Matthijs Langelaar

Efficient Kriging-based robust optimization of unconstrained problems

Abstract A novel methodology, based on Kriging and expected improvement, is proposed for applying robust optimization on unconstrained problems affected by implementation error. A modified expected improvement measure which reflects the need for robust instead of nominal optimization is used to provide new sampling point locations. A new sample is added at each iteration by finding the location at which the modified expected improvement measure is maximum. By means of this process, the algorithm iteratively progresses towards the robust optimum. It is demonstrated that the algorithm performs significantly better than current techniques for robust optimization using response surface modeling.

Modeling of a Shape Memory Alloy Active Catheter

Shape memory alloys (SMAs) have interesting properties for application in adaptive structures, and many researchers have already explored their possibilities. However, the complex behavior of the material makes the development of SMA adaptive structures a challenging task. It is generally accepted that systematic, model-based design approaches and design optimization techniques can be of great assistance in this case. Although some studies on design optimization of relatively simple SMA structures have been published, formal design optimization of more complex SMA devices still requires further exploration. By considering a typical example, i.e. an active catheter, the present paper aims to provide new insights into and solutions for the problems encountered in the practical application of model-based design approaches to SMA adaptive structures. Active catheters are equipped with integrated micro-actuators that enable controlled bending, which yields enhanced maneuverability compared to conventional catheters. Next to a detailed discussion of an SMA active catheter finite element model, a novel SMA constitutive model is introduced. This model combines an adequate representation of the experimentally observed behavior with computational efficiency. Moreover, its history-independent nature significantly simplifies sensitivity analysis. Due to these features, application of optimization techniques to shape memory alloy adaptive structures becomes a realistic possibility.

Towards the Design of a Statically Balanced Compliant Laparoscopic Grasper Using Topology Optimization

This paper presents the design of a grasping instrument for minimally invasive surgery. Due to its small dimensions a compliant mechanism seems promising. To obtain force feedback, the positive stiffness of the compliant grasper must be statically balanced by a negative-stiffness compensation mechanism. For the design of compliant mechanisms, topology optimization can be used. The goal of this paper is to investigate the applicability of topology optimization to the design of a compliant laparoscopic grasper and particularly a compliant negative-stiffness compensation mechanism. In this study, the problem is subdivided in the grasper part and the compensation part. In the grasper part the deflection at the tip of the grasper is optimized. This results in a design that has a virtually linear force-displacement characteristic that forms the input for the compensation part. In the compensation part the difference between the force-displacement characteristic of the grasper part and the characteristic of the compensation part is minimized. An optimization problem is formulated enabling a pre-stress to be incorporated, which is required to obtain the negative stiffness in the compensation part. We can conclude that topology optimization is a promising approach in the field of statically balanced compliant mechanism design, even though there is great scope improvement of the method.Copyright

Topology optimization for submerged buoyant structures

ABSTRACT This paper presents an evolutionary structural topology optimization method for the design of completely submerged buoyant modules with design-dependent fluid pressure loading. This type of structure is used to support offshore rig installation and pipeline transportation at all water depths. The proposed optimization method seeks to identify the buoy design that has the highest stiffness, allowing it to withstand deepwater pressure, uses the least material and has a minimum prescribed buoyancy. Laplaces equation is used to simulate underwater fluid pressure, and a polymer buoyancy module is considered to be linearly elastic. Both domains are solved with the finite element method. Using an extended bi-directional evolutionary structural optimization (BESO) method, the design-dependent pressure loads are modelled in a straightforward manner without any need for pressure surface parametrization. A new buoyancy inequality constraint sets a minimum required buoyancy effect, measured by the joint volume of the structure and its interior voids. Solid elements with low strain energy are iteratively removed from the initial design domain until a certain prescribed volume fraction. A test case is described to validate the optimization problem, and a buoy design problem is used to explore the features of the proposed method.

Multi-material topology optimization of viscoelastically damped structures using a parametric level set method:

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.

Topology optimization: An effective method for designing front metallization patterns of solar cells

Optimal front electrode design is one of the approaches to improve the performance of solar cells. This work introduces the application of topology optimization (TO) to design complex front metallization patterns for solar cells. TO optimizes the distribution of electrode material on the front surface of the solar cell, such that its power production is maximized. It serves to achieve a local voltage distribution on the front surface that allows maximum possible current to flow across the solar cell. To demonstrate the capability of TO, it is applied over three different configurations - square-shaped, rectangular and circular. The results presented here demonstrate that TO can be an effective method to design complex front electrode patterns. In addition, it helps to reduce the amount of electrode material used in the solar cell, thereby reducing the net cost per kWh of power output.

Robust optimization of 2x2 multimode interference couplers with fabrication uncertainties

In this paper, we propose a novel design-for-manufacture strategy for integrated photonics which specifically addresses the commonly encountered scenario in which probability distributions of the manufacturing variations are not available, however their bounds are known. The best design point for the device, in the presence of these uncertainties, can be found by applying robust optimization. This is performed by minimizing the maximum realizable value of the objective with respect to the uncertainty set so that an optimum is found whose performance is relatively immune to fabrication variations. Instead of applying robust optimization directly on a computationally expensive simulation model of the integrated photonic device, we construct a cheap surrogate model by uniformly sampling the simulated device at different values of the design variables and interpolating the resulting objective using a Kriging metamodel. By applying robust optimization on the constructed surrogate, the global robust optimum can be found at low computational cost. As an illustration of the methods general applicability, we apply the robust optimization approach on a 2x2 multimode interference (MMI) coupler. We robustly minimize the imbalance in the presence of uncertainties arising from variations in the fabricated design geometry. For this example device, we also study the influence of the number of sample points on the quality of the metamodel and on the robust optimization process.

Modeling and design of shape memory alloy actuators

This paper presents the application of systematic model-based design techniques to the design of shape memory alloy (SMA) actuators. Shape memory alloys are promising materials for (micro-)actuation, because of the relatively large deformations and forces that can be achieved. However, the complex constitutive behavior and the fact that several physical domains (electrical, thermal and mechanical) play a role makes it difficult to design effective SMA actuators with complex shapes and layouts. For this reason, design optimization techniques are expected to play an important role in the further development of SMA actuators. The present paper presents shape and topology optimization of SMA structures and shows the effectiveness of these design approaches by several representative examples.

Level Set Based Topology Optimization with Stress Constraints and Consistent Sensitivity Analysis

For aeronautical applications of topology optimization, it is of importance to develop topology optimization techniques, that can handle stress constraints in an efficient and accurate manner. The development of such topology optimization techniques is a challenging task due to the local nature of the stress constraints, their highly non-linear behaviour with respect to the design variables and the so-called singularity phenomenon. An accurate sensitivity analysis is essential for these type of problems with multiple constraints. In this paper, we propose a methodology of dealing with stress constraints in a level set based framework. In this framework, the level set function nodal values are related to element densities by an exact Heaviside projection. Stress relaxation and constraint aggregation techniques are used to deal with the singularity phenomenon and the local nature of the stress, respectively. A constrained optimization problem is then solved, in which the design variables (the level set nodal values) are updated in the projected steepest-descent direction, which is determined using a consistent sensitivity analysis.We demonstrate the effectiveness of this technique on two numerical examples. The results show that the level set method with a consistent sensitivity analysis allows for the treatment of multiple constraints by using constrained optimization techniques.

Bounded-but-unknown uncertainty optimization of micro-electro-mechanical systems

Publisher Summary This chapter presents a paper that explores techniques to carry out uncertainty-based optimization of micro-electro-mechanical structures (MEMS). The optimization technique used relies on sequential approximate optimization through multipoint approximations. This paper proposes a method that is tested and demonstrated for the uncertainty optimization of MEMS by means of a microstructure used for measurement of residual stresses. When dealing with MEMS, because of their small dimensions, tolerances on shapes are relatively high. The variations in shape introduced by the manufacturing process can have a significant effect on the mechanical behavior of MEMS. This paper presents an approach based on bounded-but-unknown uncertainty optimization to deal with the uncertainties. This technique can handle large uncertainties safely and efficiently through a parallel computing technique. Optimization of the present MEMS structure can be extended by including all design variables. Similar optimization of MEMS can be carried out by applying compressive strains, in which case, a buckling constraint becomes necessary.