Topology and Size Optimization

Chapter 2 - Growth Method for the Size, Topology, and Geometry Optimization of Truss Structures

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.

Most robotic applications demand lightweight and high-speed manipulators for considerably reducing the consumed power and achieving high production rates. The two ways for seeking such high-speed arms are; applying advanced control algorithms and/or performing an extensive optimization of the arm structure itself. Therefore, the topology optimization technique is proposed here for obtaining an optimal robot arm design from both structure and control viewpoints. Results of some researches, that have been previously accomplished by size and shape optimization, were encouraging enough to extend and propose this optimization approach. The method of moving asymptotes (MMA) as an optimization algorithm, the finite element analysis (FEA) by ANSYS, and the time-optimal control method are integrated to gain an optimum design capable of attaining the minimum traveling time. The proposed methodology focuses on performing different comparisons between the proposed optimum topological designs and their initial designs for different robot arms’ sizes and materials. It also distinguishes between the proposed optimum design and the previously achieved one by size optimization under the same operational conditions. Therefore, the significance of the proposed technique is emphasized. It shows that the traveling time is reduced by 44.8%, while the previous work only achieved 23.5%. In addition, the mass is reduced to nearly half of its initial value, taking into account the air damping as the real case in all terrestrial applications.

The manifold microchannel (MMC) heat sink has been widely studied for liquid-cooling of power-dense electronic components. Conventionally, thermal-fluid performance of an MMC heat sink is analyzed via unit cell simulations and designed by varying the rectangular fin and channel geometries, namely size optimization. To further explore the performance potential of the MMC heat sink, this paper proposes topology optimization (TO) to design the optimal freeform fin/channel geometry to maximize heat transfer performance while minimizing the required pumping power. The heat transfer physics in an MMC heat sink is governed by conjugate heat transfer between an incompressible laminar fluid and a heated conductor. The MMC heat sink fin/channel geometry design is formulated as a material distribution problem in a periodic unit cell. Since TO describes the geometry non-parametrically, it facilitates innovative designs through the exploration of arbitrary shapes. The physics-governed design optimization problem is solved by mathematical programming using design sensitivities and an iterative gradient-based method. The thermal-fluid performance is presented for both conventional size optimization and the proposed TO approach, considering the heat transfer performance versus the required pumping power. It is demonstrated that the TO designed fin/channel geometries outperform those obtained through size optimization. Due to the shape complexity associated with the TO designed fin/channel geometries, they are not readily suitable for conventional manufacturing processes, e.g., machining and metal die-casting. However, such out-of-box designs fully exploit the flexibility offered by the latest advanced manufacturing processes, e.g., additive manufacturing and rapid investment casting.

Mathematical optimization theories are employed for the design of structures in structural optimization. Structural optimization is being widely utilized for practical problems due to well-developed commercial software systems. Three representative structural optimization systems such as Genesis, MSC Nastran and OptiStruct are investigated and evaluated by solving various test examples in different scales. The design capabilities of three software systems are explored and the performances of the systems are compared. The performance of structural optimization depends on the quality of the optimum solution and the computational time, and these aspects are compared from an application viewpoint. For a fair comparison, the same formulations are utilized, and the same optimization methods are employed for each example. Also, the same system environment is prepared, and the same optimization parameters are used. Additionally, various design options of each software system are tested for the best performance. Linear static response size, shape, topology, topometry and topography optimizations are applied to the examples and the results are compared. No system seems to be the best in all cases and each system has advantages and disadvantages depending on the application. In general, Genesis is excellent in computational time while OptiStruct gives excellent optimum solutions, in size, topometry and topology optimizations. Meanwhile, MSC Nastran presents good solutions in shape and topography optimizations.

The Next Generation Very Large Array (ngVLA) project to replace the VLA telescope in New Mexico is just beginning. As a part of the initial Community Studies phase, we have contributed the concept design of a 15m feed-low wheel and track design. This telescope, the Next Generation Dish Verification Antenna 15m (ngDVA-15) follows on from the DVA-1 and DVA-2 antennas developed at the Dominion Radio Astrophysical Observatory (DRAO) between 2012 and the present day. This paper will concentrate on the design and optimization process for the ngDVA-15 back-up structure. Topology and free-size optimization were used to develop the initial design concepts. Both methods helped to steer the back-up structure in the initial design phase, but ultimately engineering intuition also played a role. Topology optimization can lead directly to useful solutions in some cases but hardware and software limitations still limit the physical size of the model. Also, topological routines cannot yet correctly model truss-type networks with no moment transfer at the joints, and optimizing structures with only gravitational loads proved to be challenging for the current generation of optimization routines. Size optimization was also used once the design was sufficiently refined. The initial stage of design involved minimization of reflector surface deflections under gravitational loads only. FEA modelling of surface deflections together with in-house developed fitting algorithms were used to determine primary surface accuracy. Surface accuracies of better than 80 microns RMS were achieved which met the initial design goal for telescope operation at 120GHz.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

In this study, inertial amplification induced phononic band gaps are attained by performing structural optimization on a compliant unit cell mechanism of a one-dimensional periodic structure. First of all, stop band characteristics of the lumped parameter model of the unit cell mechanism is discussed. Next, the distributed parameter model of the compliant unit cell is presented. In order to obtain wide and deep inertial amplification induced stop bands, both size and topology optimization methods are utilized considering the distributed parameter model of the unit cell mechanism. The band gap characteristics of the infinite periodic size and topologically optimized mechanisms are compared. Moreover, vibration transmissibility of the finite periodic size and topologically optimized mechanisms are calculated and the effect of number of unit cells is discussed. Finally, a parametric study is carried out to demonstrate the effect of topology optimization design space volume fraction on the band gap limits.

A several cycles of design-verification-modification are needed during traditional design, which is very time-consuming. Topology optimization is rapidly expanding in the recent years in the field of structural mechanics. Currently it is widely applied to structural design. The combination of topology optimization and sizing and/or shape optimization has been adopted for flight vehicle structural design, which results possible better designs. In the paper, continuum structural topology optimizations as well as size optimization are combined for a folding wing structural design. A structure optimization problem is established using Solid Isotropic Material with Penalization (SIMP) method, it consists of the thickness variable of the skin and the relative element density variables of the tip part of the folding wing. The design objective is to minimize the compliance of the whole structure, and the constraints are structural mass constraints and stress constraints. The problem was solved based on commercial software package HyperWorks™. The resulting design shows that a new tip structure which satisfies the requirements of stiffness and strength was reconstructed.

ABSTRACTA comprehensive solution for bus frame design is proposed to bridge multi-material topology optimization and cross-sectional size optimization. Three types of variables (material, topology and size) and two types of constraints (static stiffness and frequencies) are considered to promote this practical design. For multi-material topology optimization, an ordered solid isotropic material with penalization interpolation is used to transform the multi-material selection problem into a pure topology optimization problem, without introducing new design variables. Then, based on the previously optimal topology result, cross-sectional sizes of the bus frame are optimized to further seek the least mass. Sequential linear programming is preferred to solve the two structural optimization problems. Finally, an engineering example verifies the effectiveness of the presented method, which bridges the gap between topology optimization and size optimization, and achieves a more lightweight bus frame than traditional single-material topology optimization.

A new fuzzy strategy for size and topology optimization of truss structures

as a comparatively new developed stochastic method particle swarm optimization (PSO), it is widely applied to various kinds of optimization problems especially of nonlinear, non-differentiable or non-convex types. In this paper, a modified guaranteed converged particle swarm algorithm (MGCPSO) is proposed in this paper, which is inspired by guaranteed converged particle swarm algorithm (GCPSO) proposed by von den Bergh. In this paper, the sizing and topological optimization problems of steel framed structures subjected to stress and displacement constraints are selected to illustrate the performance of the presented optimization algorithm. The obtained competitive results show that the MGCPSO exhibit good performance due to improved global searching ability.

The objective of this paper is to obtain an optimal concept design of aircraft wing. Topology optimization is used to yield an optimized shape and material distribution for a set of loads and constraints within a given design space. Initially a solid wing was considered as design space and meshed using hexahedral elements to derive the optimal location of spars and ribs such that the structure has minimum compliance. Load data includes flight, fuel and engine loads. The wing was constrained in all degrees of freedom at the root. It was shown that the results can be used to derive an appropriate configuration similar to the existing design practices. A new geometry with spars, ribs, hinge locations and lug attachments was next considered. The skin was meshed with shell elements. Hinge loads were also included. The optimization gave a box section for front spar, channel section for rear spar, truss pattern for ribs and V shaped member for hinges. Using this global material distribution a component level topology optimization was performed. The concept design is realized in to CAD and then a composite free-size optimization is performed to determine material distribution and ply drop regions etc. Finally a composite size and shape optimization is done.

실제 대부분의 공학 문제들은 크고 작은 비선형성을 내포한다. 구조물의 최적설계 과정에서는 다수의 구조물 사이에 발생하는 접촉이나 비선형 물성치를 가지는 재료, 또는 대변형을 고려해야만 한다. 그러나 민감도 계산이 고가이기 때문에 비선형성을 최적화에 고려하는 것은 매우 어렵다. 따라서 비선형 정적 반응 위상최적설계를 위하여 등가하중법을 사용한다. 등가하중이란 비선형 해석에서 유발되는 반응장과 동일한 반응장을 유발하는 선형 정적하중이다. 등가하중법은 치수/형상최적설계를 위하여 연구되어 왔다. 위상최적설계는 치수/형상최적설계에 비하여 설계변수가 많기 때문에 기존의 등가하중법을 그대로 적용할 수 없기 때문에 위상최적설계를 위하여 등가하중법을 확장하고 수정한다. 간단한 예제를 통하여 등가하중법을 이용한 위상최적설계 결과가 수치적으로 도출한 결과와 유사함을 보이고 실제 공학 예제의 위상최적설계를 통하여 기존의 선형 정적 위상최적설계와 결과를 비교한다.

Convexity-oriented reliability-based topology optimization (CRBTO) in the time domain using the equivalent static loads method