Optimal riser design in sand casting process by topology optimization with SIMP method I: Poisson approximation of nonlinear heat transfer equation

The optimal design of a casting feeding system is considered. The problem is formulated as the volume constrained topology optimization and is solved with the finite element analysis, explicit design sensitivity, and numerical optimization. In contrast to the traditional topology optimization where the objective function is defined on the design space, in the presented method, the design space is a subset of the complement of the objective function space. To accelerate optimization procedure, the nonlinear unsteady heat transfer equation is approximated with a Poisson-like equation. The feasibility of the presented method is supported with illustrative examples.     

Adhesive surface design using topology optimization

Tailoring adhesive properties between surfaces is of great importance for micro-scale systems, ranging from managing stiction in MEMS devices to designing wall-scaling gecko-like robots. A methodology is introduced for designing adhesive interfaces between structures using topology optimization. Structures subjected to external loads that lead to delamination are studied for situations where displacements and deformations are small. Only the effects of adhesive forces acting normal to the surfaces are considered. An interface finite element is presented that couples a penalty contact formulation and a Lennard–Jones model of van der Waals adhesive forces. Two- and three dimensional design optimization problems are presented in which adhesive force distributions are designed such that load-displacement curves of delaminating structures match target responses. The design variables describe the adhesive energy per area of the interface between the surfaces, as well as the geometry of the delaminating structure. A built-in length scale in the formulation of the adhesion forces eliminates the need for filtering to achieve comparable optimal adhesive designs over a range of mesh densities. The resulting design problem is solved by gradient based optimization algorithms evaluating the design sensitivities by the adjoint method. Results show that the delamination response can be effectively manipulated by the method presented. Varying simultaneously both adhesive and geometric parameters yields a wider range of reachable target load-displacement curves than in the case varying adhesive energy alone.     

Reliability optimization of topology communication network design using an improved ant colony optimization

Network design problem is a well-known NP-hard problem which involves the selection of a subset of possible links or a network topology in order to minimize the network cost subjected to the reliability constraint. To overcome the problem, this paper proposes a new efficiency algorithm based on the conventional ant colony optimization (ACO) to solve the communication network design when considering both economics and reliability. The proposed method is called improved ant colony optimizations (IACO) which introduces two addition techniques in order to improve the search process, i.e. neighborhood search and re-initialization process. To show its efficiency, IACO is applied to test with three different topology network systems and its results are compared with those obtained results from the conventional approaches, i.e. genetic algorithm (GA), tabu search algorithm (TSA) and ACO. Simulation results, obtained these test problems with various constraints, shown that the proposed approach is superior to the conventional algorithms both solution quality and computational time.     

Viscoelastic material design with negative stiffness components using topology optimization

An application of topology optimization to design viscoelastic composite materials with elastic moduli that soften with frequency is presented. The material is a two-phase composite whose first constituent is isotropic and viscoelastic while the other is an orthotropic material with negative stiffness but stable. A concept for this material based on a lumped parameter model is used. The performance of the topology optimization approach in this context is illustrated using three examples.     

A review of optimization of cast parts using topology optimization

This is the second part of a two-paper review of optimization of cast parts. In the first paper, we focused on the application of the original topology optimization codes. The problems with the interpretation has been shown and discussed. In this paper, we introduce TopShape to overcome this lack. It is able to take manufacturing constraints for cast parts into account. The features of TopShape and its results will be discussed and compared with the result of the commercial code OptiStruct. Furthermore, a new design alternative for cast parts will be derived.     

Piezoresistive sensor design using topology optimization

Piezoresistive materials, materials whose resistivity properties change when subjected to mechanical stresses, are widely utilized in many industries as sensors, including pressure sensors, accelerometers, inclinometers, and load cells. Basic piezoresistive sensors consist of piezoresistive devices bonded to a flexible structure, such as a cantilever or a membrane, where the flexible structure transmits pressure, force, or inertial force due to acceleration, thereby causing a stress that changes the resistivity of the piezoresistive devices. By applying a voltage to a piezoresistive device, its resistivity can be measured and correlated with the amplitude of an applied pressure or force. The performance of a piezoresistive sensor is closely related to the design of its flexible structure. In this research, we propose a generic topology optimization formulation for the design of piezoresistive sensors where the primary aim is high response. First, the concept of topology optimization is briefly discussed. Next, design requirements are clarified, and corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several design examples of piezoresistive sensors are presented to confirm the usefulness of the proposed method.     

A review of optimization of cast parts using topology optimization

In recent years, there has been considerable progress in the optimization of cast parts with respect to strength, stiffness, and frequency. Here, topology optimization has been the most important tool in finding the optimal features of a cast part, such as optimal cross-section or number and arrangement of ribs. An optimization process with integrated topology optimization has been used very successfully at Adam Opel AG in recent years, and many components have been optimized. This two-paper review gives an overview of the application and experience in this area. This is the first part of a two-paper review of optimization of cast parts.Here, we want to focus on the application of the original topology optimization codes, which do not take manufacturing constraints for cast parts into account. Additionally, the role of shape optimization as a fine-tuning tool will be briefly analyzed and discussed.     

Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.     

A review of homogenization and topology optimization III-topology optimization using optimality criteria

This is the first part of a three-paper review of homogenization and topology optimization, viewed from an engineering standpoint and with the ultimate aim of clarifying the ideas so that interested researchers can easily implement the concepts described. In the first paper we focus on the theory of the homogenization method where we are concerned with the main concepts and derivation of the equations for computation of effective constitutive parameters of complex materials with a periodic micro structure. Such materials are described by the base cell, which is the smallest repetitive unit of material, and the evaluation of the effective constitutive parameters may be carried out by analysing the base cell alone. For simple microstructures this may be achieved analytically, whereas for more complicated systems numerical methods such as the finite element method must be employed. In the second paper, we consider numerical and analytical solutions of the homogenization equations. Topology optimization of structures is a rapidly growing research area, and as opposed to shape optimization allows the introduction of holes in structures, with consequent savings in weight and improved structural characteristics. The homogenization approach, with an emphasis on the optimality criteria method, will be the topic of the third paper in this review.     

Minimization of sound radiation from vibrating bi-material structures using topology optimization

Up to now, work on topological design optimization of vibrating structures against noise radiation has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, and minimization of the dynamic compliance subject to harmonic loading on the structure. In this paper, we deal with topology optimization problems formulated directly with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. It is assumed that air is the acoustic medium and that a feedback coupling to the structure can be neglected. Certain conditions are assumed that imply that the sound power emission from the structural surface can be obtained in a simpler way than by solving Helmholz’ integral equation. Hereby, the computational cost of the structural-acoustical analysis is substantially reduced. Several numerical results are presented and discussed for plate- and pipe-like structures with different sets of boundary and loading conditions.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

Design of an energy-absorbing structure using topology optimization with a multimaterial model

To accommodate the dual objectives of many engineering applications, one objective to minimize the mean compliance for the stiffest structure under normal service conditions and the other objective to maximize the strain energy for energy absorption during excessive loadings, topology optimization with a multimaterial model is applied to the design of an energy-absorbing structure in this paper. The effective properties of the three-phase material are derived using a spherical microinclusion model. The dual objectives are combined in a ratio formation. Numerical examples from the proposed method are presented and discussed.     

Large-scale parallel topology optimization using a dual-primal substructuring solver

Parallel computing is an integral part of many scientific disciplines. In this paper, we discuss issues and difficulties arising when a state-of-the-art parallel linear solver is applied to topology optimization problems. Within the topology optimization framework, we cannot readjust domain decomposition to align with material decomposition, which leads to the deterioration of performance of the substructuring solver. We illustrate the difficulties with detailed condition number estimates and numerical studies. We also report the practical performances of finite element tearing and interconnection/dual–primal solver for topology optimization problems and our attempts to improve it by applying additional scaling and/or preconditioning strategies. The performance of the method is finally illustrated with large-scale topology optimization problems coming from different optimal design fields: compliance minimization, design of compliant mechanisms, and design of elastic surface wave-guides. The authors acknowledge the support of the Air Force Office of Scientific Research (AFOSR) under grant FA9550-05-1-0046. The computational facility was obtained under the grant AFOSR-DURIP FA9550-05-1-0291.     

Design of phononic materials/structures for surface wave devices using topology optimization

We develop a topology optimization approach to design two- and three-dimensional phononic (elastic) materials, focusing primarily on surface wave filters and waveguides. These utilize propagation modes that transmit elastic waves where the energy is contained near a free surface of a material. The design of surface wave devices is particularly attractive given recent advances in nano- and micromanufacturing processes, such as thin-film deposition, etching, and lithography, which make it possible to precisely place thin film materials on a substrate with submicron feature resolution. We apply our topology optimization approach to a series of three problems where the layout of two materials (silicon and aluminum) is sought to achieve a prescribed objective: (1) a grating to filter bulk waves of a prescribed frequency in two and three dimensions, (2) a surface wave device that uses a patterned thin film to filter waves of a single or range of frequencies, and (3) a fully three-dimensional structure to guide a wave generated by a harmonic input on a free surface to a specified output port on the surface. From the first to the third example, the resulting topologies increase in sophistication. The results demonstrate the power and promise of our computational framework to design sophisticated surface wave devices.     

Topology optimization of 2D continua for minimum compliance using parallel computing

Topology optimization is often used in the conceptual design stage as a preprocessing tool to obtain overall material distribution in the solution domain. The resulting topology is then used as an initial guess for shape optimization. It is always desirable to use fine computational grids to obtain high-resolution layouts that minimize the need for shape optimization and postprocessing (Bendsoe and Sigmund, Topology optimization theory, methods and applications. Springer, Berlin Heidelberg New York 2003), but this approach results in high computation cost and is prohibitive for large structures. In the present work, parallel computing in combination with domain decomposition is proposed to reduce the computation time of such problems. The power law approach is used as the material distribution method, and an optimality criteria-based optimizer is used for locating the optimum solution [Sigmund (2001)21:120–127; Rozvany and Olhoff, Topology optimization of structures and composites continua. Kluwer, Norwell 2000]. The equilibrium equations are solved using a preconditioned conjugate gradient algorithm. These calculations have been done using a master–slave programming paradigm on a coarse-grain, multiple instruction multiple data, shared-memory architecture. In this study, by avoiding the assembly of the global stiffness matrix, the memory requirement and computation time has been reduced. The results of the current study show that the parallel computing technique is a valuable tool for solving computationally intensive topology optimization problems.     

Interior point multigrid methods for topology optimization

In this paper, a new multigrid interior point approach to topology optimization problems in the context of the homogenization method is presented. The key observation is that nonlinear interior point methods lead to linear-quadratic subproblems with structures that can be favourably exploited within multigrid methods. Primal as well as primal-dual formulations are discussed. The multigrid approach is based on the transformed smoother paradigm. Numerical results for an example problem are presented. Received February 15, 1999     

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

This paper discusses a new structural optimization method, based on topology optimization techniques, using frame elements where the cross-sectional properties can be treated as design variables. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush–Kuhn–Tucker (KKT) conditions and a complementary strain energy-based approach. Based on the above, the optimal rotational angle of each frame element is obtained as a function of the balance of the internal moments. The above methodologies are applied to problems of minimizing the mean compliance and maximizing the eigen frequencies. Several examples are provided to show the utility of the presented methodology.