Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

Multi-material compliant mechanisms design enables potential design possibilities by exploiting the advantages of different materials. To satisfy mechanical/thermal impedance matching requirements, a method for multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition is presented in this study. In the optimization model, the element stacking method is employed to describe the material distribution and handle material-dependent boundary condition. The maximization of the output displacement of the compliant mechanism is developed as the objective function and the structural volume of each material is the constraint. Fictitious domain approach is applied to circumvent the numerical instabilities in topology optimization problem with geometrical nonlinearities. The method of moving asymptotes is applied to solve the optimization problem. Several numerical examples are presented to demonstrate the validity of the proposed method. The optimal topologies of the compliant mechanisms obtained by the proposed method can satisfy the specified material-dependent boundary condition.

Coupling Moving Morphable Voids and Components Based Topology Optimization of Hydrogel Structures Involving Large Deformation

A coupling of moving morphable void and component approach for the topology optimization of hydrogel structures involving recoverable large deformation is proposed in this paper. In this approach, the geometric parameters of moving morphable voids and components are set as design variables to respectively describe the outline and material distribution of hydrogel structures for the first time. To facilitate the numerical simulation of large deformation behavior of hydrogel structures during the optimization process, the design variables are mapped to the density field of the design domain and the density field is then used to interpolate the strain energy density function of the element. Furthermore, the adjoint sensitivity of the optimization formulation is derived and combined with the gradient-based algorithm to solve the topology optimization problem effectively. Finally, two representative numerical examples of the optimization of isotropic hydrogel structures are used to prove the effectiveness of the proposed method, and the optimization design of an anisotropic bionic hydrogel structure is presented to illustrate the applicability of the method. Experimental results are also presented to demonstrate that the explicit topologies obtained from the method can be directly used in the manufacture of hydrogel-based soft devices.

Structural stability and artificial buckling modes in topology optimization

This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)

In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The proposed concept is proved through two examples of heat conduction on manifolds.

Evolutionary Discrete Multi-Material Topology Optimization Using CNN-Based Simulation Without Labeled Training Data

Multi-material topology optimization problem under total mass constraint is a challenging problem owning to the incompressibility constraint on the summation of the usage of the total materials. A novel optimization approach is proposed here that utilizes the wide search space of the genetic algorithm, and greatly reduced computational effects achieved from the direct structure-performance mapping. The former optimization is carefully designed based on our recent theoretical insights, while the latter simulation is derived via a novel convolutional neural network based simulation which does not rely on any labeled simulation data but is instead designed based on a physics-informed loss function. As compared with results obtained using latest approach based on density interpolation, structures of better compliances are observed under acceptable computational costs, as demonstrated by our numerical examples.

Topology Optimization Design and Experimental Research of a 3D-Printed Metal Aerospace Bracket Considering Fatigue Performance

In the aerospace industry, spacecraft often serve in harsh operating environments, so the design of ultra-lightweight and high-performance structures is a major requirement in aerospace structure design. In this article, a lightweight aerospace bracket considering fatigue performance was designed by topology optimization and manufactured by 3D-printing. Considering the requirements of assembly with a fixture for fatigue testing and avoiding stress concentration, a reconstructed model was presented by CAD software before manufacturing. To improve the fatigue performance of the structure, this article proposes the design idea of abstracting the practiced working condition of the bracket subjected to cycle loads in the vertical direction via a multiple load-case topology optimization problem by minimizing compliance under a variety of asymmetric extreme loading conditions. Parameter sweeping was used to improve the computational efficiency. The mass of the new bracket was reduced by 37% compared to the original structure. Both numerical simulation and the fatigue test were implemented to support the validity of the new bracket. This work indicates that the integration of the proposed topology optimization design method and additive manufacturing can be a powerful tool for the design of lightweight structures considering fatigue performance.

Imaging of small penetrable obstacles based on the topological derivative method

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Topological design of freely vibrating bi-material structures to achieve the maximum band gap centering at a specified frequency

The topological design of structures to avoid vibration resonance for a certain external excitation frequency is often desired. This paper considers the topology optimization of freely vibrating bi-material structures with fixed/varying attached mass positions, targeting at maximizing the frequency band gap centering at a specified frequency. A band gap measure index is proposed to measure the size of the band gap with a specified center frequency. Aiming at maximizing this measure index, the topology optimization problem is formulated on the basis of the material-field series-expansion (MFSE) method, which greatly reduces the number of design variables and at the same time keeps the capability to describe relatively complex structural topologies with clear boundaries. As the considered optimization problem is highly non-linear and may yield multiple local minima, a sequential Kriging-based optimization solution strategy is employed to effectively solve the optimization problem. This solution strategy exhibits a relatively strong global search capability and requires no sensitivity information. With the present topology optimization model and the gradient-free algorithm, relative large band gaps with specified center frequencies have been obtained for 2D beams and 3D plates, without specifying the frequency orders between which the desired band gap occurs in prior.

Lattice shells composed of two families of curved Kirchhoff rods: an archetypal example, topology optimization of a cycloidal metamaterial

A nonlinear elastic model for nets made up of two families of curved fibers is proposed. The net is planar prior to the deformation, but the equilibrium configuration that minimizes the total potential energy can be a surface in the three-dimensional space. This elastic surface accounts for the stretching, bending, and torsion of the constituent fibers regarded as a continuous distribution of Kirchhoff rods. A specific example of fiber arrangement, namely a cycloidal orthogonal pattern, is examined to illustrate the predictive abilities of the model and assess the limit of applicability of it. A numerical micro–macro-identification is performed with a model adopting a standard continuum deformable body at the level of scale of the fibers. A few finite element simulations are carried out for comparison purposes in statics and dynamics, performing modal analysis. Finally, a topology optimization problem has been carried out to change the macroscopic shear stiffness to enlarge the elastic regime and reduce the risk of damage without excessively losing bearing capacity.

Topology optimization incorporating external variables with metamodeling

The objective of conventional topology optimization is to optimize the material distribution for a prescribed design domain. However, solving the topology optimization problem strongly depends on the settings specified by the designer for the shape of the design domain or their specification of the boundary conditions. This contradiction indicates that the improvement of structures should be achieved by optimizing not only the material distribution but also the additional design variables that specify the above settings. We refer to the additional design variables as external variables. This paper presents our work relating to solving the design problem of topology optimization incorporating external variables. The approach we follow is to formulate the design problem as a multi-level optimization problem by focusing on the dominance-dependence relationship between external variables and material distribution. We propose a framework to solve the optimization problem utilizing the multi-level formulation and metamodeling. The metamodel approximates the relationship between the external variables and the performance of the corresponding optimized material distribution. The effectiveness of the framework is demonstrated by presenting three examples.