Overhang Constraint Research Articles

Design and validation of 3D self-supporting structures and printing paths for multi-axis additive manufacturing

Additive manufacturing (AM) has become a widely used tool for fabricating components with complex geometries. However, the overhang effect induced by gravity often necessitates additional supports to prevent collapse and warping during the printing process. To address this issue, previous studies incorporated overhang constraints to the topology optimisation to create self-supporting structures. Nevertheless, these studies primarily focused on 3-axis AM, which deposits material in a single direction and often compromises structural stiffness to achieve self-supporting designs. In response, this study aims to design 3D self-supporting structures tailored for multi-axis AM. By leveraging the rotatable base platform of multi-axis systems, this approach automatically identifies optimised local build directions and the corresponding structural topology to minimise overhangs. The effectiveness of this approach is demonstrated through several numerical examples, with results validated numerically via printing simulations in VERICUT and physically using a multi-axis Wire Arc Additive Manufacturing (WAAM) machine. The results indicate that the performance degradation caused by 3-axis-based overhang constraints can be reduced to a negligible level with the multi-axis-based approach.

Layout and geometry optimization design for 3D printing of self-supporting structures

As the demand for high-performance structures in various scenarios continues to rise, the complexity of engineering structures also increases, necessitating the development of advanced design methods and the additive manufacturing (AM) of sophisticated structures. While the layout optimization method based on the ground structure technique can produce optimized designs, the gravity-induced overhang effect during the printing process often requires additional support materials. The use of additional support materials during the printing process can result in higher material costs or the need for post-processing to remove the support structures, significantly hindering the adoption of AM in practice. This paper presents an optimization framework to obtain self-support optimization designs and provides a practical validation for the effectiveness of the proposed framework. Firstly, a self-support point-line structure is obtained via the layout and geometry optimization, considering overhang constraints. Secondly, the point-line structure is transformed into a physical model with nodal expansion considered (i.e., taking into account the overlapping of members at nodes). Finally, the physical models are sliced and printed using both a plastic Fused Deposition Modeling (FDM) printer and a metal Wire Arc Additive Manufacturing (WAAM) printer. The results confirm that the proposed process is effective for both plastic and metal printing, demonstrating its exceptional versatility.

Topology optimisation of self-supporting structures based on the multi-directional additive manufacturing technique

ABSTRACT Although additive manufacturing (AM) continues to gain widespread adoption, the overhang problem remains a critical issue affecting printing quality. The design of self-supporting structures via topology optimisation approaches has been extensively studied. However, current optimisation research predominantly focuses on 3-axis AM machines, overlooking the more recently developed multi-axis machines. Moreover, the performance sacrifice due to overhang constraints in 3-axis AM can be significant, especially in structures with small volume fractions. To address this, we propose a two-step approach considering overhang constraints for multi-axis AM. This approach begins with a structure optimised using traditional topology optimisation. In the first step, a new optimisation problem determines printing surfaces for the given structure. If the proportion of unprintable elements isn't satisfactory, a second re-optimisation step is carried out to further reduce the unprintable proportion. Several examples demonstrate the effectiveness of the proposed approach. Notably, the significant performance sacrifice associated with the 3-axis AM approach becomes negligible when applying our multi-axis AM-based method.

Topology optimization with geometric constraints for additive manufacturing based on coupled fictitious physical model

The combination of topology optimization and laser powder bed fusion (LPBF), a kind of metal additive manufacturing, has attracted attention because of its ability to manufacture complex optimal structures with metal materials. However, LPBF must satisfy geometric constraints, e.g., overhang constraint and closed cavity exclusion constraint. Several previous studies proposed the fictitious physics model (FPM) to describe and consider these constraints. However, there exists a problem where the objective of the mechanical model (MM) describing physical phenomena conflicts with that of the FPM, resulting in poor convergence. To solve the convergence problem, we propose a coupled fictitious physics model (CFPM) in this paper. In the CFPM, the material constant in the MM is varied in the regions that violate the geometric constraints defined by the FPM such that the objective function of the MM worsens. Then, the objective of the FPM is integrated into that of the MM, potentially improving convergence. This paper formulates the CFPM and performs sensitivity analysis on representative optimization problems considering geometric constraints for LPBF. In addition, we verify through numerical examples whether the CFPM can lead to an optimal structure that satisfies the geometric constraints and can improve convergence. The proposed method to couple the two models can also be applied to topology optimization considering various geometric constraints in other manufacturing requirements.

Concurrent topology optimization of parts and their supports for additive manufacturing with thermal deformation constraint

A typical manufacturing failure in powder bed additive manufacturing (AM) is caused by the collision between the already printed structure and the powder recoater due to large thermal deformation. This paper presents a density-based topology optimization (TO) approach to concurrently design parts and their supports that are not susceptible to such a manufacturing failure. The thermal deformation during the layer-by-layer AM process is predicted based on an inherent strain method, and the top surfaces' upward deformations are constrained below the powder layer thickness to avoid recoater collision. To increase the design freedom of TO, the parts and their supports are composed of lattice unit cells with different volume fractions, whose effective stiffness matrixes are predicted by the numerical homogenization and surrogate models. Besides, an overhang constraint and a two-field-based length scale control formulation are also utilized, ensuring overall manufacturability. With the proposed approach, lightweight structures with optimized mechanical properties and controllable manufacturing qualities can be obtained. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

An Evolutive-Deformation approach to enhance self-supporting areas in Additive Manufacturing designs

Additive Manufacturing (AM) technology has matured rapidly in recent years, opening an engineering design freedom front when combined with Topology Optimization (TO). Although there is no doubt about their potential to provide optimal parts, there still exists a wide gap between them which reduces the efficiency of the design process. Overhang constraints in TO are still limited, therefore the designs generated by these algorithms are not yet ready for being directly manufactured. They usually need support structures to avoid droops or warps, which is time-consuming, costly and can lead to the loss of the optimal path since designers are required to manually redesign the geometry. The proposed approach combines both design and AM constraints into an automatic workflow in which the geometry provided by the TO software is evolved to minimize support structures for any printing direction while preserving its structural performance. The NSGA-II algorithm is coupled with a Free-Form Deformation (FFD) method to develop different geometries, while fitness is evaluated with FEM analysis. The framework provides Pareto Fronts with the most promising printing directions and geometries in terms of support structures, stiffness and weight. This multi-objective optimization approach that aims to improve TO parts manufacturability is applied to two case studies and one real-world part, highlighting on average a reduction of support structures of around 30%, whereas mass is practically preserved and stiffness decreased by 5%.

Topology optimization of shell-infill structures considering buckling constraint

This paper presents a density-based topology optimization approach to design shell structures and non-uniform infills concurrently for efficient stiffness and stability. The buckling load factors are computed by linearized buckling analysis, the lower bound of which is constrained to ensure the structural stability. Besides, an overhang constraint and a two-field-formulation-based length scale control approach are utilized, ensuring that the optimized structures satisfy the geometry requirements for additive manufacturing(AM). By solving the topology optimization problem, the shell geometry and the infill layout can reach a desirable match such that the structural stability is ensured and the stiffness is also optimized. Numerical examples show that the stability of the shell-infill structure optimized by the proposed approach can be increased significantly at the cost of a slight degradation of stiffness comparing to that optimized without the buckling constraint.

Topology Optimization of Self-supporting Porous Structures Based on Triply Periodic Minimal Surfaces

With the advent of additive manufacturing (AM), topology optimization (TO) has become increasingly important in structural design. A key component of structural design is generating the interior shape of an object under predefined force conditions and specific constraints. Fabricating such models by layer-based AM suffers from the problem of adding and removing interior supporting structures, which can produce artifacts in the final product. In this paper, we propose an algorithm to design a self-supporting porous structure by integrating overhang constraints into the topology optimization framework. A minimum thickness constraint is also built into the optimization process to automatically enforce printability of the resulting structures. We utilize triply periodic minimal surfaces (TPMSs) to represent interior structures which can be analyzed, optimized and stored directly using analytical functions. We apply several acceleration methods including super element strategy, multigrid algorithm and GPU-based solver to handle models comprising of several million of elements efficiently. Numerical results indicate that the optimized interior structures obtained by our approach exhibit improved printability as they largely satisfy manufacturing requirements on overhang angles and minimal thicknesses.

Stress-based form-finding of gridshells for Wire-and-Arc Additive Manufacturing considering overhang constraints

The design of spatial truss networks for fabrication using Wire-and-Arc Additive Manufacturing (WAAM) is addressed, combining funicular analysis and optimization. At first, a characterization of the structural behavior of the printed bars is provided based on available experimental tests. Interpolation laws are given both for the yielding stress and the critical stress in compression, depending on the printing direction. Then, dealing with networks with fixed plan projection, a minimization problem is formulated in terms of any independent subset of the force densities and of the height of the restrained nodes. The maximum value of the ratio of the axial force in each branch of the network to the relevant yielding/critical force is adopted as objective function. Local enforcements are prescribed to set lower and upper bounds for the vertical coordinates of the nodes and to control the overhang angle with respect to the vertical direction in the AM process. Gridshells retrieved by the proposed approach are presented and compared to those found when seeking for spatial networks with minimum horizontal reactions, disregarding or considering overhang constraints. Peculiar features of the achieved layouts are pointed out.

Topology optimization for the design of a 3D-printed rotating shaft balance

Rotating shaft balances (RSBs) are devices that are used to measure rotor blade forces and moments of wind tunnel models during wind tunnel tests. The design of an RSB can be challenging, because it has to comply with many and sometimes contradicting requirements such as high stiffness and high strain gauge bridge outputs. The manufacturing of a conventional RSB consists of different subsequent steps, which can be time consuming, expensive and associated with many risks. Therefore, in this work, the authors investigate if a RSB can be designed by topology optimization and manufactured by 3D printing. A topology optimization method was developed with as design objective the minimization of strain energy with constraints for the volume of the RSB’s midsection, defined stresses at strain gauge locations used for the measurement of axial force and torque and an overhang constraint for additive manufacturing. The optimal preliminary design found by topology optimization was translated into a final printable design with the highest bridge sensitivity for axial force and torque, sufficient output for in-plane forces and moments and an acceptable safety factor on strength for combined loads. After adding extra supports required for printing, the RSB was successfully printed in metal by the laser powder bed fusion process, resulting in a product without external defects. The same topology optimization and manufacturing method can potentially be used for other balance types, leading to a reduction in total lead time and manufacturing costs while increasing the design freedom.

Addressing topology optimization with overhang constraints for structures subjected to self-weight loads

This paper investigates the topology optimization of structures subjected to self-weight loads with self-supporting constraints for additive manufacturing. The integration of topology optimization procedures and additive manufacturing techniques can make the most of their advantages, and there is significant interest today in integrating both approaches. Imposing overhang constraints in topology optimization has been addressed, but primarily for classical topology optimization problems with fixed external loads, not design-dependent loads. This work combines an effective numerical procedure for contour evaluation with a modified version of the power-law model for low densities to eliminate the problems that arise when self-weight loads are considered. The overhang edge detection is based on the Smallest Univalue Segment Assimilating Nucleus (SUSAN) method, and a variable mask size technique is used to avoid eventual dripping problems. The proposed constraint function evaluates the overhang globally and allows control of the formation of unsupported contours for maximum stiffness design problems when self-weight loads are present. Several numerical experiments demonstrate the proposed method's effectiveness and robustness.

Three-dimensional topology optimization considering overhang constraints with B-spline parameterization

In this paper, a B-spline parameterization based topology optimization method is presented to design 3D self-supporting structures for additive manufacturing (AM). B-spline parameterization being independent of the FE mesh is used to represent the density field characterizing the material layout of the structure. Heaviside projection and Boolean operations are applied to ensure the obtention of a clear topology configuration within a free-form design domain. Three specific constraints are formulated for AM: (i). The overhang angle constraint imposed on the structural boundaries in an integral form. (ii). The pyramid constraint aiming to avoid undesired inverted-cone features by constraining the values of density field at detection points uniformly distributed in the B-spline parameterized domain. (iii). The boundary gradient constraint imposed to deal with V-shaped cross-section features appearing on the boundary of the design domain by constraining the corresponding direction of the gradient of the B-spline density field. Meanwhile, the minimum feature size control is employed to deal with V-shaped cross-section features inside the design domain. Representative examples are dealt with to demonstrate the effectiveness of the proposed method. Numerical results show that the proposed method is effective to solve 3D problems.

Concurrent topology optimization of shells with self-supporting infills for additive manufacturing

This paper presents a systematic design optimization approach for shells with self-supporting infills for Additive Manufacturing (AM). The design workflow includes a concurrent Topology Optimization (TO) of the shells and the infills using a density based TO approach, followed by a model reconstruction that is tailored to guarantee a precise overhang control on the output Boundary-represented (B-rep) geometry. In the TO model, a new overhang constraint is developed to ensure that the TO result satisfying an overhang angle is defined on a basis of the discrete mesh elements. The TO process is stabilized by utilizing an adaptive parameter updating strategy and a two-field based formulation is proposed to control the minimum length scale. The topology optimized result is re-constructed into a B-rep model afterwards, in which the maximum overhang span of the explicit geometry is strictly controlled to satisfy the manufacturability requirement of an actual AM process. By applying the proposed TO and the associated geometry reconstruction together, the optimized infills are not only self-supporting but also can support the optimized shells from the structural inside. Truly manufacturable shell–infill structures with desirable mechanical properties can be obtained regardless of the voxel granularity of TO. Numerical examples and AM prototypes are given to demonstrate the effectiveness and the applicability of the proposed approach.

Topology optimization of additively manufactured fluidic components free of internal support structures

This paper integrates projection-based approaches for implementing overhang constraints with fluid topology optimization to design additively manufactured fluidic components that do not require internal support structures. Internal support structures are challenging, potentially impossible to remove in complex fluid networks, yet would degrade fluidic performance if left within the part. This presents a major challenge in coupling topology optimization with additive manufacturing in the design of fluid components. The proposed approach leverages past work in overhang constraints for solid mechanics, including projection formulations and adjoint sensitivity analysis, and considers incompressible Navier–Stokes equations for laminar fluid flow. The approach is demonstrated on 2D and 3D fluid topology optimization problems to minimize pressure drop and constrain mass flow rates in pipes and manifolds. Resulting designs are crisp, logical, satisfy performance constraints, and satisfy overhang constraints, eliminating the need for internal support structures.

Automated design of additive manufactured flow components with consideration of overhang constraint

When designing parts for additive manufacturing (AM), users must consider manufacturing restrictions specific to the chosen AM production technology. For material extrusion or laser powder bed fusion (L-PBF), users need to follow design rules such as avoiding geometries with critical overhangs. If users create the 3D part geometry manually using computer-aided design (CAD), the consideration of design rules can be challenging and time-consuming. Especially for complex-shaped parts, novice designers may need multiple loops to analyze and modify CAD features for manufacturability. This manual process prevents users to quickly transfer the layout design of a part into the corresponding production-ready 3D part geometry. Therefore, it is highly desirable to automate the manual CAD process, including the consideration of AM restrictions. This work aims to automate the CAD-based design of AM parts with fluid flow channels. For this purpose, the work presents automated procedures that generate and modify design features such that they automatically comply with the AM overhang constraint. The procedures focus on flow components such as hydraulic manifolds and include design features such as support-free flow channels, integrated and sacrificial supports, and other features such as boreholes, interfaces, ribs, and channel branches. To enforce the overhang constraint in the generation of features, users define the part orientation to the build direction, and values for the minimum build angle and maximum allowed diameter of horizontally oriented circular cross-sections. As a benchmark, the work demonstrates the procedures by revisiting an earlier AM hydraulic manifold. Given restrictions of L-PBF of stainless steel, the study uses the procedures to generate manufacturable 3D manifold designs for different part orientations. One of the manifold variants is fabricated to show the manufacturability of the generated 3D part designs. The work finishes by discussing the benefits of the procedures, their transferability, and enhancements to generate manufacturable and functionally optimized designs.

On preventing the dripping effect of overhang constraints in topology optimization for additive manufacturing

This article falls within the scope of topology optimization for Additive Manufacturing processes and proposes an alternative strategy to prevent the phenomenon known as the Dripping Effect. The Dripping Effect is when an overhang constraint is imposed on topology optimization processes for Additive Manufacturing and is defined as the formation of oscillatory contour trends within the prescribed threshold angle. Although these drop-like formations constitute local minimizers of the constraint function, they do not provide a printable feature, and, therefore, they neither eliminate the need to form temporary support structures. So far, there has been no general agreement on how to prevent the Dripping Effect, so this work aims to introduce a strategy that effectively prevents it, and that at the same time may be easy to extrapolate to other types of geometric overhang restrictions. This paper provides a study of the origin of the Dripping Effect and gives detailed instructions on how the proposed prevention strategy is applied. In addition, several benchmark examples where the Dripping Effect is prevented are shown.

Structural topology optimization of layout and raster angle for additive manufacturing technology with the shadow density filter

The present research contributes in the structural topology optimization with the manufacturing limitation called the overhang constraint and the optimization of the anisotropic material properties. For the optimization with self-supporting structure, the overhang-free shadow filter method is developed. To consider the anisotropic material property, the raster angles of each layer (the printing direction used to print structures) are optimized simultaneously with topology. By adding the raster angles as the design variables, it is possible to find out optimal layouts as well as optimal raster angles considering the anisotropicity. Several numerical examples of compliance minimization problem are solved to demonstrate the validity and effectiveness of the present density filter and to show the importance of the raster angle.

Topology optimization of self-supporting infill structures

This paper presents a density-based topology optimization approach to design self-supporting and lightweight infill structures with efficient mechanical properties for enclosed structural shells. A new overhang constraint is developed based on the additive manufacturing (AM) filter to ensure that the infills are not only self-supporting in a specified manufacturing direction but can also provide necessary supports to the external shell for successful manufacturing. Two-field–based parametrization and topology optimization formulations are used to impose minimum length scales and to avoid the impractical design solutions that exhibit one-node connection structural members. Besides, a localized volume constraint is utilized to achieve a porous infill pattern. By solving the optimization problem, a shell-infill design can be obtained with very few overhang elements that can be easily post-processed without affecting the mechanical properties of the overall structure. As a result, the optimized design contains no overhang elements and exhibits a better mechanical property than that with predefined periodic infill patterns of the same weight. Numerical examples are given to demonstrate the effectiveness and applicability of the proposed approach.

Topology optimization of easy-removal support structures for additive manufacturing

This paper presents a density-based topology optimization approach to design easy-removal support structures for additive manufacturing (AM). First, a multi-field structural parameterization is proposed for topology optimization by considering AM filtering technique that ensures the physical design being self-support. An easy-removal constraint is developed to generate porous structural patterns in the contact region between the support structures and its surroundings. An improved formulation is further proposed to prevent obtaining impractical solutions which contain one-node connection in the structural members. Besides, an overhang constraint and a design-dependent self-weight load are considered. As a result, the optimized support structures are self-support, able to support the overhang regions of the given prototype and possesses excellent mechanical properties to bear the self-weight of the entire AM part. It can be easily removed from both the prototype and the baseplate. Numerical examples and discussions are given to demonstrate its effectiveness and applicability.

Additive manufacturing and topology optimization: A design strategy for a steering column mounting bracket considering overhang constraints

In the present paper, the use of the topology optimization in a metal Additive Manufacturing application is discussed and applied to an automotive Body-in-White component called dash. The dash is in the front area of the Body-in-White, between the left-hand-side shock-tower and the Cross Car Beam, and its task is to support the steering column. The dash under investigation is an asymmetric rib-web aluminium casting part. The influence of Additive Manufacturing constraints together with modal and stiffness targets is investigated in view of mass reduction. The constraints drive the topology result towards a feasible and fully self-supporting Additive Manufacturing solution. A simplified finite element model of the steering column and of the Body-in-White front area is presented, and the limiting assumption of isotropic material for Additive Manufacturing is discussed. The optimization problem is solved with a gradient-based method relying on the Solid Isotropic Material with Penalization and on the RAtional Material with Penalization algorithms, considering the overhang angle constraint with given build directions. Three metals are tested: steel, aluminium and magnesium alloys. Topology optimization results with and without overhang angle constraints are discussed and compared. The aluminium solution, preferred for its lesser weight, has been preliminarily redesigned following the optimization results. The new dash concept has been validated by finite element considering stiffness, modal responses, and buckling resistance targets. The proposed dash design weighs 721 g compared to the 1537 g of the reference dash, with a weight reduction of 53%, for the same structural targets.