Bi-directional evolutionary topology optimization of continuum structures subjected to inertial loads

Evolutionary topology optimization of continuum structures including design-dependent self-weight loads

A method for the non-probabilistic reliability optimization on frequency of continuum structures with uncertain-but-bounded parameters is proposed. The objective function is to maximize the non-probabilistic reliability index of frequency requirement.The corresponding bi-level optimization model is built, where the constraints are applied on the material volume in the outer loop and the limit state equation in the inner loop. The non-probabilistic reliability index of frequency requirement is derived by the analytical method for the continuum structure with the uncertain elastic module and mass density. Further, the sensitivity of the non-probabilistic reliability index with respect to the design variables is analyzed. The topology optimization in the outer loop is performed by a bi-directional evolutionary structural optimization (BESO) method, where the numerical techniques and the optimization procedure of BESO method are presented. Numerical results show that the proposed BESO method is efficient, and convergent optimal solutions can be achieved for a variety of optimization problems on frequency non-probabilistic reliability of continuum structures.

Stress-based topology optimization and nonlinear structural topology optimization is gaining increasing attention in order to make topology optimization more realistic. Thus, this paper extends current concepts of topology optimization to the design of structures made of nonlinear materials. An extended bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of material nonlinear structures is proposed in this work. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low-density elements. The maximum von Mises stress is approximated by the p-norm global stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topological variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several 2D benchmark design problems.

Topology optimization of material nonlinear continuum structures under stress constraints

The effectiveness and efficiency of the bi-directional evolutionary structural optimization (BESO) method has been demonstrated on the problems of minimizing compliance of structures with f ixed external loads. This paper considers the minimization of the mean compliance of continuum structure subjected to design-dependent gravity loads. Due to the non-monotonous behaviour for this type ofthe optimization problems, the extended BESO method using discrete design variables has difficulty in obtaining convergent solutions for such problems. In this paper, a new BESO method is developed based on the sensitivity number computation utilizing an alternative material interpolation scheme. Several examples are presented to demonstrate the capabilities of the proposed method for achieving convergent optimal solutions for structures with design-dependent gravity loads.

The evolutionary structural optimization (ESO) method developed by Xie and Steven (Comput Struct 49(5):885–896, 162), an important branch of topology optimization, has undergone tremendous development over the past decades. Among all its variants, the convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) method developed by Huang and Xie (Finite Elem Anal Des 43(14):1039–1049, 48) allowing both material removal and addition, has become a widely adopted design methodology for both academic research and engineering applications because of its efficiency and robustness. This paper intends to present a comprehensive review on the development of ESO-type methods, in particular the latest convergent and mesh-independent BESO method is highlighted. Recent applications of the BESO method to the design of advanced structures and materials are summarized. Compact Malab codes using the BESO method for benchmark structural and material microstructural designs are also provided.

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.

Topology optimization with meshless density variable approximations and BESO method

Concurrent topology optimization of structures and their composite microstructures

Evolutionary topology optimization of fiber reinforced composite laminates for maximum stiffness

In order to solve the problem that the weight of large scale theodolite's casting or steel plate welded structure is too heavy, lightweight design of large scale turntable based on topology optimization of continuum structure is investigated. Topology optimization could have better optimization efficiency because it can provide the optimized distribution of material and gain optimized structure in conceptual design phase of the structural design. In order to obtain lightweight and high stiffness structure, a truss turntable based on topology optimization of continuum structure is presented, and the validity of this lightweight structure is examined by finite element analysis. Comparing to the traditional welding steel turntable, the lightweight turntable, without changing the static displacement, can lose 386.48 kg(lightweight ratio is 26.7%), and its first-order natural frequency raises from 167.02Hz to 173.71Hz. Meanwhile, in other aspects this turntable also has better performance than traditional structure.

Discrete ground structure topology optimization design methods have to date received considerable attention in structural engineering. An alternative class of structural topology optimization methods, which have not yet received much attention in structural engineering, but which have undergone considerable development in the past decade, are the so-called continuum formulations. In this work, a continuum structural topology optimization formulation is presented and applied to the concept design optimization of structural bracing systems that are needed to stiffen tall structures against sidesway under lateral-wind and seismic-type loading. Although demonstrated here in the context of these specific design examples, continuum structural topology optimization methods are believed to hold potential as a design tool for a wide range of civil engineering type structures. A variety of continuum topology design formulations, including static compliance minimization and eigenvalue optimization, are explored, and solution parameters are varied to show that a number of design possibilities can be realized as solutions.

Topology optimization of continuum structures is a recent field in structural optimization. However, an increasing research activity in this area has been developed since the statement of the very first formulations. These formulations try to obtain the most adequate material distribution that satisfies the imposed structural limitations. The existence or absence of material in each part of the domain is usually defined by using a continuum variable (the relative density) in order to avoid dealing with a discrete optimization problem. This continuum approach of the material properties present important advantages since conventionaloptimization algorithms can be used. However, numerical models must be considered in order to develop the structural analysis for intermediate values of the relative densities. In this paper, we present some improvements in a minimum weight approach of the structural topology optimization problem. The main goal of this paper is to present an improved formulation that tries to reach binary 0-1 material distributions by using a continuum approach of the design variables. Furthermore, a perimeter penalization is included in the objective function to simplify the solutions obtained. In addition, some computational aspects are considered in order to reduce the computational effort. Finally, we compare the solutions obtained by using these formulations in two application examples.

Topology optimization is the procedure of determining the connectivity, shape and location of voids inside a given design domain. This chapter proposes a quantum-inspired evolutionary algorithm (QEA) for structural topology optimization. It reviews the formulation of the continuum structural topology optimization model and the characteristics of quantum computing. The chapter also proposes the detailed implementation of a QEA-based topology optimization. It discusses two issues: the density-based continuum structural topology optimization formulation and the characteristics of quantum computing, which may be conducive to reducing the computational expense of topology optimization. The entire theoretical procedure of quantum-inspired topology optimization, which mainly combines FEM analysis, design sensitivity solution and quantum-inspired search, is accomplished for continuum structures. As the experimental implementation of quantum computation needs initialization, coherent manipulation, control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult.

Stress-based multi-material structural topology optimization considering graded interfaces