In multi-scale topology optimization methods, the analysis encompasses two distinct scales: the macro-scale and the micro-scale. The macro-scale refers to the overall size and dimensions of the structural domain being studied, while the micro-scale pertains to the periodic unit cell that constitutes the macro-scale. This unit cell represents the entire structure or component targeted for optimization. The primary objective of this research is to present a simplified MATLAB code that addresses the multi-scale concurrent topology optimization challenge. This involves simultaneously optimizing both the macro-scale and micro-scale aspects, taking into account their interactions and interdependencies. To achieve this goal, the proposed approach leverages the Bi-directional Evolutionary Structural Optimization (BESO) method. The formulation introduced in this study accommodates both cellular and composite materials, dealing with both separate volume constraints and the utilization of a single volume constraint. By offering this simplified formulation and harnessing the capabilities of the multi-scale approach, the research aims to provide valuable insights into the concurrent optimization of macro- and micro-scales. This advancement contributes to the field of topology optimization and enhances its applications across various engineering disciplines.

This study aims to describe the numerical modeling and nonlinear finite element analysis of typical spinal braces as a first step towards optimizing their topology for 3D printing. Numerical simulation was carried out in Abaqus CAE software Version 2021, utilizing a CAD (Meshmixer Version 3.5.474) scan of an actual spinal brace. Boundary conditions were defined by means of contact surfaces between the human body and the supporting pads located in the interior of the brace. The process of tightening the straps on the rear face of the brace was simulated via appropriate imposed displacements. The response is described through the deformations and developing stresses of the brace and the contact pressures in the areas of interaction with the human body. Parametric analysis indicated that increasing the cross-sectional thickness or elastic modulus of the brace material results in higher maximum von Mises stresses and lower displacements. The comparison between 3D-printed and conventional braces highlighted the potential of 3D-printing technology to achieve comparable performance with customized designs, leveraging the constitutive properties of 3D-printed material obtained from tension tests. The tension tests demonstrated that the 3D-printed material achieved higher values of modulus of elasticity compared to traditional brace materials. Finally, the topology optimization criteria to be applied for the design of spinal braces in the next step of this ongoing research are briefly described.

The main part of the computational cost required for solving the problem of optimal material design with extreme properties using a topology optimization formulation is devoted to solving the equilibrium system of equations derived through the implementation of the finite element method (FEM). To reduce this computational cost, among other methodologies, various model order reduction (MOR) approaches can be utilized. In this work, a simple Matlab code for solving the topology optimization for the design of materials combined with three different model order reduction approaches is presented. The three MOR approaches presented in the code implementation are the proper orthogonal decomposition (POD), the on-the-fly reduced order model construction and the approximate reanalysis (AR) following the combined approximations approach. The complete code, containing all participating functions (including the changes made to the original ones), is provided.

Customized wrist splints, particularly for upper extremity orthoses like wrist support braces, are commonly used across numerous clinical scenarios. However, the traditional process for producing personalized wrist splints is largely manual and highly dependent on the expertise of orthopedic specialists. This experience-based approach often leads to suboptimal outcomes, necessitating further refinement of the designs. Recent advancements in Additive Manufacturing (AM) have brought significant innovation to various industries, including orthopedics. This study aims to present a comprehensive methodology that integrates advanced design tools, like 3D Scanning, with digital manufacturing techniques to produce tailored wrist splints. The produced hand brace aims to offer enhanced mechanical performance and comfort by precisely fitting an individual’s anatomy while minimizing material usage and weight. To achieve optimal design efficiency, the study explores the application of a topology optimization (TO) approach for design, while the manufacturing process utilizes Fused Deposition Modeling (FDM), an evolving technology within the additive manufacturing (AM) sector.

In this work, a simple, easy to use MATLAB code is presented for the optimal design of materials for 3D domains. For the optimal design of materials, the theoretical framework of topology optimization and that of homogenization were utilized to develop a formulation where the design of the micro-structure of the material is affected among others by the loading and boundary conditions of the 3D macro domain. The final result of the micro-scale can then be converted into an stl file, which can be utilized for 3D printing; however, the continuity of the unit cells when assembled to form the macro structure should be taken into account. The transition of the design of the material problem formulation from 2D to 3D domains generates drastically increased computational needs in order to perform the design procedures, which might narrow its formulation scales and the corresponding sizes of the adopted finite element discretization. Thus, in addition to the optimal design of materials implementation, the utilization of three different model order reduction (MOR) approaches is presented, aiming to assist towards the reduction of the computational cost of the two scales formulation. On-the-fly reduced order model, proper orthogonal decomposition (POD), and approximate reanalysis (AR) following the combined approximations are the three approaches adopted for the purposes of this study, while the code implementation enables the addition of new ones easily.

Customized wrist splints, particularly for upper extremity orthoses like wrist support braces, are commonly used across numerous clinical scenarios. However, the traditional process for producing personalized wrist splints is largely manual and highly dependent on the expertise of orthopedic specialists. This experience-based approach often leads to suboptimal outcomes, necessitating further refinement of the designs. Recent advancements in Additive Manufacturing (AM) have brought significant innovation to various industries, including orthopedics. This study aims to present a comprehensive methodology that integrates advanced design tools ,like 3D Scanning, with digital manufacturing techniques to produce tailored wrist splints. The produced hand brace aims to offer enhanced mechanical performance and comfort by precisely fitting an individual’s anatomy while minimizing material usage and weight. To achieve optimal design efficiency, the study explores the application of a Topology Optimization (TO) approach for design, while the manufacturing process utilizes Fused Deposition Modeling (FDM), an evolving technology within the Additive Manufacturing (AM) sector.