Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain. This paper surveys topology optimization of continuum structures from the year 2000 to 2012. It focuses on new developments, improvements, and applications of finite element-based topology optimization, which include a maturation of classical methods, a broadening in the scope of the field, and the introduction of new methods for multiphysics problems. Four different types of topology optimization are reviewed: (1) density-based methods, which include the popular Solid Isotropic Material with Penalization (SIMP) technique, (2) hard-kill methods, including Evolutionary Structural Optimization (ESO), (3) boundary variation methods (level set and phase field), and (4) a new biologically inspired method based on cellular division rules. We hope that this survey will provide an update of the recent advances and novel applications of popular methods, provide exposure to lesser known, yet promising, techniques, and serve as a resource for those new to the field. The presentation of each method's focuses on new developments and novel applications.

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A survey of structural and multidisciplinary continuum topology optimization: post 2000

This review provides a detailed overview of the energy harvesting technologies associated with piezoelectric materials along with the closely related sub-classes of pyroelectrics and ferroelectrics. These properties are, in many cases, present in the same material, providing the intriguing prospect of a material that can harvest energy from multiple sources including vibration, thermal fluctuations and light. Piezoelectric materials are initially discussed in the context of harvesting mechanical energy from vibrations using inertial energy harvesting, which relies on the resistance of a mass to acceleration, and kinematic energy harvesting which directly couples the energy harvester to the relative movement of different parts of a source. Issues related to mode of operation, loss mechanisms and using non-linearity to enhance the operating frequency range are described along with the potential materials that could be employed for harvesting vibrations at elevated temperatures. In addition to inorganic piezoelectric materials, compliant piezoelectric materials are also discussed. Piezoelectric energy harvesting devices are complex multi-physics systems requiring advanced methodologies to maximise their performance. The research effort to develop optimisation methods for complex piezoelectric energy harvesters is then reviewed. The use of ferroelectric or multi-ferroic materials to convert light into chemical or electrical energy is then described in applications where the internal electric field can prevent electron–hole recombination or enhance chemical reactions at the ferroelectric surface. Finally, pyroelectric harvesting generates power from temperature fluctuations and this review covers the modes of pyroelectric harvesting such as simple resistive loading and Olsen cycles. Nano-scale pyroelectric systems and novel micro-electro-mechanical-systems designed to increase the operating frequency are discussed.

/pdf/piezoelectric-and-ferroelectric-materials-and-structures-for-39myuuqvo7.pdf

Piezoelectric and ferroelectric materials and structures for energy harvesting applications

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Using Mpi Portable Parallel Programming With The Message Passing Interface

Computer Methods in Applied Mechanics and Engineering

Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, for example, machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-to-optimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors' perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

/pdf/current-and-future-trends-in-topology-optimization-for-7k1902v47j.pdf

Current and future trends in topology optimization for additive manufacturing

This paper introduces a new approach to multiscale optimization, where design optimization is applied at two scales: the macroscale, where the structure is optimized, and the microscale, where the material is optimized. Thus, structure and material are optimized simultaneously. We approach multiscale design optimization by linearizing and formulating a new way to decompose into macro and microscale design problems in such a way that solving the decomposed problems separately lead to an overall optimum solution. In addition, the macro and microstructural designs are coupled tightly through homogenization and inverse homogenization. This approach is generic in that it allows any number of unique microstructures and can be applied to a wide range of design problems. An advantage of decomposing the problem in this physical way is that it is potentially straight forward to specify additional design requirements at a specific scale or in specific regions of the design domain. The decomposition approach also allows an easy parallelization of the computational methodology and this enables the computational time to be maintained at a practical level. We demonstrate the proposed approach using the level-set topology optimization at both scales, i.e. macrostructural topological design and microstructural topology of architected material. A series of optimization problems, minimizing compliance and compliant mechanism are solved for verification and investigation of potential benefits.

/pdf/simultaneous-material-and-structural-optimization-by-1agpi3aajm.pdf

Simultaneous material and structural optimization by multiscale topology optimization

Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. This paper introduces an efficient and accurate approach to robust structural topology optimization. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This new approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level-set-based topology optimization method are then used to demonstrate the proposed approach.

Introducing Loading Uncertainty in Topology Optimization

Robust topology optimization has long been considered computationally intractable as it combines two highly expensive computational strategies. This paper considers simultaneous minimization of expectancy and variance of compliance in the presence of uncertainties in loading magnitude, using exact formulations and analytically derived sensitivities. It shows that only a few additional load cases are required, which scales in polynomial time with the number of uncertain load cases. The approach is implemented using the level set topology optimization method. Shape sensitivities are derived using the adjoint method. Several examples are used to investigate the effect of including variance in robust compliance optimization.

/pdf/robust-topology-optimization-minimization-of-expected-and-3333b7c0nb.pdf

Robust Topology Optimization: Minimization of Expected and Variance of Compliance

https://purehost.bath.ac.uk/ws/files/124578121/cnc_datafusion_framework_MSSP.pdf

Multi-sensor data fusion framework for CNC machining monitoring

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

https://link.springer.com/content/pdf/10.1007%2Fs00158-014-1174-z.pdf

H. Alicia Kim

Papers

Simultaneous material and structural optimization by multiscale topology optimization

Introducing Loading Uncertainty in Topology Optimization

Robust Topology Optimization: Minimization of Expected and Variance of Compliance

Multi-sensor data fusion framework for CNC machining monitoring

Introducing the sequential linear programming level-set method for topology optimization