Evolutionary Structural Optimization Method Research Articles

Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD) treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO) method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.

The ESO method revisited

This paper examines the evolutionary structural optimisation (ESO) method and its shortcomings. By proposing a problem statement for ESO followed by an accurate sensitivity analysis a framework is presented in which ESO is mathematically justifiable. It is shown that when using a sufficiently accurate sensitivity analysis, ESO method is not prone to the problem proposed by Zhou and Rozvany (Struct Multidiscip Optim 21(1):80---83, 2001). A complementary discussion on previous communications about ESO and strategies to overcome the Zhou-Rozvany problem is also presented. Finally it is shown that even the proposed rigorous ESO approach can result in highly inefficient local optima. It is discussed that the reason behind this shortcoming is ESO's inherent unidirectional approach. It is thus concluded that the ESO method should only be used on a very limited class of optimisation problems where the problem's constraints demand a unidirectional approach to final solutions. It is also discussed that the Bidirectional ESO (BESO) method is not prone to this shortcoming and it is suggested that the two methods be considered as completely separate optimisation techniques.

Shape optimization of strut-and-tie models in masonry buildings subjected to landslide-induced settlements

When dealing with landslide structural damage assessment, considering that the scale of the analysis is territorial, it is both technically impossible and economically inconvenient to perform generalized and, at the same time, detailed investigations. In these cases, it is therefore necessary to implement various levels of detail, depending on the size of the analysis, the objectives, the available time and the economic constraints. This multilevel approach usually seems to be the most effective and useful because it allows to calibrate the available resources.The first level of the analysis, necessarily quick and relatively superficial, should be extended to all the buildings of the territory under study. The objective is to identify those buildings that require a deeper investigation. In this scenario, models based on classical structural mechanics seem to be difficult to apply for a rapid crack pattern diagnosis. This is why a new approach, based on a simple model (i.e. the Load Path Method, LPM), has been proposed by Palmisano and Elia (2013). However, according to Palmisano and Elia (2013) the LPM is very useful for rapidly searching the ‘most plausible solution’ instead of the exact solution. To find the solution, optimization algorithms are necessary. In this scenario, this article aims to show how the Bi-directional Evolutionary Structural Optimization method by Yang et al. (1999) can be very useful to optimize the strut-and-tie models obtained by using the Load Path Method.

Concurrent design of composite macrostructure and cellular microstructure under random excitations

In this paper, a method for the concurrent topology optimization of macrostructural material distribution and periodic microstructure under random excitations is proposed. The sensitivity analysis of dynamic response with respect to design variables in two scales, i.e., macro and micro scales, is presented. The corresponding concurrent topology optimization of macrostructure and microstructure is established, where the objective function is to minimize the displacement response mean square (RMS) of the prescribed degree of freedom while volume constraints are applied to the macromaterial distribution and phase materials. The optimization problem is solved using a bi-directional evolutionary structural optimization (BESO) method. Several examples are presented to demonstrate the effectiveness of the proposed method.

Two-scale optimal design of structures with thermal insulation materials

This paper introduces a two-scale topology optimization approach by integrating optimized structures with the design of their materials. The optimization aims to find a multifunctional structure composed of homogeneous porous material. Driven by the multi-objective functions, macrostructural stiffness and material thermal conductivity, stiff but lightweight structures composed of thermal insulation materials can be achieved through optimizing the topologies of the macrostructures and their material microstructure simultaneously. For such a two-scale optimization problem, the effective properties of materials derived from the homogenization method are applied to the analysis of macrostructure. Meanwhile, the displacement field of the macrostructure under given boundary conditions is used for the sensitivity analysis of the material microstructure. Then, the bi-directional evolutionary structural optimization (BESO) method is employed to iteratively update the macrostructures and material microstructures by ranking elemental sensitivity numbers at the both scales. Finally, some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed optimization algorithm. A variety of optimal macrostructures and their optimal material microstructures are obtained.

Topology optimization for microstructures of viscoelastic composite materials

The viscoelastic response of materials is often utilized for wide applications such as vibration reduction devices. This paper extends the bi-directional evolutionary structural optimization (BESO) method to the design of composite microstructure with optimal viscoelastic characteristics. Both storage and loss moduli of composite materials are calculated through the homogenization theory using complex variables. Then, the BESO method is established based on the sensitivity analysis. Through iteratively redistributing the base material phases within the unit cell, optimized microstructures of composites with the desirable viscoelastic properties will be achieved. Numerical examples demonstrate the effectiveness of the proposed optimization method for the design of viscoelastic composite materials. Various microstructures of optimized composites are presented and discussed. Meanwhile, the storage and loss moduli of the optimized viscoelastic composites are compared with available theoretical bounds.

A New ESO-Based Method to Find the Optimal Topology of Structures Subject to Multiple Load Conditions

In the field of topology optimization problems, the Evolutionary Structural Optimization (ESO) method is one of the most popular and easy to use. When dealing with problems of reasonable difficulty, the ESO method is able to give very good results in reduced times and with a limited request of computational resources. Generally, main applications of this method are addressed to the definition of the optimal topology of a component subjected to a single load condition. In this work, a new methodology, based on the ESO approach, is introduced for the study of the optimal topology of a component subjected to multiple load conditions. The new procedure, entirely developed in the APDL programming language, has been tested with a holed plate subject to two different load conditions; the obtained results are promising in terms of mass reduction and structural performances.

Structural Stiffness Optimization Under Dynamic Loads

Most studies are focused on topology optimization techniques under external static loads. However, all forces are dynamic in real world. Mathematical optimization with dynamic loads is almost impossible in a large-scale problem. Thus, the bi-directional evolutionary structural optimization method (BESO) is extended to the topology optimization problem of structure under transient dynamic loading. Structural stiffness optimization is performed with the objective of reducing the mean compliance during the whole load-time history. By the dynamical analysis, the stiffness optimization model is established based on BESO method. In this method, the material volume is taken as the constraint condition, and the minimum mean compliance of structure is taken as the objective function. A cantilever under harmonic load has been taken as a numerical example to show the effectiveness of the proposed approach.

Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems

This article presents an evolutionary topology optimization method for compliance minimization of structures under design-dependent pressure loads. In traditional density based topology optimization methods, intermediate values of densities for the solid elements arise along the iterations. Extra boundary parametrization schemes are demanded when these methods are applied to pressure loading problems. An alternative methodology is suggested in this article for handling this type of load. With an extended bi-directional evolutionary structural optimization method associated with a partially coupled fluid–structure formulation, pressure loads are modelled with hydrostatic fluid finite elements. Due to the discrete nature of the method, the problem is solved without any need of pressure load surfaces parametrization. Furthermore, the introduction of a separate fluid domain allows the algorithm to model non-constant pressure fields with Laplace's equation. Three benchmark examples are explored in order to show the achievements of the proposed method.

SIMP-Based Evolutionary Structural Optimization Method for Topology Optimization

Unreasonable parameters may lead to a phenomenon of the numerical instability in evolutionary structural optimization method (ESO). In this paper the improved SIMP-based ESO method for the structural compliance sensitivity is presented to solve the problem of checkerboard pattern. The method depends on the sensitivity analysis results that indicate the contribution of each unit for the whole structural performance to delete and to add elements. At the same time, the method in combination with a sensitivity redistribution technology of controlling checkerboard pattern is used to realize that each element’s contribution or impact factor of the whole structural performance has a smooth transition. The instance shows that the method is reasonable and different parameters will affect the optimized results. The optimal values of parameters can be seen obviously finally.

Topology optimization of compliant mechanisms with desired structural stiffness

This paper develops a bi-directional evolutionary structural optimization (BESO) method for topological design of compliant mechanisms. The design problem is reformulated as maximizing the flexibility of the compliant mechanism subject to the mean compliance and volume constraints. Based on the finite element analysis, a new BESO algorithm is established for solving such an optimization problem by gradually updating design variables until a convergent solution is obtained. Several 2D and 3D examples are presented to demonstrate the effectiveness of the proposed BESO method. A series of optimized mechanism designs with or without hinge regions are obtained. Numerical results also indicate that the flexibility and hinge-related property of the optimized compliant mechanisms can be controlled by the desired structural stiffness.

Designing orthotropic materials for negative or zero compressibility

There has been considerable interest in materials exhibiting negative or zero compressibility. Such materials are desirable for various applications. A number of models or mechanisms have been proposed to characterize the unusual phenomena of negative linear compressibility (NLC) and negative area compressibility (NAC) in natural or synthetic systems. In this paper we propose a general design technique for finding metamaterials with negative or zero compressibility by using a topology optimization approach. Based on the bi-directional evolutionary structural optimization (BESO) method, we establish a systematic computational procedure and present a series of designs of orthotropic materials with various magnitudes of negative compressibility, or with zero compressibility, in one or two directions. A physical prototype of one of such metamaterials is fabricated using a 3D printer and tested in the laboratory under either unidirectional loading or triaxial compression. The experimental results compare well with the numerical predictions. This research has demonstrated the feasibility of designing and fabricating metamaterials with negative or zero compressibility and paved the way towards their practical applications.

Structural-Acoustic Topology Analysis Based on Evolutionary Structural Optimization

Application of the evolutionary structural optimization (ESO) approach for structural acoustic optimization is investigated. Combining the sizing optimization, a more appropriate rejection criterion for ESO was put forward. There is a trial of applying modified evolutionary structural optimization (MESO) method in dynamic response problem. Finally, the topology optimization of plate structure under harmonic loading as example, the MESO approach is conducted. The numerical results show that the MESO is feasible in topology optimization analysis; and it expands the application of traditional ESO theory.

From a quasi-static fluid-based evolutionary topology optimization to a generalization of BESO

A new algorithm is proposed for topology optimization based on a fluid dynamics analogy. It possesses characteristics similar to most well-known methods, such as the Evolutionary Structural Optimization (ESO)/Bidirectional Evolutionary Structural Optimization (BESO) method due to Xie and Steven (1993, “A Simple Evolutionary Procedure for Structural Optimisation.” Computers and Structures 49 (5): 885–896.), which works with discrete values, and the Solid Isotropic Material with Penalization (SIMP) method due to Bendsøe (1989, “Optimal Shape Design as aMaterial Distribution Problem.” Structural Optimization 1 (4): 193–202.) and Zhou and Rozvany (1991, “The COCAlgorithm–Part II: Topological, Geometry and Generalized Shape Optimization.” Computer Methods in Applied Mechanics and Engineering 89 (1–3): 309–336.) (using Optimality Criterion (OC) or Method of Moving Asymptotes (MMA)), which works with intermediate values, as it is able to work both with discrete and intermediate densities, but always yields a solution with discrete densities. It can be proven mathematically that the new method is a generalization of the BESO method and using appropriate parameters it will operate exactly as the BESO method. The new method is less sensitive to rounding errors of the matrix solver as compared to the BESO method and is able to give alternative topologies to well-known problems. The article presents the basic idea and the optimization algorithm, and compares the results of three cantilever optimizations to the results of the SIMP and BESO methods.

Topology Optimization of Photonic Band Gap Crystals

This paper proposes a new topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method for the design of photonic band gap crystals. The photonic crystals are assumed to be periodically composed of two given dielectric materials. Based on the finite element analysis, the proposed BESO algorithm gradually re-distributes dielectric materials within the unit cell until the resulting photonic crystals possess a maximal band gap at the desirable frequency level. Numerical examples for both transverse magnetic (TM) and transverse electric (TE) polarizations are presented, and the optimized photonic crystals exhibit novel patterns markedly different from traditional designs of photonic crystals.

An Application of Bi-Directional Evolutionary Structural Optimisation for Optimising Energy Absorbing Structures Using a Material Damage Model

The Bi-directional Evolutionary Structural Optimisation (BESO) method is a numerical topology optimisation method developed for use in finite element analysis. This paper presents a particular application of the BESO method to optimise the energy absorbing capability of metallic structures. The optimisation objective is to evolve a structural geometry of minimum mass while ensuring that the kinetic energy of an impacting projectile is reduced to a level which prevents perforation. Individual elements in a finite element mesh are deleted when a prescribed damage criterion is exceeded. An energy absorbing structure subjected to projectile impact will fail once the level of damage results in a critical perforation size. It is therefore necessary to constrain an optimisation algorithm from producing such candidate solutions. An algorithm to detect perforation was implemented within a BESO framework which incorporated a ductile material damage model.

Application of Topological Optimisation Technology to Bridge Design

This paper presents the application of modern topology optimisation technology to bridge design. Topology optimisation aims to determine the best locations and shapes of cavities in the design domain and therefore is capable of effectively dealing with structural design of infrastructure such as bridges. Several methods of topology optimisation have been developed during the past three decades, among which the evolutionary structural optimisation (ESO) method is popular because of its simplicity in software implementation and effectiveness in solving a wide range of engineering problems. The development of ESO and its advanced version bi-directional evolutionary structural optimisation (BESO) has reached a level of maturity nowadays. Applications of this technique have emerged around the world especially in the past decade. In this paper, the implementation of this technique in structural design is presented, with a particular focus on the design of various bridges. The design applications involve the consideration of different constructional requirements such as support types and selections of the elevation/span. Geometric constraints are also taken into account in the design problem, such as the periodic constraint with which a variety of architecturally aesthetic yet structurally efficient designs are produced. This paper aims to present the application of this promising technology to bridge design and to reveal its potential in a wider range of applications.

Truss Optimization Based on the Evolutionary Structural Optimization

The Evolutionary Structural Optimization (ESO) as an important structural topology optimization method has been widely used in many fields of engineering optimization. However, due to some technical constraints, the use of ESO for the truss optimization is relatively less. A method for truss optimization that combines the ESO method and the Stress Ratio method is proposed in this paper. This method solves the problems of ESO for truss optimization that the sectional area of bars cannot be changed and the speed of optimization cannot be easily controlled. It can be widely used in truss optimization and can get the same good result as other methods (such as GA and SA, etc.). Furthermore, the method proposed in this paper has the advantage that it can be easily programmed in the commercial software (such as Ansys and Abaqus, etc.) owing to its relatively simple optimization principle.

Topology Optimization for Constrained Layer Damping Plates Using Evolutionary Structural Optimization Method

The evolutionary structural optimization (ESO) is used to optimize constrained damping layer structure. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, the elements of constrained damping layers and modal loss factor are considered as design variable and objective function, while damping material consumption is considered as a constraint. The sensitivity of modal loss factor to design variable is further derived using modal strain energy analysis method. Numerical example is used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout.

Research on Topology Optimization Design Based on Finite Unit Analysis of the Flywheel Hub

Topology optimization design is to ensure the normal functioning of the machine, remove the invalid element structure makes the best structure to maintain the structure and keep the stress or strain level close to the same in each part of the security configuration, the pursuit of the best efficiency, lightest weight , smallest, or the longest service life and so on. Traditional structural optimization design one or several parameters set as the primary determination. This method only to the extent required. With the development and analysis of the efficiency of the computer, we have introduced in the design of finite element analysis. This article uses the basic evolutionary structural optimization method In this paper, load the hub topology optimization analysis of different groups.