Topology Optimization Of Continuum Structures Research Articles

Reformulation for stress topology optimization of continuum structures by floating projection

Stress topology optimization of continuum structures is an important topic for structural design and has been widely investigated. However, stress topology optimization itself is ill-conditioned and the resulting optimized designs highly depend on the used parameters, mesh size, and so on. In this paper, stress minimization and stress-constrained topology optimization problems are reformulated by introducing a global measure of an optimized design, the average solid stress. The floating projection topology optimization method is established with ε-relaxation and the p-norm function. Due to the modified problem formulations, the optimized design becomes insensitive to the selection of p in the p-norm function once p is large enough, such as p=16, to ensure the total elimination of stress concentration. Numerical results show the uniform stress distribution of optimized designs, demonstrating the effectiveness of the proposed method. Some findings on the elimination of stress concentration, mesh-independent optimized topology, equivalent smooth design, and impractical design are presented and discussed.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

A fully automatic computational framework for beam structure design from continuum structural topology optimization

A fully automatic computational framework for beam structure design from continuum structural topology optimization

Robust topology optimization of truss-like continuum structures under uncertain loads based on cloud model

The traditional structural performance may be seriously degraded due to applied indeterministic cases. A novel framework for robust topology optimization of truss-like continuum considering uncertain loads is presented. The robust optimization formula is constructed as minimizing the weighted sum of expectancy and standard variance of structural compliance with volume constraints. In this framework, both the magnitude and direction of applied loads are uncertain and independent. Truss-like continuum provides the topology optimal structure theoretically. Based on the classic truss-like optimization method, the statistical moments of compliance are accurately evaluated utilizing a bivariate cloud model tool. An effective strategy based on linear decoupling is reported to largely reduce the total number of finite element analysis. The optimization is achieved with gradient-based mathematic programming. Several numerical examples demonstrate a better structural robust performance obtained by the proposed algorithm than the traditional one.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.

Efficient two-phase approach to reliability-based discrete variable topology optimization of continuum structures with multimodal distributions

In practical applications, some random variables follow multimodal distributions. However, conventional reliability analysis methods in reliability-based topology optimization (RBTO), such as the first order reliability method, often result in considerable computational errors when dealing with problems involving multimodal distributions. Consequently, the corresponding RBTO design is incredible. Moreover, the RBTO problem also faces the challenge of high computational cost. To this end, this paper proposes an efficient two-phase approach for RBTO of continuum structures with multimodal distributions combining sequential approximate integer programming with trust region (SAIP-TR) and direct probability integral method (DPIM). Firstly, DPIM is advanced to address the difficult problems of failure probability estimation and efficient sensitivity analysis under multimodal distributions. Secondly, a reliability-based discrete variable topology optimization framework based on SAIP-TR and DPIM is established, which yields clear topology configurations and facilitates engineering manufacturing. Owing to the merit of SAIP-TR, the original RBTO process is divided into two phases: the first phase performs deterministic topology optimization, and the second phase focuses on RBTO. Moreover, an adaptive selection strategy of representative points, considering structural compliance as performance function, is devised to further enhance computational efficiency. Finally, several examples illustrate high efficiency and accuracy of the proposed approach. The multimodal random variable and the random field are employed separately to describe global and local uncertainties in materials. In contrast, the optimized result considering global material uncertainty is more suitable for additive manufacturing. The proposed approach also presents potential in handling complex RBTO problems with random fields.

Combination of the guide-weight criterion and BESO method for fast and stable topology optimization of two-dimensional continuum structures

Combination of the guide-weight criterion and BESO method for fast and stable topology optimization of two-dimensional continuum structures

Dynamic topology optimization of continuum structures considering moving mass excitations

The structures excited by the moving mass are widely existed in nature and engineering. The dynamic loads are related to time and space and greatly affect structural performances. However, the moving mass problems have not been considered in the topology optimization design of continuum structures. Therefore, this paper proposes a novel dynamic topology optimization method to design the continuum structures considering moving mass excitations. Firstly, the finite element formulation is established to solve the dynamic responses for the moving mass excitations by using the HHT-α method. Secondly, in the density-based framework, the dynamic topology optimization problem is formulated to minimize the mean strain energy constrained with the total volume, whose interpolation scheme is the rational approximation of material properties. Thirdly, the sensitivities of the optimization problem are derived by using the adjoint variable method in the discretize-then-differentiate scheme. Finally, numerical examples demonstrate the effectiveness of the proposed method and the influence of the moving mass excitations on the topological structures.

Topology Optimization of Continuum Structures Based on Binary Hunter-Prey Optimization Algorithm

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used to solve the problems that the BESO method of topology optimization has, such as easily falling into the local optimal value and being unable to obtain the optimal topology configuration; the metaheuristic algorithm was able to solve the topology optimization model’s low computational efficiency and could easily produce intermediate elements and unclear boundaries. Firstly, the BHPO algorithm was constructed by discrete binary processing using the s-shape transformation function. Secondly, BHPO-BESO topology optimization theory was established by combining the BHPO algorithm with BESO topology optimization. Using the sensitivity information of the objective function and the updated principle of the meta-heuristic of the BHPO algorithm, a semi-random search for the optimal topology configuration was carried out. Finally, numerical simulation experiments were conducted by using the three typical examples of the cantilever beam, simply supported beam, and clamping beam as optimization objects and the results were compared with the solution results of BESO topology optimization. The experimental results showed that compared with BESO, BHPO-BESO could find the optimal topology configuration with lower compliance and maximum stiffness, and it has higher computational efficiency, which can solve the above problems.

Robust topology optimization of continuum structures with smooth boundaries using moving morphable components

Robust topology optimization of continuum structures with smooth boundaries using moving morphable components

Τopology Optimization under a Single Displacement Constraint Using a Strain Energy Criterion

Based on a previous concept that has been successfully applied to the sizing optimization of truss and frame structures, this work extends and improves the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. To make the proposed methodology transparent to other researchers and at the same time meaningful, the numerical value of the displacement constraint was taken to be equal to that obtained through the well-known Solid Isotropic Material with Penalization (SIMP) method under the same boundary conditions and the same external forces. The proposed method is more efficient than the SIMP method while leading to topologies very close to those obtained by the latter.

Data-driven topology optimization (DDTO) for three-dimensional continuum structures

Data-driven topology optimization (DDTO) for three-dimensional continuum structures

Robust reliability-based topology optimization for stress-constrained continuum structures using polynomial chaos expansion

Robust reliability-based topology optimization for stress-constrained continuum structures using polynomial chaos expansion

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

Due to the inevitable involvement of multisource uncertainties related to the load, material property and geometry in practical engineering designs, robust topology optimization (RTO) has recently attracted increasing attention to account for these uncertain effects. However, the majority of the existing RTO works are concerned with single source uncertainty, and very few studies have considered the multisource (hybrid) uncertainties simultaneously. To this end, a comparative study on the hybrid uncertainties (HU), i.e., material-loading, geometric-loading, material-geometric, and material-geometric-loading uncertainties, for RTO of continuum structures is presented in this paper. A truncated Karhunen-Loeve expansion is adopted for uncertainty representation and a sparse grid collocation method for uncertainty propagation of the objective function and constraints. Effects of the various HU on the compliance and robust design are comprehensively investigated and compared with the RTO models under individual component uncertainty using two continuum benchmarks. An important observation from the results is that the hybrid uncertainty model is a conservative state, and the resulting RTO designs tend towards those with loading uncertainty only.

Topology Optimization of Strength-Safe Continuum Structures Considering Random Damage

Spacecraft in the aerospace field and military equipment in the military field are at risk of being impacted by external objects, which can cause local damage to the structure. The randomness of local damage is a new challenge for structural design, and it is essential to take random damage into account in the conceptual design phase for the purpose of improving structure’s resistance to external shocks. In this article, a random damaged structure is assumed to have damages of the same size and shape at random locations, and the random damage is considered as multiple damage conditions of the structure. In order to improve the randomness and comprehensiveness of the multiple damage conditions, the stacking strategy is used to generate the distribution of the damage area. Following this strategy, the topology optimization design of the random damaged structure, which is to minimize the weight of the structure with a constraint on the stress of the structure under multiple damage conditions, is formulated based on the independent continuous mapping (ICM) method. The dual sequence quadratic programming (DSQP) algorithm combined with the stress globalization method is adopted to solve the optimization problem. The numerical examples demonstrate the effectiveness and applicability of the proposed method in the topology optimization of strength-safe continuum structures.

A Modified Quantum-Inspired Genetic Algorithm for Continuum Structural Topology Optimization

Topology optimization and quantum computing have evolved rapidly over the past three decades. Previous topological optimum design methods suffered from financial burden and mathematical complexity. To overcome these shortcomings, a modified quantum-inspired evolutionary algorithm-based topology optimization method is proposed. This nested approach combines the classic solid isotropic microstructure with the penalization method and the double chains quantum genetic algorithm to establish an integral topology optimization framework. The former is utilized to determine the search direction of design variable updating. Meanwhile, the latter ensures abundant search diversity. The validity and feasibility of the developed methodology are eventually demonstrated by several application examples. The results indicate that the proposed optimization framework is independent of initial values and can lead to optimized structures. In addition, it will be more appropriate and effective if this strategy is deployed on a quantum computer in the future.

A framework for plasticity‐based topology optimization of continuum structures

AbstractIn this paper, a framework is proposed for topology optimization of continuum structures considering plasticity. The method merges the rigid‐plastic analysis and the density‐based topology optimization. To obtain a clean black‐and‐white design, the density in the objective function is penalized using an exponential function. The solution of the final plasticity‐based topology optimization problem exhibits as a sequence of second‐order cone programming (SOCP) problems that can be resolved efficiently using the advanced primal‐dual interior point method. Compared to the conventional stress‐constrained topology optimization techniques, the developed method accounts for plasticity and the finite element analysis of structures does not need to be carried out separately. Furthermore, the proposed method requires no relaxation techniques for imposing local stress‐constrain and possesses good computational efficiency for large‐scale problems.

Thermo-elastic topology optimization of continuum structures subjected to load allocation constraints

Thermo-elastic topology optimization of continuum structures subjected to load allocation constraints

Stress-based topology optimization of continuum structures under harmonic force excitation

In this paper, a new optimization method for the maximum von Mises stress minimization design of continuum structures subjected to harmonic force excitation is proposed. By using an extended Bi-directional Evolutionary Structural Optimization (BESO) method, the intermediate density elements with high stress state are avoided. To reduce the computational cost, the global von Mises stress is approximately measured by using a global stress measure based on the p-norm. Both sensitivities and topological variables are filtered to overcome the highly nonlinear stress behavior and stabilize the optimization procedure. A series of comparisons have been conducted to validate the effectiveness and practicability of the method on two-dimensional and three-dimensional benchmark design problems. The influence of varying excitation frequencies, damping and boundary conditions on the optimized results and the mode shapes are considered. The optimized results indicate that the proposed approach has good convergence and can achieve a reasonable design that effectively reduces the stress concentration effect at the critical stress areas. Strength of engineering structure under harmonic load is improved.

Three-field floating projection topology optimization of continuum structures

Topology optimization using the variable substitution among three fields can achieve a design with desired solid and/or void features. This paper proposes a three-field floating projection topology optimization (FPTO) method using the linear material interpolation. The implicit floating projection constraint is used as an engine for generating a 0/1 solution at the design field. The substitution filtering and projection schemes enhance the length scale and solid/void features to accelerate the formation of structural topology in the physical field. Meanwhile, the three-field FPTO method can be extended to robust formulation, which obtains the eroded, intermediate, and dilated designs with the same topology. The most distinct feature of the FPTO method lies in the adoption of the linear material interpolation scheme, which makes many topology optimization problems straightforward. As an example, the proposed three-field FPTO algorithm is further applied to the design of shell-infill structures using the linear multi-material interpolation scheme. The distribution of the shell material is generated through a simple filtering scheme, and the shell thickness is accurately controlled by the filter radius. Numerical examples are presented to demonstrate the effectiveness and advantage of the proposed three-field FPTO method.