Graded porous structures can improve the design performance with a smooth transition of material properties over the domain. We present a multi-physics topology optimization approach for designing ...functionally graded porous structures. As an application, we present a formulation to optimize heat dissipating structures to enhance structural and thermal performance. The pore size, resolution, and porosity of the structures can be controlled to obtain optimized mechanical and thermal performances. Several controlling schemes are introduced which can tailor the design of the porous structures. Design approaches based on the functional variation of porosity, pore size and sensitivity-based porosity control are employed. Numerical examples with different structural loads, thermal loads and boundary conditions are presented to verify the formulation and show the efficacy of the implementation. We also investigate the effect of the controlling parameters on the overall design. The proposed formulation shows good promise to design functionally graded porous structures with targeted porosity in multi-physics systems.
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•A design approach to generate porous structures guided by multi-physics topology optimization is presented.•Schemes to design functionally graded controllable porous structures based on porosity and pore size gradation are introduced.•A sensitivity-based controlling scheme is adopted to obtain physics based graded porous structures.
This paper presents a multi-resolution implementation in 3D for multi-material topology optimization problem. An alternating active-phase algorithm where the problem at hand is divided into a series ...of the traditional material–void phase topology optimization is employed for the multi-material problem. Different levels of discretization are used for the displacement mesh, design variable mesh and density mesh which provides higher resolution designs for the solutions. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Simple block coordinate descent method similar to the Gauss–Seidel technique is used to solve the subproblems. Several 3D numerical examples are presented to demonstrate the ease and the effectiveness of the proposed implementation. Incorporating the multi-resolution method into the multi-material approach, robust designs with improved resolution can be achieved for real life problems with complex geometries.
Hierarchical lattices are structures composed of self-similar or dissimilar architected metamaterials that span multiple length scales. Hierarchical lattices have superior and tunable properties when ...compared to conventional lattices, and thus, open the door for a wide range of material property manipulation and optimization. Using finite element analysis, we investigate the energy absorption capabilities of 3D hierarchical lattices for various unit cells under low strain rates and loads. In this study, we use fused deposition modeling (FDM) 3D printing to fabricate a dog bone specimen and extract the mechanical properties of thermoplastic polyurethane (TPU) 85A with a hundred percent infill printed along the direction of tensile loading. With the numerical results, we observed that the energy absorption performance of the octet lattice can be enhanced four to five times by introducing a hierarchy in the structure. Conventional energy absorption structures such as foams and lattices have demonstrated their effectiveness and strengths; this research aims at expanding the design domain of energy absorption structures by exploiting 3D hierarchical lattices. The result of introducing a hierarchy to a lattice on the energy absorption performance is investigated by varying the hierarchical order from a first-order octet to a second-order octet. In addition, the effect of relative density on the energy absorption is isolated by creating a comparison between a first-order octet lattice with an equivalent relative density as a second-order octet lattice. The compression behaviors for the second order octet, dodecahedron, and truncated octahedron are studied. The effect of changing the cross-sectional geometry of the lattice members with respect to the energy absorption performance is investigated. Changing the orientation of the second-order cells from 0 to 45 degrees has a considerable impact on the force-displacement curve, providing a 20% increase in energy absorption for the second-order octet. Analytical solutions of the effective elasticity modulus for the first- and second-order octet lattices are compared to validate the simulations. The findings of this paper and the provided understanding will aid future works in lattice design optimization for energy absorption.
Bone replacement implants for craniofacial reconstruction require to provide an adequate structural foundation to withstand the physiological loading. With recent advances in 3D printing technology ...in place of bone grafts using autologous tissues, patient-specific additively manufactured implants are being established as suitable alternates. Since the stress distribution of these structures is complicated, efficient design techniques, such as topology optimization, can deliver optimized designs with enhanced functionality. In this work, a two-scale topology optimization approach is proposed that provides multi-material designs for both macrostructures and microstructures. In the first stage, a multi-resolution topology optimization approach is used to produce multi-material designs with maximum stiffness. Then, a microstructure with a desired property supplants the solid domain. This is beneficial for bone implant design since, in addition to imparting the desired functional property to the design, it also introduces porosity. To show the efficacy of the technique, four different large craniofacial defects due to maxillectomy are considered, and their respective implant designs with multi-materials are shown. These designs show good potential in developing patient-specific optimized designs suitable for additive manufacturing.
Symmetric Galerkin Boundary Element Method presents an introduction as well as recent developments of this accurate, powerful, and versatile method. The formulation possesses the attractive feature ...of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard continuous elements to be used for evaluation of hypersingular integrals. FEATURES Written in a form suitable for a graduate level textbook as well as a self-learning tutorial in the field. Covers applications in two-dimensional and three-dimensional problems of potential theory and elasticity. Additional basic topics involve axisymmetry, multi-zone and interface formulations. More advanced topics include fluid flow (wave breaking over a sloping beach), non-homogeneous media, functionally graded materials (FGMs), anisotropic elasticity, error estimation, adaptivity, and fracture mechanics. Presents integral equations as a basis for the formulation of general symmetric Galerkin boundary element methods and their corresponding numerical implementation. Designed to convey effective unified procedures for the treatment of singular and hypersingular integrals that naturally arise in the method. Symbolic codes using Maple® for singular-type integrations are provided and discussed in detail. The user-friendly adaptive computer code BEAN (Boundary Element ANalysis), fully written in Matlab®, is available as a companion to the text. The complete source code, including the graphical user-interface (GUI), can be downloaded from the web site http://www.ghpaulino.com/SGBEM_book. The source code can be used as the basis for building new applications, and should also function as an effective teaching tool. To facilitate the use of BEAN, a video tutorial and a library of practical examples are provided.
Restoring normal function and appearance after massive facial injuries with bone loss is an important unsolved problem in surgery. An important limitation of the current methods is heuristic ad hoc ...design of bone replacements by the operating surgeon at the time of surgery. This problem might be addressed by incorporating a computational method known as topological optimization into routine surgical planning. We tested the feasibility of using a multiresolution three-dimensional topological optimization to design replacements for massive midface injuries with bone loss. The final solution to meet functional requirements may be shaped differently than the natural human bone but be optimized for functional needs sufficient to support full restoration using a combination of soft tissue repair and synthetic prosthetics. Topological optimization for designing facial bone tissue replacements might improve current clinical methods and provide essential enabling technology to translate generic bone tissue engineering methods into specific solutions for individual patients.
In density-based topology optimization, the design space is parameterized by assigning a density to each element that discretizes the domain. However, establishing a limit on the maximum attainable ...thickness of the structural components in this framework is non-trivial. To control the thickness, knowledge of both the central axis of the components and the elements that reside beyond a specified thickness is required for penalizing the correct design variables. This study proposes a geometric constraint-based method for exerting control over the maximum allowable thickness of the structural members in topology optimization. The central axis of the structural components is traced by identifying the inflection points of the density distribution, where the density is locally maximum. By computing the angle of the spatial gradient of the density distribution and taking their divergence, the inflection points can be reliably located in all regions of the design domain. Based on geometric information, domains of elements beyond the specified thickness from the inflection points are constructed. Then, a constraint is defined to penalize material formation only in these elements. As a result, control over the maximum thickness of the structural components can be achieved during topology optimization. The framework can also be utilized to regulate the minimum thickness of the structural components by enforcing material formation within a specified thickness. Special measures are implemented to enable the formation of junction regions within the domain while preserving the imposed thickness constraint. The proposed method is applied to topology optimization of minimum compliance and heat conduction problems to demonstrate its applicability.
With the emergence of additive manufacturing technology, patient-specific cranial implants using 3D printing have massively influenced the field. These implants offer improved surgical outcomes and ...aesthetic preservation. However, as additive manufacturing in cranial implants is still emerging, ongoing research is investigating their reliability and sustainability. The long-term biomechanical performance of these implants is critically influenced by factors such as implant material, anticipated loads, implant-skull interface geometry, and structural constraints, among others. The efficacy of cranial implants involves an intricate interplay of these factors, with fixation playing a pivotal role. This study addresses two critical concerns: determining the ideal number of fixation points for cranial implants and the optimal curvilinear distance between those points, thereby establishing a minimum threshold. Employing finite element analysis, the research incorporates variables such as implant shapes, sizes, materials, the number of fixation points, and their relative positions. The study reveals that the optimal number of fixation points ranges from four to five, accounting for defect size and shape. Moreover, the optimal curvilinear distance between two screws is approximately 40 mm for smaller implants and 60 mm for larger implants. Optimal fixation placement away from the center mitigates higher deflection due to overhangs. Notably, a symmetric screw orientation reduces deflection, enhancing implant stability. The findings offer crucial insights into optimizing fixation strategies for cranial implants, thereby aiding surgical decision-making guidelines.
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•Automated cross-sectional extraction for branching structures is presented.•Methodology utilized skeletonization of object as reference for sampling planes.•Surface mesh is sliced to ...extract a 2D point cloud.•Filter algorithm for exclusion of peripheral slicing is presented.•Several case studies demonstrate capabilities and limitations of the method.
Many applications rely on scanned data, which can come from a variety of sources: optical scanners, coordinate measuring machines, or medical imaging. We assume that the data input to these applications is an unorganized point cloud or mesh of vertices. The objective may be to find particular features (medical diagnostics or reverse engineering) or comparison to some reference geometry (e.g. dimensional metrology). This paper focuses on the feature fitting of a segmented point cloud, specifically for branched, organic structures or structural frames, and targets non-monolithic geometries. In this paper, a methodology is presented for the automated recovery of cross-sectional shapes using centrally located curves. We assume a triangulated surface mesh is generated from the scanned point cloud. This surface mesh is the starting point for our methodology. We then find the curve skeleton of the part which abstractly describes the global geometry and topology. Next after segmenting the curve skeleton into non-branching segments, orthogonal planes to the curve skeleton segments, at preset or adaptive intervals, make slices through the surface mesh edges. The intersection points are extracted creating a 2D point cloud of the cross section. A number of application specific post-processing operations can be performed after obtaining the 2D point cloud cross sections and the curve skeleton paths including: calculations such as area or area moments of inertia, feature fitting or recognition, and digital shape reconstruction. Case studies are presented to demonstrate capabilities and limitations, and to provide insight into appropriate uses and adaptations for the presented methodology.
Malignant central airway obstruction can cause severe breathing difficulty in a patient that requires surgical intervention or stent implantation to alleviate it. A predictive model to identify the ...onset of this event as the central airway is progressively compressed by tumor growth will be helpful for clinicians to plan for medical intervention. We present such a model to simulate tumor compression of the trachea and the resulting change in airflow dynamics to estimate the level of stenosis that will cause severe breathing difficulties. A patient-specific model of trachea was generated from acquired Computed Tomography (CT) scans for the simulations. The compression of this trachea due to tumor growth is modeled using nonlinear contact simulations of ellipsoidal tumors with the trachea. Computational fluid dynamics (CFD) is employed to simulate the turbulent airflow during inhalation in the stenosed trachea. From the CFD simulated flow fields, the power loss due to airflow through the domain is calculated. The results show that when the obstruction in the trachea reaches 50%, compared to the undeformed model, the power loss can rise to more than 66%. A measure of breathing difficulty can be derived by correlating it with the power loss. Thus, medical intervention can be predicted based on the degree of stenosis if the induced power loss exceeds a threshold that causes severe breathing discomfort.
•Power loss for breathing in patients with tracheal lesions is studied in this work.•Stenosis of 3D models is mimicked by contact simulation with ellipsoidal tumors.•Turbulent airflow in the stenosed trachea models is simulated using CFD.•For 50% stenosis, the power loss during inhalation rises to more than 66%.•Using a tumor growth model, the proposed method may predict when to operate on the patient.
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