complex shapes. Furthermore, TO supports multi-disciplinary design goals, such as thermal management or fluid dynamics by integrating additional physics-based simulations into the optimization procedure. In industries like furniture, aerospace, automotive, and biomedical engineering, TO is a particularly valuable asset for reducing weight and material usage, which directly impacts performance and sustainability. By automating the exploration of several design possibilities and pushing the boundaries of traditional engineering fields, TO enables designers to create innovative, high-performance products that meet both functional and economic requirements [4]. Finally, it should be noted that its integration into the design process fosters a balance between creativity, efficiency, and practicality, leading to superior product outcomes. FEA is a computational-based tool widely employed during the product design process to simulate, analyze, and optimize the structural, thermal, and fluid dynamics behavior of a product under various conditions [5]. Its application begins in the early stages of design, where CAE (Computer Aided Engineering) models are developed to evaluate the performance of conceptual models, ensuring that they meet functional requirements such as strength, stiffness, and durability. By breaking down complex geometries into smaller, manageable elements, FEA allows designers to predict how a product will respond to real-world forces, vibrations, and other phenomena. This predictive capability reduces the need for physical prototyping, saving time and costs while enabling rapid iteration and refinement of designs [6]. During the detailed design phase, FEA is applied to identify potential failure points, stress concentrations, and areas of excessive deformation, guiding engineers in making informed design modifications to enhance performance and reliability.