Flexible structures (FS) are thin shells with a pattern of holes. The stiffness of the structure in the normal direction is reduced by the shape of gaps rather than by the choice of the material based on mechanical properties such as Young’s modulus. This paper presents virtual prototyping of 3D printed flexible structures with selected planar patterns using laboratory testing and computer modeling. The objective of this work is to develop a non-linear computational model evaluating the structure’s stiffness and its experimental verification; in addition, we aimed to identify the best of the proposed patterns with respect to its stiffness: load-bearing capacity ratio. Following validation, the validated computational model is used for a parametric study of selected patterns. Nylon—Polyamide 12—was chosen for the purposes of this study as an appropriate flexible material suitable for 3D printing. At the end of the work, a computational model of the selected structure with modeling of load-bearing capacity is presented. The obtained results can be used in the design of external biomedical applications such as orthoses, prostheses, cranial remoulding helmets padding, or a new type of adaptive cushions. This paper is an extension of the conference paper: “Modeling and Testing of 3D Printed Flexible Structures with Three-pointed Star Pattern Used in Biomedical Applications” by authors Repa et al.

This paper presents a new design procedure for production of a transtibial prosthesis bed stump by three-dimensional (3D) printing with topological optimization. The suggested procedure combines the medical perspective with finite element analysis and facilitates regaining the symmetry in patients with transtibial prosthesis, which leads to life improvement. The particular focus of the study is the weight reduction of the lower part of the bed stump, while taking into account its stiffness and load-bearing capacity. The first part of the work deals with the analysis of the subject geometry of the bed stump, which is usually oversized in terms of the weight and stiffness that are necessary for the current application. In the second part, an analysis of walking biomechanics with a focus on the impact and rebound phases is presented. Based on the obtained information, a spatial model of the lower part of the bed stump is proposed in the third phase, in which the finite element method is described. In the fourth part, the topological optimization method is used for reducing the structure weight. In the last part, the results of the designed model are analyzed. Finally, the recommendations for the settings of the method are presented. The work is based on the practical industry requirements, and the obtained results will be reflected in the design of new types of transtibial prosthesis.

Topology optimization is a modern method for optimizing the material distribution in a given space, automatically searching for the ideal design of the product. The method aims to maximize the design performance of the system regarding given conditions. In engineering practice, a given space is first described using the finite element method and, subsequently, density-based method with solid isotropic material with penalty. Then, the final shape is found using a gradient-based method, such as the optimality criteria algorithm. However, obtaining the ideal shape is highly dependent on the correct setting of numerical parameters. This paper focuses on the sensitivity analysis of key formulations of topology optimization using the implementation of mathematical programming techniques in MATLAB software. For the purposes of the study, sensitivity analysis of a simple spatial task—cantilever bending—is performed. This paper aims to present the formulations of the optimization problem—in this case, minimization of compliance. It should be noted that this paper does not present any new mathematical formulas but rather provides an introduction into the mathematical theory (including filtering methods and calculating large-size problems using the symmetry of matrices) as well as a step-by step guideline for the minimization of compliance within the density-based topology optimization and search for an optimal shape. The results can be used for complex commercial applications produced by traditional manufacturing processes or by additive manufacturing methods.

The spring-loaded camming device (SLCD), also known as “friend”, is a simple mechanism used to ensure the safety of the climber through fall prevention. SLCD consists of two pairs of opposing cams rotating separately, with one (single-axle SLCD) or two (dual-axle SLCD) pins connecting the opposing cams, a stem, connected to the pins, providing the attachment of the climbing rope, springs, which simultaneously push cams to a fully expanded position, and an operating element controlling the cam position. The expansion of cams is thus adaptable to allow insertion or removal of the device into/from a rock crack. While the pins, stem, operating element, and springs can be considered optimal, the (especially internal) shape of the cam allows space for improvement, especially where the weight is concerned. This paper focuses on optimizing the internal shape of the dual-axle SLCD cam from the perspective of the weight/stiffness trade-off. For this purpose, two computational models are designed and multi-step topology optimization (TOP) are performed. From the computational models’ point of view, SLCD is considered symmetric and only one cam is optimized and smoothened using parametric curves. Finally, the load-bearing capacity of the new cam design is analyzed. This work is based on practical industry requirements, and the obtained results will be reflected in a new commercial design of SLCD.

Steel-wire rope is a mechanical component that has versatile uses and on which human lives depend. One of the basic parameters that serve to describe the rope is its load-bearing capacity. The static load-bearing capacity is a mechanical property characterized by the limit static force that the rope is able to endure before it breaks. This value depends mainly on the cross-section and the material of the rope. The load-bearing capacity of the entire rope is obtained in tensile experimental tests. This method is expensive and sometimes unavailable due to the load limit of testing machines. At present, another common method uses numerical modeling to simulate an experimental test and evaluates the load-bearing capacity. The finite element method is used to describe the numerical model. The general procedure for solving engineering tasks of load-bearing capacity is by using the volume (3D) elements of a finite element mesh. The computational complexity of such a non-linear task is high. Due to the usability of the method and its implementation in practice, it is necessary to simplify the model and reduce the calculation time. Therefore, this article deals with the creation of a static numerical model which can evaluate the load-bearing capacity of steel ropes in a short time without compromising accuracy. The proposed model describes wires using beam elements instead of volume elements. The output of modeling is the response of each rope to its displacement and the evaluation of plastic strains in the ropes at selected load levels. In this article, a simplified numerical model is designed and applied to two constructions of steel ropes, namely the single strand rope 1 × 37 and multi-strand rope 6 × 7-WSC.