Topology Optimization (TO) is an established method for the development of high strength and lightweight structural components. However, its results have to be geometrically revised to obtain a computational model that meets product development requirements. Design has to be in accordance with manufacturing constraints. Geometry reconstruction therefore still is a typically manual and tedious task, but increasingly supported by computational and automated approaches. In this paper, the inclusion of a casting constraint in an automated Medial Axis based reconstruction method is presented. Since the Medial Axis provides cross-section values by the computation of maximally inscribed spheres, this information is used for geometry reconstruction and even further for the purposeful adaption of the cross-section to match Heuver's circle method. Thereby, the directed solidification of molten material is considered. With a predefined feeder position, the demonstrator of a suspension control arm is used to show the application of the method. Resulting CAD-models are also structurally evaluated for their stiffness characteristics.

Polygon meshes and particularly triangulated meshes can be used to describe the shape of different types of geometry such as bicycles, bridges, or runways. In engineering, such polygon meshes can occur as finite element meshes, resulting from topology optimization or laser scanning. This article presents an automated parameterization of polygon meshes into a parametric representation using subdivision surfaces, especially in topology optimization. Therefore, we perform surface skeletonization on a volumetric grid supported by the Euclidian distance transformation and topology preserving and shape-preserving criterion. Based on that surface skeleton, an automated conversation into a Subdivision Surface Control grid is established. The final mid-surface-like parametrization is quite flexible and can be changed by variating the control gird or the local thickness.

Nowadays, a large number of different tools that support early phases of design are available to engineers. In the past decade a specialized set of CAD-based tools were developed, that support the ideation process by generating different design alternatives according to the criteria given by the designer. Two types of tools are discussed in this paper: topology optimization and generative design tools. To investigate to what extent these tools are suitable for use in early design phases and what are the main differences between them, a study was conducted on an industrial case.

This paper presents how numerical optimization methods, like topology optimization, and new design possibilities through additive manufacturing (AM) can be used for structural improvements of the load introduction points in sandwich structures. A new design approach is presented, which allows a direct load-path optimized integration of the load introduction point into the sandwich core. The corresponding methodical procedure is shown and the application is demonstrated exemplarily for a sandwich structure with a honeycomb core. The advantages for design science are that the new design possibilities of AM can be considered and used when designing the load introduction points. Thus, the additional reinforcements of the sandwich structures to absorb locally introduced forces in the lightweight structure can be minimized. This enables a meaningful technical comparison and it can be decided in the future whether such a design can be used for sandwich structures under economic aspects. In addition, the influence of the initial and boundary conditions on the design is presented and discussed in this paper. The challenges of optimizing multiple load introduction points simultaneously as well as the special aspects to be considered when transferring the design approach to larger sandwich structures are also highlighted.

This study presents an optimal design procedure including topology optimization and size–shape optimization methods to maximize mechanical advantage (which is defined as the ratio of output force to input force) of the synthesized compliant mechanism. The formulation of the topology optimization method to design compliant mechanisms with multiple output ports is presented. The topology-optimized result is used as the initial design domain for subsequent size–shape optimization process. The proposed optimal design procedure is used to synthesize an adaptive compliant gripper with high mechanical advantage. The proposed gripper is a monolithic two-finger design and is prototyped using silicon rubber. Experimental studies including mechanical advantage test, object grasping test, and payload test are carried out to evaluate the design. The results show that the proposed adaptive complaint gripper assembly can effectively grasp irregular objects up to 2.7 kg.

In this article, the material distributive topology-based design optimization of ultra-wide band (UWB) antenna is proposed by using improved binary particle swarm optimization (BPSO) with finite difference time domain (FDTD) method. In the improved BPSO implementation, the velocity of each particle is calculated based on complete set of bits of particle position vector. The V-shaped transfer function is employed to transform all real values of velocities to values in the interval [0,1]. The fitness function of all the particles in BPSO algorithm are computed parallely by using FDTD simulation. The usage of FDTD and the parallel computation helps in analyzing the broadband frequency characteristics of the antenna with a single simulation run. The return loss of the optimized UWB antenna obtained from FDTD, Computer Simulation Technology (CST) simulation and practical measurement are in good agreement and show good impedance matching.

This paper presents topology optimization of capillary, the typical two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method. The two-phase flow is described by the diffuse-interface model with essential no slip condition imposed on the wall, where the singularity at the contact line is regularized by the molecular diffusion at the interface between two immiscible fluids. The level set method is utilized to express the fluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface. Based on the variational procedure for the total free energy of two-phase flow, the Cahn-Hilliard equations for the diffuse-interface model are modified for the two-phase flow with implicit boundary expressed by the level set method. Then the topology optimization problem for the two-phase flow is constructed for the cost functional with general formulation. The sensitivity analysis is implemented by using the continuous adjoint method. The level set function is evolved by solving the Hamilton-Jacobian equation, and numerical test is carried out for capillary to demonstrate the robustness of the proposed topology optimization method. It is straightforward to extend this proposed method into the other two-phase flows with two immiscible fluids.

In this article, two methods to develop and optimize accompanying building spatial and structural designs are compared. The first, a coevolutionary method, applies deterministic procedures, inspired by realistic design processes, to cyclically add a suitable structural design to the input of a spatial design, evaluate and improve the structural design via the finite element method and topology optimization, adjust the spatial design according to the improved structural design, and modify the spatial design such that the initial spatial requirements are fulfilled. The second method uses a genetic algorithm that works on a population of accompanying building spatial and structural designs, using the finite element method for evaluation. If specific performance indicators and spatial requirements are used (i.e., total strain energy, spatial volume, and number of spaces), both methods provide optimized building designs; however, the coevolutionary method yields even better designs in a faster and more direct manner, whereas the genetic algorithm based method provides more design variants. Both methods show that collaborative design, for example, via design modification in one domain (here spatial) to optimize the design in another domain (here structural) can be as effective as monodisciplinary optimization; however, it may need adjustments to avoid the designs becoming progressively unrealistic. Designers are informed of the merits and disadvantages of design process simulation and design instance exploration, whereas scientists learn from a first fully operational and automated method for design process simulation, which is verified with a genetic algorithm and subject to future improvements and extensions in the community.

Based on the boundary vorticity-flux theory, topology optimization of the caudal fin of the three-dimensional self-propelled swimming fish is investigated by combining unsteady computational fluid dynamics with moving boundary and topology optimization algorithms in this study. The objective functional of topology optimization is the function of swimming efficiency, swimming speed and motion direction control. The optimal caudal fin, whose topology is different from that of the natural fish caudal fin, make the 3D bionic fish achieve higher swimming efficiency, faster swimming speed and better maneuverability. The boundary vorticity-flux on the body surface of the 3D fish before and after optimization reveals the mechanism of high performance swimming of the topology optimization bionic fish. The comparative analysis between the swimming performance of the 3D topology optimization bionic fish and the 3D lunate tail bionic fish is also carried out, and the wake structures of two types of bionic fish show the physical nature that the swimming performance of the 3D topology optimization bionic fish is significantly better than the 3D lunate tail bionic fish.

This paper presents a new technique for shape and topology optimization of fluid channels using generative design synthesis methods. The proposed method uses the generative abilities of graph grammars with simulation and analysis power of conventional computational fluid dynamics methods. The graph grammar interpreter GraphSynth is used to carry out graph transformations, which define different topologies for a given multiple-inlet multiple-outlet problem. After evaluating and optimizing the generated graphs, they are first transformed into meaningful three-dimensional shapes. These solutions are then analyzed by a computational fluid dynamics solver for final evaluation of the possible solutions. The effectiveness of the proposed method is checked by solving a variety of available test problems and comparing them with those found in the literature. Furthermore, by solving very complex large-scale problems, the robustness and effectiveness of the method is tested. To extend the work, future research directions are presented.

Searching for the optimal partitioning of a domain leads to the use of the adjoint methodin topological asymptotic expansions to know the influence of a domain perturbation on acost function. Our approach works by restricting to local subproblems containing theperturbation and outperforms the adjoint method by providing approximations of higherorder. It is a universal tool, easily adapted to different kinds of real problems and doesnot need the fundamental solution of the problem; furthermore our approach allows toconsider finite perturbations and not infinitesimal ones. This paper provides theoreticaljustifications in the linear case and presents some applications with topologicalperturbations, continuous perturbations and mesh perturbations. This proposed approach canalso be used to update the solution of singularly perturbed problems.

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal design, in particular shape and topology optimization, and are most often solved numerically utilizing a finite element approach. Within the FV framework for control in the coefficients problems the main difficulty we face is the need to analyze the convergence of fluxes defined on the faces of cells, whereas the convergence of the coefficients happens only with respect to the “volumetric” Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise.We provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example.

In topology optimization problems, we are often forced to deal with large-scale numericalproblems, so that the domain decomposition method occurs naturally. Consider a typicaltopology optimization problem, the minimum compliance problem of a linear isotropicelastic continuum structure, in which the constraints are the partial differentialequations of linear elasticity. We subdivide the partial differential equations into twosubproblems posed on non-overlapping sub-domains. In this paper, we consider the resultingproblem as multilevel one and show that it can be written as one level problem

This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.

The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the Hamiltonian; next the solution to its stationary Hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the Hamiltonian function can be explicitly formulated and when the Jacobian is sparse, but becomes impractical otherwise (e.g. for non local control constraints). An error estimate for the difference between exact and approximate objective functions is derived, depending only on the difference of the Hamiltonian and its finite dimensional regularization along the solution path and its L2 projection, i.e. not on the difference of the exact and approximate solutions to the Hamiltonian systems.

The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization/reconstruction algorithms. From the theoretical viewpoint, the expression of the topological sensitivity is well-established in many situations where the governing p.d.e. system is of elliptic type. This paper focuses on the derivation of such formulas for parabolic and hyperbolic problems. Different kinds of cost functionals are considered.

The goal of this paper is to study the so-called worst-case or robustoptimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst,compliance when the loads are subject to some unknown perturbations.We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm tocompute it. Then, in the framework of Hadamard method, wecompute the directional shape derivative of this criterion which isused in a numerical algorithm, based on the level set method,to find optimal shapes that minimize the worst-case compliance.Since this criterion is usually merely directionally differentiable,we introduce a semidefinite programming approach toselect the best descent direction at each step of agradient method. Numerical examples are given in 2-d and 3-d.

The evolutionary structural optimization method is improved and extended to elastic-plastic topology optimization for the first time. An adaptive rejection ratio is proposed to control the number of removal elements without destroying the symmetric pattern in each evolution. Two performance indices suitable for elastic-plastic topology optimization are also proposed and examined. The performance indices can be used to investigate the material efficiency of structures in different evolutionary stages, and to serve as stop criteria in the evolutionary process. Moreover, an interactive special purpose computer analysis and graphics system is developed to visualize the topology in the evolutionary process. Finally, the effects of yield stress, Young's modulus, and the prescribed displacement in an elastic-plastic analysis on the obtained topology are discussed.

We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S, which is the total work of the pressure and internal forces at the equilibrium displacement. In order to prevent from homogenization we add a penalization on the perimeter of S. We propose an approximation of our problem in the framework of Γ-convergence, based on an approximation of our three phases by a smooth phase-field. We detail the numerical implementation of the approximate energies and show a few experiments.