Integrated Topology Optimization Research Articles

Topological design of compliant smart structures with embedded movable actuators

In the optimal configuration design of piezoelectric smart structures, it is favorable to use actuation elements with certain predefined geometries from the viewpoint of manufacturability of fragile piezoelectric ceramics in practical applications. However, preserving the exact shape of these embedded actuators and tracking their dynamic motions presents a more challenging research task than merely allowing them to take arbitrary shapes. This paper proposes an integrated topology optimization method for the systematic design of compliant smart structures with embedded movable PZT (lead zirconate titanate) actuators. Compared with most existing studies, which either optimize positions/sizes of the actuators in a given host structure or design the host structure with pre-determined actuator locations, the proposed method simultaneously optimizes the positions of the movable PZT actuators and the topology of the host structure, typically a compliant mechanism for amplifying the small strain stroke. A combined topological description model is employed in the optimization, where the level set model is used to track the movements of the PZT actuators and the independent point-wise density interpolation (iPDI) approach is utilized to search for the optimal topology of the host structure. Furthermore, we define an integral-type constraint function to prevent overlaps between the PZT actuators and between the actuators and the external boundaries of the design domain. Such a constraint provides a unified and explicit mathematical statement of the non-overlap condition for any number of arbitrarily shaped embedded actuators. Several numerical examples are used to demonstrate the effectiveness of the proposed optimization method.

Integrated topology optimization with embedded movable holes based on combined description by material density and level sets

This paper presents a novel topology description model for topology optimization problems with embedded movable holes, combining the ability of the level set model for accurate geometrical description of the prescribed hole shapes, and the high efficiency of the material density-based method. By this means, any arbitrary hole shapes can be represented accurately and smoothly, while the topological changes can be easily handled by the material distribution model. An explicit mathematical expression is defined to obtain the actual structural layout by combing both models. Moreover, an effective model for the non-overlap constraint is proposed in a unified and systematic manner to avoid the overlaps between the holes and between each hole and the design domain boundary. Therein, the non-overlap constraint for all the embedded holes is imposed as a single explicit integral constraint over the design domain, thus avoiding the difficulties in the overlap detection of multiple arbitrary-shaped geometries. Such a non-overlap constraint is accurate and differentiable, facilitating an analytical design sensitivity analysis. Numerical examples are given to demonstrate the effectiveness and efficiency of the present method.

Integrated topology optimization and optimal control for vibration suppression in structural design

This paper presents a topology design methodology for structures with active vibration control. The methodology takes into account the structural effect of the control forces and includes the modal control design. Location points for the actuation forces are chosen a priori. Structural topology optimization is used for distributing material on a fixed domain, using continuum finite element discretization for the static and free vibration analyses. Optimal control for transient response in modal space is used to derive the control force. The cost function for the optimization combines the strain energy and the control energy. Results of the numerical simulations validates the proposed methodology.

Topology optimization for braced frames: Combining continuum and beam/column elements

This paper describes an integrated topology optimization technique with concurrent use of both continuum four-node quadrilateral finite elements and discrete two-node beam elements to design structural braced frames that are part of the lateral system of a high-rise building. The work explores the analytical aspects of optimal geometry for braced frames to understand the underlying behavior and provides a theoretical benchmark to compare numerical results. The influence of the initial assumptions for the interaction between the quadrilaterals and the frame members are discussed. Numerical examples are given to illustrate the present technique on high-rise building structures.

Topology optimization of periodic cellular solids based on a superelement method

It is well known that the structural performance of lightweight cellular solids depends greatly on the design of the representative volume element (RVE). In this article, an integrated topology optimization procedure is developed for the global stiffness maximization of 2D periodic and cyclic-symmetry cellular solids. A design variable linking technique and a superelement method are applied to model the structural periodicity and to reduce the computing time. In order to prevent the numerical instabilities associated with checkerboards in the design process, the quadratic perimeter constraint is used. Finally, the topology optimization problem is solved by the dual optimization algorithm. Several numerical examples are used to test the efficiency of the optimization procedure. Results show that the optimal topology of the RVE is not unique. It greatly depends on the size of the RVE. The computing efficiency can be greatly improved by means of the superelement technique. Also, for the optimal solution, the equivalent torsional rigidity has been compared with what is in the literature, to check the structural efficiency of the obtained topology. It has been observed that the current topology solution has the strongest rigidity when the same volume fraction of solid-phase materials is used.

Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique

AbstractDielectric resonator antennas (DRAs) are a relatively new class of antenna that utilizes the radiation phenomena of dielectric resonators in open space. Since mainly analytical approaches have been applied to investigate DRA designs, the current DRA forms are limited to simple geometric shapes and high‐performance DRAs with complex shapes have not yet been developed. Topology optimization is capable of yielding high‐performance structures, and has been extensively applied to a variety of structural optimization problems. Applying it to the task of DRA design may be extremely useful for the design of high‐performance antennas. On the other hand, the finite difference time domain (FDTD) method has been used to numerically evaluate general antenna performance, since it is numerically robust during time domain analyses and can handle complex models. Thus, the integration of topology optimization with the FDTD method has the potential to enable innovative designs of advanced antennas that offer exceptional performance. In this research, we propose a new topology optimization method for the design of DRAs that aim to operate with enhanced bandwidths, using the FDTD method. First, the concept of topology optimization is briefly discussed, and a way to integrate topology optimization with the FDTD method is proposed. Next, design requirements are clarified and the corresponding objective functions and the optimization problem are formulated. An optimization algorithm is constructed based on these formulations. Finally, several DRA design examples are presented to confirm the usefulness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

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.

Interbody fusion cage design using integrated global layout and local microstructure topology optimization.

An approach combining global layout and local microstructure topology optimization was used to create a new interbody fusion cage design that concurrently enhanced stability, biofactor delivery, and mechanical tissue stimulation for improved arthrodesis. To develop a new interbody fusion cage design by topology optimization with porous internal architecture. To compare the performance of this new design to conventional threaded cage designs regarding early stability and long-term stress shielding effects on ingrown bone. Conventional interbody cage designs mainly fall into categories of cylindrical or rectangular shell shapes. The designs contribute to rigid stability and maintain disc height for successful arthrodesis but may also suffer mechanically mediated failures of dislocation or subsidence, as well as the possibility of bone resorption. The new optimization approach created a cage having designed microstructure that achieved desired mechanical performance while providing interconnected channels for biofactor delivery. The topology optimization algorithm determines the material layout under desirable volume fraction (50%) and displacement constraints favorable to bone formation. A local microstructural topology optimization method was used to generate periodic microstructures for porous isotropic materials. Final topology was generated by the integration of the two-scaled structures according to segmented regions and the corresponding material density. Image-base finite element analysis was used to compare the mechanical performance of the topology-optimized cage and conventional threaded cage. The final design can be fabricated by a variety of Solid Free-Form systems directly from the image output. The new design exhibited a narrower, more uniform displacement range than the threaded cage design and lower stress at the cage-vertebra interface, suggesting a reduced risk of subsidence. Strain energy density analysis also indicated that a higher portion of total strain energy density was transferred into the new bone region inside the new designed cage, indicating a reduced risk of stress shielding. The new design approach using integrated topology optimization demonstrated comparable or better stability by limited displacement and reduced localized deformation related to the risk of subsidence. Less shielding of newly formed bone was predicted inside the new designed cage. Using the present approach, it is also possible to tailor cage design for specific materials, either titanium or polymer, that can attain the desired balance between stability, reduced stress shielding, and porosity for biofactor delivery.

Interpreting results from topology optimization using density contours

The topology optimization result using material distribution method is a density distribution of the finite elements in the design domain. Interpreting this result has been a major difficulty for integrating topology optimization and shape optimization into an automated structure design procedure. It is also one of the factors that limit the extension of the optimization methods of two-dimensional structures into three-dimensional structures. This paper presents a process for integrating topology optimization and shape optimization. In this process, density contours are used to interpret the topology optimization result, and then further integrate with shape optimization. This is a fully automated procedure, since during this process no human interpretation or intervening is required. This procedure can be extended to the topology and shape optimization of three-dimensional structures. The optimizations of two- and three-dimensional structures are presented in design examples.