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This paper is to present an important issue of fatigue failure in the design of multi-fasteners jointed structure. To avoid failure in the connection area, Sines criterion is utilized. Fatigue constraints are handled in the context of stress based topology optimization. To eliminate the high stresses caused by the finite element modeling, the control volume is defined to evaluate the stress states around the fasteners. The standard topology optimization is extended to minimize the structural compliance with fatigue failure constraints. To address singularity problems related to stress constraints, q-p relaxation is used. P-norm is used as the constraints aggregation scheme. Basing on the above, the design sensitivity of fatigue constraints is derived and calculated. The proposed method is verified by a numerical example of an assembled I-beam. The comparisons of the numerical results have shown the effect of the fatigue constraint.

• 2-D turbulent natural convection heat sink is optimized using topology optimization. • The k-ω turbulent model which is one of RANS models is employed. • Some modifications of the original turbulent natural convection model are developed. • Effects of the Grashof number on optimal designs are investigated. • The solid thermal conductivity significantly affects optimal results. The geometric structure of two-dimensional (2-D) heat sinks cooled by turbulent natural convection is optimized using a density-based topology optimization approach. The governing equations are the coupled equations of the k - ω turbulent equation, which is one type of the Reynolds-Averaged Navier-Stokes (RANS) equations, and the thermal convection-diffusion equation based on the Bousinessq approximation. In order to facilitate topology optimization, we make some modifications to the original governing equations to control the fluid/solid distribution by introducing a material density as the design variable. Specifically, several penalization terms are added to the original k - ω turbulent model for immersing the solid material, and the thermophysical properties are interpolated to obtain a generalized thermal equation suitable for both the fluid and solid materials. During the optimization process, the design variable is updated according to the gradient information obtained through adjoint-based sensitivity analysis. In numerical examples, the effects of the Grashof number and the solid thermal conductivity on optimal configurations are, respectively, investigated for two types of heat sinks. The numerical results indicate that the Grashof numbers and the solid thermal conductivity can significantly affect the optimal results; the flow channels will become narrower to accommodate the flow and heat transfer conditions with the increase of the Grashof number; and the design characteristics and heat transfer performance vary greatly for increasing the solid thermal conductivity when the conductivity is low, while at the case of high conductivity, this variation slows down obviously. [ABSTRACT FROM AUTHOR]

With the rapid development of 3D printing technology, lattice structures have been widely utilized in structural designs aimed at vibration resistance due to their excellent performance. In this study, considering the moderate improvement of vibration suppression property of existing graded lattice, we introduce high-damping material into the optimization framework and further enhance the vibration resistance ability of gradient lattices. This framework extends the existing framework of stiffness and mass distribution to incorporate the distribution of stiffness, mass, and damping, which allows us to consider the damping changes with the cell configuration. Initially, the lattice cells are assigned with two different constitutive materials, one with high stiffness and the other with excellent damping properties. Different from traditional lattice units, we can obtain a series of lattice units with adjustable stiffness , mass and damping in a certain range. Via the homogenization method on the frequency domain, the complex elastic matrices about distribution of these lattice cells controlled by three parameters are obtained. In the meantime, the loss factor of these lattice cells is also obtained. A polynomial-based interpolation technique is employed to characterize the graded lattice units, which is integrated into an optimization process aimed at minimizing the lattice structures' vibration responses. Several numerical examples are presented to illustrate this framework's effectiveness, and experimental tests on 3D printed specimens are conducted to validate the numerical results. It's worth noting that under the condition that the total weight of the structure remains unchanged, this weakens the overall stiffness of the structure (the reduction of first-order natural frequency), but greatly increases the damping of the structure (with a widened resonance peak) to resist the vibration of the structure. For the lattice structures induced by damping materials, the average loss factor is 0.114, which is almost doubled to the average value of those not including the damping material. When comparing the results of the mean displacement amplitude with and without damping materials, the reduction of displacement amplitude of lattice structures is above 25 %. The methodology expands the scope of optimization design for lattice structures, moving beyond stiffness maximization to include vibration mitigation by determining the appropriate distribution of stiff and damping materials, showcasing the practical applicability of the presented methods in engineering practice. ● Dynamic topology optimization approach is developed for gradient lattice filled with damping materials. ● The complex elastic matrix of parameterized lattice filled with damping material is derived. ● Experimental results confirm the significant vibration attenuation by proper introduction of damping materials. [ABSTRACT FROM AUTHOR]

In this work, a novel design and modeling method is proposed to obtain hierarchical structures with non-uniform lattice microstructures based on density-based topology optimization. First of all, a parametric concept is proposed to generate a family of parameterized lattice microstructures that present similar topological features. In order to balance the structural performance and computational efficiency, we construct a Parameterized Interpolation for Lattice Material (PILM) model and the mathematical formulation incorporates two new design variables. At the macroscale, the relative density variable is applied to describe material volume fraction in the design domain, instead of using the pseudo-density in the Solid Isotropic Material with Penalization (SIMP) model. At the microscale, each macroelement is regarded as an individual microstructure controlled by an aspect ratio variable. The equivalent properties of parameterized lattice microstructures can be derived by interpolating the effective elastic matrixes of several typical microstructure unit cells, which avoid expensive iterative homogenization calculations during optimization procedure. Hence, the multiscale concurrent design method can optimize the macroscopic distribution and their spatially varying microstructural configurations simultaneously at an affordable computation cost. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. Furthermore, the obtained hierarchical structures with non-uniform lattice microstructures show good manufacturability and remarkably improved structural performance by means of the additive manufacturing and experimental testing, compared to the designs with uniform lattice microstructures. [ABSTRACT FROM AUTHOR]

Abstract: Integrated design of the structure topology and involved component layout is a challenging design issue when compared with traditional topology optimization. In this paper, we propose an implicit modeling approach that works completely on an Eulerian finite element mesh throughout the whole optimization process. To this aim, implicit level-set functions and R-functions are employed to describe geometrical shapes of movable components. In particular, a modified arctan function is adopted to depict the material discontinuity along the interface between the structure domain and each component domain. They are then used for material interpolations and analytical sensitivity analysis w.r.t. both pseudo-density design variables and location design variables related to the host structure and components, respectively. Based on a variety of numerical tests, it is demonstrated that considered design problems with movable components can easily be solved by extending the SIMP material model based topology optimization approach using an Eulerian mesh and the gradient-based optimization algorithm. [Copyright &y& Elsevier]

Abstract: Two kinds of design variables, i.e., pseudo-density variables associated with the framework structure and location design variables associated with connected components are involved in the layout design of multi-component systems. Although sensitivities with respect to the first ones can easily be carried out as in topology optimization, the semi-analytical method (SAM) is often used for sensitivity analysis with respect to the location design variables. Due to the geometric perturbation of the finite element mesh, the latter can then be regarded as a geometric perturbation model (GPM). In this paper, we propose a material perturbation model (MPM) using fixed finite element (FE) mesh for sensitivity analysis with respect to location design variables. The material discontinuity across the boundary between each component and the framework structure is smoothed approximately by means of a modified Heaviside function. When a location design variable of a certain component is perturbed, attached finite elements to the component boundary are assumed to undertake only a shift of material properties while the finite element mesh itself remains geometrically unchanged. As a result, analytical sensitivities with respect to location design variables are achieved as easily as for pseudo-density variables. The computing efficiency is thus improved because the velocity field for the mesh perturbation in the semi-analytical scheme is no longer needed. The MPM is illustrated by means of numerical tests, especially the design optimization of 3D multi-component systems. [Copyright &y& Elsevier]

In this paper, we propose a B-Spline Offset Feature (BSOF) for feature-driven topology optimization. The feature is inspired from the geometric morphology of worms characterized by an elongated cylindrical, bilaterally symmetric, and well-segmented body along a highly deformable directrix. B-spline is used to define the directrix with its outward and inward offsets outlining the BSOF. This definition endows the BSOF with high deformability such as self-folding and self-intersection. To construct the implicit level-set function (LSF), the BSOF is decomposed into a sequence of segments whose LSFs can easily be constructed by Kreisselmeier–Steinhauser (KS) function. Regular or irregular shaped segments are identified by the deformation gradient. Irregular segments involving geometrical singularities, e.g. distorted and concave segments, are replaced with convex hulls. The stiffest structure design and compliant mechanism synthesis are studied to illustrate the effectiveness and advantages of the proposed BSOF for topology optimization. • Bio-inspired B-Spline Offset Feature (BSOF) is proposed for topology optimization. • The BSOF retains high deformability of self-folding and self-intersection. • The feature segmentation method is developed to construct the LSF of BSOF. • Convex hull replacement of irregular segments can stable the optimization process. [ABSTRACT FROM AUTHOR]

In this paper, a feature-driven topology optimization method is developed. This is the first study on layout design of multiple engineering features using level-set functions (LSFs) and Boolean operations. The novelty of this work is threefold. First, multiple engineering features of arbitrary shape are considered as basic design primitives and topology variation is achieved via the layout and shape optimization of the features. Kreisselmeier–Steinhauser (KS) function constructed by means of Boolean operations is adopted as the LSF, which uses an implicit function to ensure a smooth description and topological changes of basic features and the whole structure. Second, using a modified Heaviside function to smooth the void–solid material transition over a fixed computing mesh, a narrow-band domain integral scheme is developed for the efficient sensitivity analysis. Third, the gray material distribution regions at the feature-connecting portions are analyzed and the underlying reason for that is traced to the non-equidistant distribution of level-set contours of specific features. To avoid the gray regions, an approximated signed distance function is proposed to regularize the LSF and KS function. The bounded normalization property of the KS function is highlighted for its construction with the signed distance functions or normalized first-order approximations. Numerical examples are finally tested to demonstrate the validity and merits of the proposed feature-driven topology optimization for complicated design problems. [ABSTRACT FROM AUTHOR]

This paper presents a highly deformable Multi-Section B-Spline Offset Feature (MS-BSOF) for topology optimization. The MS-BSOF is bio-inspired from the geometric morphology of worms which is modeled with a deformable directrix and deformable cross-sections. The directrix is defined by B-spline curve. The cross-section profile in 3D case is determined by a set of control cross-section profiles, each of which is defined as a closed B-spline (CBS) to ensure high deformability. The implicit representations of the proposed 2D and 3D MS-BSOFs are formulated using the level-set function (LSF). To perform topology optimization, a topology variation modeler (TVM) is constructed with the proposed MS-BSOF within a freeform design domain modeler (FDDM). Several numerical examples are presented to demonstrate the effectiveness and merits of the MS-BSOF. • The worm-like highly deformable MS-BSOF is proposed for 2D and 3D topology optimization. • Parametric and implicit representations of the MS-BSOF are developed. • The rotation minimizing frame with minimal twist property is used to define the moving frame of 3D MS-BSOF. [ABSTRACT FROM AUTHOR]

Surface flows can represent the motions of the viscous and incompressible fluid at the solid/fluid interfaces. This paper presents a topology optimization approach for surface flows and extends the design space of topology optimization of fluidic structures onto the curved surfaces in the forms of 2-manifolds corresponding to the geometrical configurations of the solid/fluid interfaces. The presented approach is implemented by filling a porous medium onto the 2-manifolds. An artificial Darcy friction is correspondingly added to the area force term of the surface Navier-Stokes equations used to describe the surface flows and the physical area forces are penalized to eliminate their existence in the fluidic regions and to avoid the invalidity of the porous medium based topology optimization model. Topology optimization for the steady and unsteady surface flows has been executed by iteratively evolving the impermeability of the porous medium, where the impermeability is interpolated by the material density derived from a design variable. The related partial differential equations are solved by using the surface finite element method. Numerical examples have been provided to demonstrate this topology optimization approach for the surface flows, including the boundary velocity driven flows, the area force driven flows and the convection-diffusion flows. [ABSTRACT FROM AUTHOR]

This paper presents a B-spline based topology optimization method to design self-supporting structures for additive manufacturing (AM). The density field of the structure is represented by B-spline parameterization together with Heaviside function through Boolean operation. Two constraints are constructed for overhang control. One concerns the overhang angle constraint to structural boundaries and is formulated in an integral form within a narrowband region identified by the density gradient norm. The density gradient is obtained by directly computing the derivatives of the B-spline density field. The other concerns the constraint to avoid undesired V-shaped areas and is formulated by limiting the density values at detection points uniformly distributed in the design domain. Several examples are dealt with to demonstrate the effectiveness of the proposed method. It is shown that the proposed overhang control scheme is independent of the FE mesh with the help of B-spline parameterization and works well with free-form design domains. • A B-spline based topology optimization method with overhang constraint is proposed. • The density gradient is computed by differentiating directly the B-spline function. • The blurry structural boundary is identified by the density gradient norm. • V-shaped areas are avoided by limiting density values at prescribed detection points. • The method can deal with various critical overhang angles and build directions. [ABSTRACT FROM AUTHOR]

• The moment of inertia constraint is introduced in the rudder design. • The skin compliance is proved more effective in the thermal loading rudder design. • An engineering-oriented post-processing is proposed for additive manufacturing. In high-speed vehicles, rudders often endure both aerodynamic pressure and thermal loads. The innovative design of rudders is of great importance for the performance of the whole vehicle. In this work, thermo-elastic topology optimization is adopted to design a typical all-movable rudder structure. The compliance of the rudder skin is considered to be a new objective and the moment of inertia of the rudder is constrained during optimization to ensure its fast response to instructions of the control system. Then sensitivity analysis of the structural compliance and the moment of inertia is carried out. Optimization results show that thermal load has a great effect on the optimized configuration and minimizing the compliance of the rudder skin gives much better design than minimizing the global compliance. Subsequently, an engineering-oriented post-processing is conducted to make the optimized design suitable for additive manufacturing. An appropriate printing direction is selected based on the layout of the optimized ribs and certain ribs are reshaped with fillets to make the rudder free of internal support structures. Besides, according to a secondary topology optimization of the ribs and the stress distribution, a set of powder-discharge holes are properly opened on the ribs so that all cavities within the rudder are connected and the metal powder inside the rudder can be discharged with little effort after manufacturing. Finally, the optimized design is successfully printed using Selective Laser Melting, demonstrating the proposed post-processing is effective for additive manufacturing. [ABSTRACT FROM AUTHOR]

• A new data-driven topology optimization (DDTO) framework is proposed. • Sensitivity analysis for discrete noisy material data sets is developed. • Verification of the new DDTO framework by truss structure designs. The application of structural topology optimization with complex engineering materials is largely hindered due to the complexity in phenomenological or physical constitutive modeling from experimental or computational material data sets. In this paper, we propose a new data-driven topology optimization (DDTO) framework to break through the limitation with the direct usage of discrete material data sets in lieu of constitutive models to describe the material behaviors. This new DDTO framework employs the recently developed data-driven computational mechanics for structural analysis which integrates prescribed material data sets into the computational formulations. Sensitivity analysis is formulated by applying the adjoint method where the tangent modulus of prescribed uniaxial stress-strain data is evaluated by means of moving least square approximation. The validity of the proposed framework is well demonstrated by the truss topology optimization examples. The proposed DDTO framework will provide a great flexibility in structural design for real applications. [ABSTRACT FROM AUTHOR]