Principal Stress Lines Research Articles

Continuous fiber printing path generation based on Euler diagram division

Continuous fiber printed structures are widely used in aerospace applications because of their excellent performance and high design freedom. Existing path planning methods optimize the continuous fiber printing direction by stress lines or discrete angles, but these methods are far from perfect printing paths and lack planning for connectivity relations. In this study, a planning method for continuous fiber printing paths based on constructing Eulerian circuits from a weighted undirected graph is proposed. The principal stress lines are transformed into a weighted undirected graph, which divides the Eulerian subgraph by splitting the common nodes to plan the continuous fiber printing path circuit. Subsequently, the printing structure parameters are optimized based on simulation analysis. The experimental results, taking MBB (Messerschmitt-Bolkow-Blohm) beams as an example, show that the printing path designed in this paper improves the structural strength by 52.9% and the structural stiffness by 81.7% compared with the conventional printing path.

Exceptional mechanical performance by spatial printing with continuous fiber: Curved slicing, toolpath generation and physical verification

This work explores a spatial printing method to fabricate continuous fiber-reinforced thermoplastic composites (CFRTPCs), which can achieve exceptional mechanical performance. For models giving complex 3D stress distribution under loads, typical planar-layer based fiber placement usually fails to provide sufficient reinforcement due to their orientations being constrained to planes. The effectiveness of fiber reinforcement could be maximized by using multi-axis additive manufacturing (MAAM) to better control the orientation of continuous fibers in 3D-printed composites. Here, we propose a computational approach to generate 3D toolpaths that satisfy two major reinforcement objectives: (1) following the maximal stress directions in critical regions and (2) connecting multiple load-bearing regions by continuous fibers. Principal stress lines are first extracted in an input solid model to identify critical regions. Curved layers aligned with maximal stresses in these critical regions are generated by computing an optimized scalar field and extracting its iso-surfaces. Then, topological analysis and operations are applied to each curved layer to generate a computational domain that preserves fiber continuity between load-bearing regions. Lastly, continuous fiber toolpaths aligned with maximal stresses are generated on each surface layer by computing an optimized scalar field and extracting its iso-curves. A hardware system with dual robotic arms is employed to conduct the physical MAAM tasks depositing polymer or fiber reinforced polymer composite materials by applying a force normal to the extrusion plane to aid consolidation. When comparing to planar-layer based printing results in tension, up to 644% failure load and 240% stiffness are observed on shapes fabricated by our spatial printing method. We demonstrate the versatility of our approach through various complex load cases which demonstrate their successful implementation of continuous fiber printing in 3D.

Force-thermal analysis of large-area microchannel embedded cooling plate in improving thermal management of high-power density data centers

ABSTRACT A thermal management method for data centers from the server level is proposed in this paper. This paper explores the high energy consumption of the server itself, proposing a principle of microchannel shape design for a cooling plate based on the principal stress lines (PSLs). Under the condition of a uniform load, the influence of the cross-sectional shape of the microchannel on the contact thermal resistance was found to be insignificant. From the analysis of cooling plate plane, the uniformity of the stress distribution of the microchannel determined the uniformity of the contact thermal resistance, which determined the heat dissipation ability. Experiments were developed to test and verify the cooling performance of the cooling plate as well as the performance differences with the microchannels along and away from the PSLs under deformation. It was concluded that compared with the conventional serpentine microchannel, the cooling performance of the cooling plate proposed in this paper was 4.5 reduction in average temperature. Furthermore, when the ultra-thin cooling plate was subjected to a uniform load distribution, the microchannel along a single PSL had the best stress distribution, that is, the contact thermal resistance had the least variation.

Effect of tailored fiber deposition in 3D printed composites: application of an anisotropic phase field model

Continuous Fiber 3D printing is a relatively new technology which can allow for tailored reinforcement of critical regions in structural components, i.e., stress concentrations, following principal stress lines. The influence the fiber deposition path has on the mechanical and failure behavior of such components is assessed using an anisotropic phase field model. A comparison with experimental results for notched unidirectional composite plates, available in the literature, demonstrates the ability of the method to produce satisfactory predictions for unidirectional reinforcement paths. The analysis is then extended to Open-Hole and Double Edge-Notched tension coupons of both unidirectional and variable stiffness reinforcement patterns. It is observed that the strength obtained for the components made with a reinforcement pattern that follows the principal stress lines is markedly higher than that for the equivalent unidirectionally reinforced ones. It is highlighted that the improvement in strength deriving from the tailored fiber deposition cannot be deduced solely by the analysis of the stress concentration factor but an analysis taking damage into account is necessary. In addition, the effect of the reinforcement strategy on the size effect was also explored, highlighting how the tailored fiber path leads to an increase in the failure load attainable by the specimens for all the dimensions analyzed.

Reinforcement detail: Stress trajectory‐oriented corbel reinforcement

AbstractThe article presents a novel design of concrete corbels, where horizontal and vertical stirrups are replaced by main reinforcement bars that are bent down into the corbel web, following the principal stress lines. A test series of three specimen pairs of fanned‐out and conventional reinforcement design, supported by finite element analysis, shows that the same capacity can be achieved with a significantly lower amount of reinforcement steel and a higher ductility.

Bio-inspired-based structures optimization for additive manufacturing using metaheuristic Kriging

Lightweight cellular structures are investigated intensively in additive manufacturing and require optimization strategies to distribute both patterns, cross-sections sizes and type, and even materials. There exist several parametric optimization techniques that permit not only obtaining lightweight structures but also ensuring maintaining the rigidity. Among these techniques, design of experiments is time-consuming, and the values of the optimal parameters are estimated based on their possible range rather than being determined precisely. An original scientific strategy is to use the Kriging swarm optimization technique to achieve the global optimum using a minimal amount of computer simulations. Therefore, the objective of this paper is to determine the optimal cross-sections of structures using bio-inspired “L-systems”. These L-systems-based structures were created and distributed along the directions of the principal stress lines (PSLs), then mimicking material growth and distribution inside biological structures. Two PSLs directions were separately investigated for each load case; the first direction is used as a guide for the growth of L-systems and the second one serves for branch extensions and limitations. To do so, a metamodel is used upon particle swarm optimization technique (PSO) and several case studies are conducted to improve the stiffness-to-weight ratio while respecting the additive manufacturability.

A new design method for the openings of shell structures under the dual control of principal stress lines and stress contours

Current design software lacks high precision and effective control in handling complex shell opening designs. This study develops a new workflow for generating shell openings based on the exceptional modeling advantages of Grasshopper, a visual programming language integrated with the Rhino software. The process contains two critical subroutines developed in Python for data processing and transformation. One is a selection tool based on the K-nearest neighbors classification algorithm for processing principal stress line data. The classification result is the guideline for shell meshing, which substantially improves the structural rationality of mesh shells generated based on dynamic equilibrium methods and particle spring systems. Another tool developed in this study based on the computer vision library OpenCV provides the functionality to read and process stress image data. In addition, this subroutine allows multi-level control of shell opening dimensions according to stress contours. In contrast with the conventional method, the new method efficiently brings shell form under the dual control of principal stress lines and stress contours for the first time. The obtained shell-opening results indicate increased freedom in layout, shape, and smoothness. The method is applied to a free-form shell, and three typical practical examples are presented to demonstrate its structural efficiency and visual effect.

Concurrent shape and build orientation optimization for FDM additive manufacturing using the principal stress lines (PSL)

Additive Manufacturing (AM) with the consisting constantly evolving technologies is a particularly popular research area. Based on the shape forming freedom, size, shape, and topology optimization techniques can be validated by AM produced parts. However, in every manufacturing process, AM also has some adverse inherent properties. One and maybe the most significant optimization problem is the mechanical anisotropy caused by the layered structure. In this paper, a simultaneous build orientation and shape optimization method is presented. Both of the approaches are intended to increase the mechanical performance of the produced parts. Shape optimization was accomplished by varying the cross-section of the beam geometries, based on the angle between a PSL section and the characteristic load direction. To test the efficiency and validate the method 2D structures (with relatively small 3rd dimension) and their tensile properties were tested. Based on the results, we can prove that the PSL method works and help to increase the mechanical performance by 19.2% with only 7.8% size increment.

Designing Truss in Architecture: Method and Applications Based on Clustering Algorithms and Principal Stress Lines

Rationally and effectively balancing the design objectives of architecture and structure is challenging owing to the limitations of existing truss design methods. Inspired by visual design principles, this study proposes a non-black-box, parametric, and integrated solution based on principal stress lines (PSLs). The idea is to mine the potential data features of PSLs by the clustering algorithm. Clustering the endpoints and equipartition points of PSLs is the core operation of this method. The clustering results are then used to reflect the geometric features and distribution characteristics of PSLs. For this purpose, the framework of two clustering algorithms (DBSCAN and K-means) is adapted with additional functions for sorting, screening, and counting the sample size of specific clusters. Moreover, combined with the layout pattern of linear elements, the truss web number, size, and layout are defined based on the clustering results. In addition, to verify the feasibility of form-finding results, the method is applied to a cantilever truss and two practical projects: Taishan Bridge and the Wing Stairway. Finally, the application potential of this method is demonstrated by comparing its conventional trusses under the same load and support conditions (materials used, maximum displacement, and maximum axial stress). • The proposed truss generation concept is initiated from structural performance, and at the same time is highly compatible with the architect’s design demand for visual presentation. • Compared to the other conventional structural optimization methods based on principal stress lines, the workflow of truss form evolving methodology provided in the paper is non-black-box and achieves parametric visualization in the whole designing process. • There are multiple parameters to control truss webs’ number, size, and layout pattern, which makes diversified outcomes of form generation possible to meet the different requirements of the designers. • The tensile and compression members in trusses can be distinguished to effectively select their cross-sectional sizes, which are important in the accurate demonstration of material properties for both architects and engineers.

A Biomimetic Design Method for 3D-Printed Lightweight Structures Using L-Systems and Parametric Optimization

Biological structures and organisms are determined and optimized to adapt to changes and constraints imposed by the environment. The multiple functionalities and properties exhibited by such structures are currently a source of inspiration for designers and engineers. Thus, biomimetic design has been increasingly used in recent years with the intensive development of additive manufacturing to deliver innovative solutions. Due to their multifunctional properties combining softness, high stiffness, and light weight, many potential applications can be seen in the medical, aerospace, and automotive sectors. This paper introduces a biomimetic design and geometric modeling method of 3D-printed lightweight structures based on L-systems generated and distributed along their principal stress lines. Numerical simulations and parametric optimization were conducted with three case studies to demonstrate the relevance and applicability of this method in adapting mechanical structures to various load cases as well as ensuring a proper stiffness-to-weight ratio.

Effects of Cuspal Inclination and Luting Agent on Fracture Load Values in Composite Resin CAD/CAM Crowns.

The purpose of this study was to evaluate whether change in cuspal inclination influences the fracture load values of composite resin computer-aided design/computer-aided manufacturing (CAD/CAM) crowns. Abutment teeth and CAD/CAM crowns were prepared as they would be for treating a mandibular first premolar with two cusps. The CAD/CAM crowns were designed so that 1) the principal stress lines would be radially distributed from the two points of contact with the indenter to the occlusal area of the abutment (Type I), or 2) the principal stress lines would pass outside the occlusal area of the abutment (Types II and III). The CAD/CAM crowns were mounted on the abutments using one of two types of resin or polycarboxylate cement. Fracture load values were measured using a universal tester. The Type I CAD/CAM crowns exhibited the highest mean fracture load value, followed by the Type II crowns and then the Type III crowns, with significant differences seen between all types (p<0.05). The luting agent used (resin or polycarboxylate cement) showed no effect on the fracture load value. With the Type II and Type III crowns, significant differences in the fracture load value were observed between the Super-Bond and Hy-Bond polycarboxylate cement groups (p<0.05).

Structural form-finding of bending components in buildings by using parametric tools and principal stress lines

This paper aims to provide an efficient and straightforward structural form-finding method for designers to extrapolate component forms during the conceptual stage. The core idea is to optimize the classical method of structural form-finding based on principal stress lines by using parametric tools. The traditional operating process of this method relies excessively on the designer's engineering experience and lacks precision. Meanwhile, the current optimization work for this method is overly complicated for architects, and limitations in component type and final result exist. Therefore, to facilitate an architect's conceptual work, the optimization metrics of the method in this paper are set as simplicity, practicality, freedom, and rapid feedback. For that reason, this paper optimizes the method from three aspects: modeling strategy for continuum structures, classification processing of data by using the k-nearest neighbor algorithm, and topological form-finding process based on stress lines. Eventually, it allows architects to create structural texture with formal aesthetics and modify it in real time on the basis of structural analysis results. This paper also explores a comprehensive application strategy with internal force analysis diagramming to form-finding. The finite element analysis tool Karamba3D verifies the structural performance of the form-finding method. The performance is compared with that of the conventional form, and the comparison results show the practicality and potential of the strategy in this paper.

Metamaterials mapped lightweight structures by principal stress lines and topology optimization: Methodology, additive manufacturing, ductile failure and tests

In lightweight engineering, mechanical metamaterials (MMs) are suitable for additive manufacturing (AM) due to their geometry complexity. However, it is inevitable to bring about mechanical deviation and local yield for MMs infilled lightweight structures. In the current work, MMs mapped structures, named as MMs-TO-PSLs, are proposed. The design domain is divided into core-region, intermediate-region, and solid-region. Core-regions derived from topology optimization (TO) are mapped with MMs, of which the [100] orientations are aligned with the normal directions of principal stress lines (PSLs). The intermediate-regions are infilled with ribbons according to PSLs. The solid regions are allocated to stress concentrated areas. Finally, near isotropic mechanical response is achieved in core-region from anisotropic MMs, and the serious local deformation is eased. To validate such approach, the mapping strategy is carried out on a beam subjected to three-point bending. Metallic MMs-TO-PSLs and MMs infilled uniform lightweight structure are fabricated by selective laser melting (SLM). Elastoplastic simulations with ductile failure model are proposed to investigate the strengthen mechanism of MMs-TO-PSLs. Experimental and numerical results confirmed the ultimate strength of MMs-TO-PSLs can be 40% larger than conventional MMs infilled uniform structures.

Design of heterogeneous mesoscale structure for high mechanical properties based on force-flow: 2D geometries

Mesoscale structure (MS) design of parts unlocked by additive manufacturing has a significant impact on their mechanical and physical properties. Conventional homogeneous MS designed based on unit cells is not a globally optimal structure due to the incompatible with the variable stress field under the applied load. In contrast, naturally evolved heterogeneous MS such as bones and bamboos are perfectly adaptive to their applied loads and exhibit excellent structural efficiency. Therefore, a heterogeneous MS design method of 2D geometry based on force-flow for high mechanical properties is proposed. The generation methods of two characterization forms of force-flow, principal stress lines and load paths, force-flow guided heterogeneous MS generation method, and MS volume fraction control method are detailed. Force-flow is generated using interpolation method based on the stress information extracted from finite element analysis (FEA) results. Then, force-flow is used as a guide to generate heterogeneous MS highly coordinated with the stress field. Customization of heterogeneous MS volume fraction is achieved by regulating the sparsity of force-flow lines based on the number of seed points in the design domain. Finite element simulations and mechanical tests of different specimens demonstrate that force-flow based heterogeneous MS has higher strength and stiffness compared to homogeneous honeycomb MS and grid MS.

Improvement of a Tunable Stiffness Organ-Grasping Device by Design of a Wavy-Shaped Beam Structure

Tunable stiffness mechanisms can increase the noninvasiveness and stability of organ manipulation in laparoscopic liver resection. We have developed an organ-grasping device using beam-shaped tunable stiffness mechanism. Increasing the change ratio of stiffness will improve the performance of the device by offering high flexibility when adhering to the liver surface and high rigidity during the manipulation of the liver; however, optimal design of the beam has not been investigated. In this study, we investigate the wavy structure shape of the device that enhances the change in the ratio of stiffness. To increase the stiffness in a high-stiffness state, we used principal stress lines in the device to design the edge curve of the wavy shape material in the beams. We also investigated the arrangement of the wavy shape to decrease the stiffness in a low-stiffness state. Simulation using finite element method showed that the change ratio of stiffness was improved up to 13.0 by the new wavy shape arranged with the uniformly thick bottom of the waves.

Fabrication of doubly-curved CFRP shell structures with control over fiber directions

We introduce a fabrication method of doubly-curved shell structures by CFRP with control over fiber directions. Doubly-curved surfaces are tessellated into structured quadrilateral patches according to the purpose of use. One can design the tessellation in the parameter space, and map it to the 3D parametric surface, or use the orthogonal net of curves on surfaces such as lines of curvature, principal stretch lines, and principal stress lines. These patches, which we call generalized principal patches, are flattened onto a plane, and connected one by one by aligning the equi-length adjacent edges using translations and rotations forming generalized principal strips. Carbon fiber tows are placed onto these strips with one stroke by tailored fiber placement embroidery machines so that the fibers are not disconnected within strips. Preforms are stacked layer by layer into a mold of particular parts, and VaRTM or L-RTM method is employed to fabricate CFRP parts. We demonstrated the effectiveness of our proposed method by manufacturing an automobile hood and a marine propeller blade.

Stress-cognizant 3D printing of free-form concrete structures

3D printing enables engineers to design and manufacture geometrically complex structures. As 3D printing technology affords design freedom, it also brings along new challenges. One common property of classical 3D printing is the anisotropy arising from the filament-wise 3D printing process. This anisotropy reduces the load bearing capabilities of the 3D printed part when loaded in its weaker axes, that is the directions orthogonal to the filament. Conversely, by designing the 3D printing path through analyses of its mechanical constraints, the 3D printed part may be strengthened and printed such that it carries the majority of the load in its strongest axis, parallel to the filament (T1), thereby increasing its load-carrying capabilities. We experimentally investigated this idea by designing and printing several concrete samples following two strategies: (i) the classical strategy consisting of parallel rectilinear paths irrespective of the load distribution, and (ii) our proposed strategy consisting of paths that are as much parallel as possible to the principal stress lines. We then subjected the samples to mechanical testing. The test results confirmed that the proposed printing strategy significantly improved mechanical characteristics. Cracking patterns were also observed and discussed.

Principal stress lines based design method of lightweight and low vibration amplitude gear web

&lt;abstract&gt; &lt;p&gt;A lightweight and low vibration amplitude web design method was investigated to reduce gear weight and noise. It was based upon the relationship between length and orthogonality that the principal stress lines were designed at the gear web. By constructing a vibration control model with gear design parameters, the optimal distance was calculated. By offsetting the principal stress lines at the optimal distance, the lightweight gear web with the low vibration amplitude was then generated. A vibration experimental platform was built to verify the novel gear vibration performances, and it was compared with other gears with the same web's porosity to verify loading performance. The experimental results indicated that compared with the solid gear, the novel gear is 20.50% lighter and with a 29.46% vibration amplitude reduction.&lt;/p&gt; &lt;/abstract&gt;

Stress lines inspired structural patterns for tall buildings

In this paper, an innovative diagrid-like pattern for tall building structures is proposed. Based on the concept of principal stress trajectories, the pattern is characterized by triangular units with angle varying along width and elevation, and, being the expression of forces flow arising in the building façades, it is expected to be highly efficient and visually appealing. The idea is to model the building as a three-dimensional vertical cantilever beam with tubular section under horizontal load, and to derive the relevant principal stress lines. Then, the stress analysis results are processed, and geometrical rules are derived for generating structural grids that also satisfy constructability constraints. For this purpose, a framework for implementing and managing the stress lines concept in the preliminary structural design of tall buildings is proposed. The efficacy of the generation procedure and the efficiency of the obtained structural patterns are then verified by means of the application to tall building models characterised by different slenderness ratios, and by means of comparisons with the performance and steel weight of conventional diagrid structures.

Lattice structure design optimization coupling anisotropy and constraints of additive manufacturing

Replacing solid structures with lattice structure is a way enabled by additive manufacturing (AM) to realize part lightweight design. Conventional design optimization method based on homogeneous periodic lattice structure cannot achieve the optimal structure without taking the stress magnitude and orientation into account. A design optimization method of heterogeneous conformal lattice structure coupling constraints and anisotropy of AM based on principal stress lines (PSL) is proposed. (1) The PSL is calculated based on finite element analysis to visualize the path of load transfer. (2) The load-adapted lattice structure is generated guided by the PSL. (3) In order to further optimize lattice structure, the lattice structure optimization model is established by coupling anisotropy and constraints of AM based on the fused deposition modeling (FDM) experiment. Taking a cantilever beam as a case, the maximum force-to-weight ratio and the stiffness-to-weight ratio of the optimized heterogeneous conformal lattice structure are increased by 11.8% and 41.8% respectively compared with homogeneous conformal lattice structure, which verified the feasibility of the proposed method.